CHEMISTRY 464
ADVANCED PHYSICAL
CHEMISTRY LABORATORY
LABORATORY MANUAL
© P. S. Phillips 2010. All rights reserved.
Plot the graph, then put the data on.
There are no truths, only facts to be manipulated.
Give me six variables and I’ll fit an elephant.
Give me seven and I’ll make it’s tail wag.
INSTRUCTIONS AND GENERAL INFORMATION.
The physical chemistry laboratory is equipped for the following experiments. Students will carry out six of them. Each takes
two lab sessions. Which experiments, and when you do them, will be organized the start of term. The experiments are done
with partners.
These experiments are suites. Each suite consists of two or three experiments.
ID TOPIC
EXPERIMENT
A Activity coefficients
Activities of ions by electrochemistry (and some
programming )*
E Enzyme kinetics
Various approaches. Inhibition. Non-linear fitting.
G Thermodynamics of glycine Properties of a weak acid, pKa and thermochemistry.
H The hydrophobic effect
A study of partitioning and co-solvents to illustrate
the hydrophobic effect.
K Kinetics
A couple of kinetics experiments, mainly to illustrate
computer fitting methods.
M Micelles
CMC and aggregation numbers by fluorimetry, UVVis and conductometry .
P Permeability
A simple investigation of permeability and osmosis.
T Transitions in biomolecules
Examine the effect of phase temperature and pH on
myoglobin. Comparisons with other enzymes.
W Acidity of wines
Look at the pH of mixed diprotic acids and cations on
buffering in wine and the effect of alcohol on pKa
Some of the material required for the experiments will not have been covered in any of your classes. Background research is
an essential part of the experiments.
*May not run this year.
PERSONAL EXPERIMENT ROSTER
GROUP #
Experiment
Date/Time
Partners Name:
Phone No.
Experiment/Group rotation.
Week →
Group No.Z
1
2
3
4
5
6
Introduction:2
1
2
3
4
5
6
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CHEMISTRY LABORATORY SAFETY REGULATIONS
A chemical laboratory is a potentially dangerous environment; the most
prevalent hazards are fire, chemical burns, cuts, and poisoning.
NOTE: Safety rules only work if you obey them and encourage others to
do so. Please familiarize yourself with the following regulations.
NOTE: These regulations represent a minimum. A member of the lab
staff will inform you of variances and other regulations, or supply you
with appropriate references. If unsure about anything ask them.
NOTE: An eyewash station is available for the treatment of minor
accidents. For first aid, phone local 78111 or 807-8111. In an emergency
(i.e. one requiring police, fire, ambulance or a hazmat team) phone 911
then phone local 78111 or 807-8111. A member of the lab staff will
normally make such calls.
1. Regulations
• All accidents and incidents (near misses and spills) must be reported
immediately to a member of the lab staff.
• Students are not usually permitted to use the laboratory except during
their scheduled laboratory period.
• No student should attempt unauthorized experiments in the
laboratory, or modify any experimental apparatus.
• No student can work in a laboratory without a supervisor present
unless they have completed a WHMIS and the Chemistry Department
Safety course, and then only with the supervisors consent.
• Any student deemed dangerously incompetent or intoxicated will be
required to leave the laboratory. An incident report will be filed.
• Keep walkways clear at all times. Do not leave cupboard doors open.
the sash! It defeats the whole point of the sash.
• Do not wipe your face or eyes with gloves on!
• Water play or squirting wash bottles will not be tolerated.
• Do not kneel or sit when preparing hazardous samples. If there’s a
spill, you must be able to move fast and keep your face out of the way.
Use the center shelf of the lab bench to fill volumetric flasks to the line.
• Be sure you have received proper instruction in:
• Boiling of liquids (use boiling chips!)
• Use of separatory funnels (don’t point them at anyone)
• Use of any unfamiliar equipment or chemicals
• Insertion into or removal
of, glass tubing (rods,
thermometers, pipettes
etc.) rubber or plastic
items (tubing, pipette
bulbs, bungs etc.) e.g. see
figure for the correct way
of inserting a pipette
into a dispensing bulb.
•
Do not wave
pipettes
around
(especially
Pasteur
pipettes) around or you
will spray residual any
material around.
2. Personal Safety.
• Many of the chemicals in the laboratory are poisonous, whether taken
orally or absorbed through the skin. If any chemical is swallowed, the
supervisor should be summoned immediately. Immediately wash off
any chemical comes in contact with the skin with plenty of water.
Consult the MSDS data sheets for further information. Make sure you
know the location of the eyewash station and emergency shower.
• As a minimum students MUST wear safety glasses at all times. You
must provide your own safety glasses. Contact lenses must not be worn.
Other protection such as side shields, goggles or face shields may be
required. Make sure your goggles are sealed against the face.
• No food or drink may be bought into the laboratory. Do not chew gum
in the laboratory.
• There must be no smoking in the laboratory.
• Students should keep their arms, legs and torso covered. Students
should keep their arms, legs and torso covered. Wearing 100% cotton lab
coats is required. Most chemicals will stain or burn your clothing.
• You are not permitted to wear open toed shoes in the lab.
• Long hair should be tied back at all times.
• Unless otherwise informed assume all “unknown samples” are
dangerous, that is you must wear goggles, gloves and lab coat while
handling them.
• Assume all chemicals are corrosive or toxic by ingestion, and take
appropriate precautions.
• Never handle chemicals with your bare hands.
• While heating a substance in a vessel with a narrow mouth (e.g. a test
tube) ensure that the mouth of the vessel is not pointing at anyone,
including yourself.
• When using compressed gas, vacuum equipment, high temperature or
high voltage equipment be especially careful. Ask the laboratory
instructor for help if you are uncertain of any procedure. Strongly
corrosive or toxic materials should only be handled in the fume hood,
with the sash down, and suitable gloves on. Do no kneel to look under
Introduction:3
• Do not crush materials
with stirring rods.
2. Fire
• Students should be aware of the location and use of the fire
extinguishers in the laboratory.
• In case of fire, the flames should be extinguished with one of the
extinguishers and the supervisor notified immediately.
• If a student's clothing or hair catch fire, use the emergency shower
(make sure you know its location). If this is not possible, smother the
flames immediately with a laboratory coat or a fire blanket (know the
location of the latter)
3. Breakages, spillages and fumes
• Immediately report all breakages and minor spills of chemicals to the
supervisor or technician. A spill kit is available if needed. Know it’s
location. Spills will normally be dealt with by the laboratory staff. Failure
to report mercury spills may result in a reprimand.
• Remember that broken class is the sharpest material known.
• Any experiment involving the evolution of toxic materials, or pungent
or unpleasant odors or fumes, must be carried out in the fume hood.
• Don’t wear aftershave or cologne in the labs. It interferes with our
ability to detect fumes (they are fumes) and can mess up analyses.
4. Disposal
• Make sure all broken glass or sharps are disposed of in the appropriate
container.
• Make sure all materials are disposed of in the appropriate container
(solids, organics, halogenated solvents or inorganics)
• Beware of materials that hydrolyze rapidly, e.g. SOCl2 and acid
anhydrides; they cannot be disposed of in containers containing
alcohol or water.
• Never add hydrogen peroxide, nitric acid or any other oxidants to
organic materials (unless instructed) or into the organic disposal
container. Acetone and alcohol are a particular problem.
MARKING POLICIES
Allocation of marks will be different from usual labs. and
may vary with the experiment. As above, you start with one
or two marks less than the maximum otherwise an
unrealistic spread of marks will occur. The follow ‘items’
will be considered when marking labs.
TECHNIQUE. This mark will be assigned for things like
speed (finishing time), sloppiness, preparation (did you
read the lab. before arrival?), contribution to the laboratory
discussions, breakage’s, record of original data in your lab.
notebook, attentiveness and attitude, as well as pipetting,
weighing, titrating and other standard lab. skills. These
experiments are all straightforward and in many cases you
have done them before so odd factors like attitude will
weigh heavily – quietly sitting in a corner, noisily sitting in
a corner, or slipping out for a pint – will be viewed dimly.
Also, you will be marked on how you solved the problem
and the computer techniques used; e.g. proper choice of
data ranges, checking convergence criteria, use of special
features rather than brute force (e.g. for Excel; in-cell
iterations versus huge tables or use of named ranges).
RESULTS. Clearly, the better your technique, the better
your results should be, but since some of these experiments
are designed to produce bad results so you can use fancy
techniques to fix them up a bit, this mark is a little odd.
However, the experiments do often have built in checks,
there are certain errors that can only be achieved by
incompetence – this mark will address these.
PRESENTATION. This will be an opportunity to
demonstrate your word-processing skills, HANDWRITTEN REPORTS WILL NOT BE ACCEPTED for any
lab. reports. You will be marked on presentation e.g. clear
format, data properly identified, clear use of labels, proper
choice of axes on graphs, clear comments (in Maple).
Proper placement and sizing of titles, captions and graphs.
You MUST record your original data and any in lab. notes in
an approved lab. book. Do not submit this book with your
reports, but I will wish to see it and assign marks according
to it’s clarity and completeness. (The supplementary
questions may involve a lot of pictures or derivation in that
case it may be acceptable to hand-write that section –
check with the instructor).
REPORT. See the appropriate section for a description of
the format of your report. Most importantly, do example
calculations for one sample and tabulate the final, and some
intermediate data, for the rest of the samples. Be sure to
Introduction:4
tabulate your original data points (that is working data
point; for instance there is no need to reproduce the data
from time-runs, only the data points that arises form the
time-runs) at the start of the report. Also, at the end,
tabulate your calculated results and the literature values.
Error discussion is required for each lab. Error analysis may
also be required. Make sure you indicate the algorithms
used for doing calculations, particularly if you used a
computer. Marks are given for extra background research
and any insightful comments. (415 is a research based lab.
so these are part of your main mark, not an opportunity for
brownie points as with most labs.) Marks are deducted for;
arithmetic errors, incorrect answers, failure to answer
questions, failure to comment on results; incomplete error
discussion, lack of literature values, bad organization and
extreme untidiness, excessive neatness, and of course
handing in the lab. report late. Be sure to answer all
questions given. Not all reports are equally easy, marks
allocated to a report may vary from 10 to 15 to 20,
depending on the length and difficulty of the calculations
and questions.
PROBLEMS. Some labs. have lots of questions to answer.
In fact, some look like a lab. with a problem set attached to
the end. The problems carry significant weight.
SAFETY. Normally, physical chemistry experiments are
designed to work with safe chemicals and equipment. For
advanced courses this is neither possible nor desirable.
Place a small section in your lab. report giving toxicity
information and precautions for each (and every one) of the
chemicals used (starting material, products and byproducts). Look it up, don’t guess. If you don’t take this
seriously I won’t let you in the lab. However, remember to
use credible sources as some sources tend to over exaggerate
the hazards for legal reasons (i.e. beware of the
manufacturers literature). The WHIMIS CD-ROM is a
good place to start.
PLAGIARISM. See the separate section for details.
Basically, if you copy from somebody else or allow
somebody else to copy from you, you will get zero for that
lab. report. Repeated infractions may get you suspended.
Discussion of ideas is permitted, but the write ups must be
independent.
THE FORMAT OF A LABORATORY REPORT
IDENTIFICATION. All labs. reports should have a front
studied and the method of physical measurement made, or
of property determined.
systematic error, and estimate their limits (guesswork!). In
general, don't make the discussion too detailed, unless you
are told that an error analysis is required for that
experiment. If you are told to do a full error analysis you
need the formula in Table 3 of the Error Analysis section).
For most purposes an error analysis using Table 2 of that
section will suffice. Error analysis should be done along with
your calculations. Discussion is done as a separate section.
OBJECT OR PURPOSE. One sentence; may not be
CONCLUSIONS. Your major findings in a few lines. This
sheet that gives: Your name, the course number (Chem.309)
and section no. Name of partner (if any). Full date of
experiment (e.g. Tue. May 10th 2018). Experiment number.
Lab. Profs. name.
TITLE. This should give both the substance or system
necessary if it just duplicates the title.
PRINCIPLE OF METHOD. Briefly discuss the theory
underlying the laboratory and briefly give the principle of
the method, and use this as opportunity to write down any
equations you will use in results and calculations.
section may not be necessary if you have them clearly set
out at the beginning or end of the "discussion" section. Be
sure that you have answered all questions in the text. Also,
make any comments about the findings and there
implications for errors in this and related experiments
QUESTIONS. The question may be in the body of the
PROCEDURE. You may refer to the lab. manual for this, main body or given in a separate section at the end of the
but you should any modifications to the procedure and
indicate possible improvements and sources of errors or
other general problems. Draw diagrams of apparatus setup
if required.
RESULTS AND CALCULATIONS. Tabulating usually
saves a lot of time and space and keeps the prof. happy. Draw
graphs using a computer, unless otherwise stated. Embed
both the graphs and tables in the text. Be sure to make the
graphs readable, say 6x5 in minimum size For repeated
calculations, give one example and one only, in full. The
example calculation should be embedded in the text, but
may be hand written (try doing one by typing to see what a
pain it is). This should come more naturally than in the past
as you should be using Excel for calculations and will need
to explain them. Make sure you always compare your results
with the literature values when available. Make sure you
indicate the algorithms or programs used for doing
calculations.
DISCUSSION. This is a discussion of the results and their
errors in the context of the data processing methods used.
Benefits and shortcomings of the methods should be
discussed.
ERROR DISCUSSION/ANALYSIS. For any quant-ity
for which you have found a numerical value, give an
estimate of error limits. Do not propagate the errors in your
calculations unless an error analysis is required. Estimate
random errors from observed scatter of data either visually,
or by statistical computation. List possible sources of
Introduction:5
experiment. Clearly identify, separate and answer the
questions at the end of your report. Do not embed the
questions in the discussion or conclusions or in a long
rambling paragraph at the end. Text answers should be
typed. Numeric or algebraic questions can be handwritten.
REFERENCES. Place any references, in the standard
A.C.S. format, in this section. WEB references, with the
exception of the CHEMBOOK site are NOT acceptable. See
the section on the Internet elsewhere.
Please feel free to discuss report format and other problems
with the instructor, but do not expect detailed explanations
or corrections written on your laboratory reports.
See the A.C.S. Authors Guide (in library) for further details
on style and format of chemistry documents.
SOME NOTES ON TYPE SETTING REPORTS
All lab. reports are to be typed using a computer. I
recommend Word (and Word on the Mac at a push). Make
sure the equation editor is installed (and you know how to
use it). If you have last minute printing problems, see me, I
may accept a disk copy. For the purposes of proofing your
reports I recommend printing them out. I will supply you
with a symbol font that contains nearly all the symbols
you’ll need for chemistry, and a Greek font with some
modifications suitable for scientific work (the standard
symbol font has Greek characters, but they have to be
italicized). I usually assign some keystrokes to a macro to
turn them on or off. I will also give you some macros you
might want to use. I want you to follow some basic
typographic conventions for your report (or you’ll loose
marks). They are as follows.
a) The main body of text should be in a proportionallyspaced (e.g. not Courier) western (e.g. not Cyrillic) serif
font (e.g. Times New Roman, Garamond, School Book),
not a sans serif font (e.g Arial) or any decorative font (e.g.
Brush Script) or anything weird (e.g. Tekton). Use a normal
face, not italicized, hollow or bold. Type size should be 12,
13 or 14pt.
b) Titles should be bold, serif or sans serif, and larger than
the main text; don’t bother with anything fancy.
c) There should be a maximum of three fonts in a report
(the main text, titles, symbols). If you want some variation
on the title page you can use bold and italic (sparingly).
d) Keep it simple, no curly borders or color (except maybe
in graphs). Use bold or italic for emphasis, do not
underline.
e) Use tables for your data, don’t rely on tabs etc. Do not
box the table, a couple of lines here and there usually does
the job.
f) Note that stuff like 13 CO 2+
3 can only be typed in using
the equation editor – learn to use it.
g) The main body should be double or triple spaced (with
a 1” margin all round) so I can insert comments. However, I
will tolerate single spaced reports.
h) Diagrams can be drawn by hand, but keep them neat.
They should be captioned by a line of type. Equations must
be typed in, I suggest you reference the manual (e.g. Exp. G
eq.3) to reduce this burden. All graphs must be done by
computer, but you can manually cut and paste them into
your report if you wish (OLE works nicely, but only on fast
machines with lots of memory).
i) Do not cut and paste lumps of text from your partner’s
reports. I want to see some originality; in both the content
and the formatting (Also see the section on plagiarism).
Introduction:6
j) Watch for l’s (ells) they look like 1’s (ones). In sans serif
you get l’s (ells), 1’s (ones) and I’s (eyes).
k) Number the pages just in case the staple falls out.
If you need any help with word processing don’t hesitate to
come and see me – it’s part of the course. Office 2007 is
almost useless for lab. reports get a copy of Office 2003.
TYPOGRAPHIC CONVENTIONS FOR PAPERS
All journals have conventions that you must adhere to in
order to get a paper published in them. These conventions
vary from journal to journal, although there are some
common conventions to all journals. Below is a set of
conventions that you must adhere to for your lab. report to
be accepted. (These are over and above the format
conventions laid out elsewhere in this manual). The
conventions are based on those for A.C.S. journal and are
detailed in the A.C.S. style guide (along with a grammatical
guide and conventions for hyphenation, abbreviations,
capitalization etc., well worth a peek at). Conventions for
other journals are usually laid out in the front of the journal.
for comments.
• Use a fly page.
• Insert diagrams, graphs and tables into the text rather
than on separate pages. (Use cut and paste).
• Number the pages.
• Do not start sentences with numerals (use the word).
• Breaks and indenting for paragraphs are your choice.
• Number graphs, figures and tables clearly.
• You should use the equation editor for equations.
Calculations can be inserted into the text in hand writing
though (they are a real pain to type).
Fonts and case.
Equations, Tables & Figures.
• Use 12 pt Roman (or similar).
• Do not used bold or italic except as indicated below.
• Do not underline – ever.
• Lower case Greek letters are always italicized. Upper
Greek letters case are not.
• Mathematical variables and constants are italicized.
• Numbers and operators are not italicized.
• Vectors and tensors are bold.
• Math variables are never case sensitive (like in the
moronic C). d and D are the same.
• Element symbols are not italicized.
• Use italics for emphasis. Use bold for titles. Increasing
font size is also useful for emphasis.
• When defining a new word it is common to italicize it.
• Italicize latinates (actually optional, but I tend to do it).
• Try to make superscripts and subscripts 10pt (there’s a
macro on the disk for this).
• Symbols and axis labels in graphs should be 12pt.
Abbreviations and units.
• Units are never capitalized when spelt out.
• Abbreviations for units should be spaced, e.g. 10 km hr-1
not 10km.hr-1. I tend to ignore this rule as it leads
orphaned or widowed units.
• A list of approved abbreviations are in the A.C.S. Guide.
• All abbreviations, except as listed below, must be defined
at their point of first use.
a) The symbols for the elements.
b) the latinates (i.e., e.g., etc.).
c) at. wt., w/w, w/v, v/v, vol.
Layout. Consult the Format section for other details.
• If the report is double-spaced I can insert comments
easily, but single space is OK. I use 14pt exactly.
• Use one inch margins all round. That leaves some space
Introduction:7
• Equation numbers should be at the left margin. The
equation should be centered. Refer to the equation as eq.n.
• Label figures and tables underneath. The caption should
not exceed the with of the figure or table and should be
centered. Refer to them as Figure.n or Table.n.
References. Any consistent referencing scheme will do,
but the following is recommended. References should
preferably be numbers and grouped at the end of the report.
Do not use MS Word’s Endnote facility. Placing references in
footnotes is ok though. References should be referred to by
just a number in parenthesis or an author and a number.
Journals.
1) For sequentially numbered volumes : Name, M. Y.; Other,
A.N. , Journal Abbrv. Year, volume, pages. .
2) For individually number volumes: Same, M. Y. , Journal
Abbrv. Year, volume(issue), pages.
Books.
3) No editors: Name, M. Y.; Other, A.N. Title of the Book;
Publisher: City, Year, Chap. or page refs.
4) Editor only: Title of the Book; Ed. Name; Publisher; City,
Year, Chap. or page refs.
5) Author and editor: Author. A. N. In Title of the Book;
Editor Name, Ed.; Publisher; City, Year, Chap. or page refs.
Web pages.
You should not take reference material from the web as it is
not peer reviewed and not a permanent medium. Do look
around the page to see if it has a formal reference (most
government pages will) or has a reference from which the
material is taken. If not, note down the URL of the page and
the date you obtained the information.
For reference to other types of materials see the A.C.S. style
guide. (For which you have no reference, notice how
irritating that is) – it’s in the library). Abbreviations for
journal are also in the A.C.S. guide.
Introduction.
TYPE SETTING TECHNICAL DOCUMENTS
For hints on typesetting in general, see Robin Williams book
The Non-Designers Design Book. She also has a number of
useful tips at www.eyewire.com/magazine/columns/robin.
Some more information can also be found under
www.microsoft.com/typography/ . The hints below refer
specifically to type setting lab. reports. or lab. manuals. I’ve
attempted to set up this page according to these hints, even
if the rest of the manual is not setup that way (do as I say
not as I do).
Emphasis and Titling.
Do not use underline or ALL CAPS for emphasis or titling,
they are a hangover from the typewriter days. However, I
still find it useful to use a liberal sprinkling of DO NOT’s in
lab. manuals.
For emphasis in text use italic, bold italic or bold.
Occasionally, using a small font surrounded by white space
works well as does using a larger font.
For titling use a larger font, normal, bold or italic. If your
main text is serif (as it should be) then a larger Sans
Serif font is good. Placing a line across the page (as above)
also works well in moderation. The lines may be various
weights or doubled.
Typeface.
If you are preparing a long document readability is very
important. In print readability is best achieved by using a
classic serif font such as Times Roman, Caslon,
Garamond, Baskerville or similar (This manuals text is
set in a slightly narrow Roman font – Adobe Minion). Don’t
use anything fancy. If you are type setting a Web page or
have a lousy printer then a san-serif font such as Arial may
work better. I avoid Arial because of the confusion between I
(eye) l (el) and 1 (one). Check for appearance on screen vs.
the printer, the fonts named above (except Minion) look
quite different on screen than they do in this text. Also,
check the numbers for a given font in Times you get
1234567890 with Bulmer you get 1234567890, which
is a little ugly (especially on screen).
In general, one should not use more than two or three
typefaces per page, typically one for body text, one for titles,
one for symbols. One may add one more font to represent
computer or instrument input, Courier is usually used
for that purpose.
Introduction:8
Font Size.
As can be seen in the section above that different fonts have
different widths, heights, weights and spread, even though
they have the same point size. Times is large and open
and Caslon small and cramped so Times works well at
10pt, Caslon does not. On the other hand Caslon works
fine at 14pt, and so does Times. I use 12pt for lab.
manuals since they are usually read standing up (and I’m a
little short sighted). For reports 10pt is ok if you have a laser
printer, for inkjets 12pt is better.
Spacing.
Spacing between lines is usually set to single (which is
actually variable). For plain text this is ok, but is poor when
you’re using super/subscripts or symbols. I find spacing at
exactly 14pt (for 12pt text) works well if the “don’t center
exact height lines” option in Word is off. If you’re writing a
draft, double or triple spacing can be useful to allow for
annotations.
Spacing between words is set by using left justification (no
extra spacing) or by using full justification (spacing filled so
line exactly fits the line). Full justification is fine as long as
you don’t use narrow columns (a fine example of what can
go wrong is in the opening paragraph).
Misc.
Lines of text should not be more than (on average) eightnine words long. For large format pages that means two or
more columns. Large margins can also help. Setting up
double columns can be a little awkward and slows down the
computer. Some of the lab. manual is not set that way so I
don’t expect it in lab. reports.
PLOTTING GRAPHS.
Specific Heat
Example Graph
40.00
Series1
20.00
Series2
0.00
-4.00
1.00
The top graph is Excels default scatter plot. The scales are wrong,
the annotation too large and the plot cluttered. It is almost useless.
You should setup a custom graph in a proper format and use that as
the default..
6.00
Time(s)
Specific Heat
Example Graph
40.00
20.00
0.00
0.00
2.00
Most graphics packages give half decent graphs, however Excels
defaults settings are setup for Business slides (i.e. for appearance
not content.) However, the plots can be readily customized. Below
are a set of refinements which can also be used to as general
guidelines for plotting.
4.00
6.00
For the first step we get rid of the grid lines (only leave grid lines if
you need to read data of the graph) and the gray background which
reduces contrast. The legend is also deleted. Again, legends are
useful when working off the graphs, but for reports the legend
should be below the graph along with other information. Note how
the graph rescales when the legend is removed.
Time(s)
Here we have removed the remaining background color and the
joining lines. There is no measured data between the points so we
can’t put a line there. We have also just changed the annotation to
normal typeface. If you intend to reduce the figure you should scale
the annotation accordingly. For reports annotation should match
your text size (10-12pt). If you are making slides, overheads or
reducing graphs, it will need to be bigger (18-24 pt often works).
The title has been moved to the bottom and numbered.
Specific Heat
40.00
30.00
20.00
10.00
0.00
0.00
1.00
2.00 3.00
Time(s)
4.00
Figure 1. Example Graph
The final step is to remove both figure and axis boxes, they serve no
purpose. The title has been removed and replaced by text from
Word because you can’t do anything fancy in Excel - in this case
simply to put the legend in. Note that it is centered below the graph.
The axes have been tidied up, the span has been corrected, decimal
places reduced and tick marks added. The least square fit lines have
been added. The data points have been changed to black and made
easily distinguishable.
35
Specific Heat
Most of these changes are accessible by left clicking on the graph,
then right clicking to access the various properties.
30
25
20
0
1
2
Time(s)
3
4
Figure 1. A plot of Cv vs. Vent time for the Clement –
Desormes’. Dots at 20C, squares at 30C
Introduction:9
These graphs have been cut and paste in. If you do that, make sure
they are a decent size, including the annotation. (see exp.P for some
bad examples. Graphs can be presented on a separate
page if necessary.
PRESENTING TABLES.
Time(s)
4.03
3.25
3.32
3.06
2.6
2.28
1.75
1.31
0.96
0.66
P1 (cmHg)
76.49
76.67
76.57
76.73
76.63
76.52
76.6
76.58
76.6
76.51
Time(s)
4.03
3.25
3.32
3.06
2.60
2.28
1.75
1.31
0.96
0.66
Excel’s default tables are nearly as poor as the graphs. Here
we will illustrate how to tidy them up.
Cv
28.04099
26.34766
26.65888
26.85892
26
25.06601
25.01056
24.84336
24.65
24.25748
P1
(cmHg)
76.49
76.67
76.57
76.73
76.63
76.52
76.60
76.58
76.60
76.51
Generally you should cut and paste in from Excel in-line to
the text, but if the table is very large it should be presented on
a separate page, in landscape mode if neccessary. Either way
the default cut & paste table is poorly laid out with lots of
clutter and white space.
Cv
28.04
26.35
26.66
26.86
26.00
25.07
25.01
24.84
24.65
24.26
Vent
Time(s)
Pressure, P1
(cmHg)
Cv
J/mol-1
4.03
3.25
3.32
3.06
2.60
2.28
1.75
1.31
0.96
0.66
76.49
76.67
76.57
76.73
76.63
76.52
76.60
76.58
76.60
76.51
28.0
26.4
26.7
26.9
26.0
25.1
25.0
24.8
24.7
24.3
Table 2. Vent times, initial pressure, P1, and
calculated specific heat, Cv , for the ClementDesormes experiment.
Introduction:10
Center the text and the table. The number of decimals are
made uniform to clean up the appearance and allow a more
meaningful column alignment and spacing. The heavy grid
has also been removed. The grids can serve a purpose in
large multicolumn data look-up table, but generally they just
clutter the table.
The final step is to tidy up the table headings (centered
vertically and horizontally) and add subscripts. Use the
equation editor if necessary. A caption has also been added
along with a light grid.
Number formatting has been changed to reflect the correct
number of significant figure. You may want to change the
font type and size to match your text as well.
A final note: Try to avoid E or exponential notation if
necessary rescale your data to µM or whatever. e.g. use 0.234
not 2.34E-01 or 2.34x10-1 (the latter is the lesser of two
evils). Use 0.345µM, not 3.45x10-7M and certainly not
0.000000345M. Also remember to limit the number of
decimal places, Excel defaults to something too large.
USING FIGURES
Figures are rarely prepared in situ they are usually prepared
separately then cut and paste (manually or electronically)
into the document. The only real exceptions are sketches in
your lab. notebook. Regardless of the type of figure they all
need a figure number and caption placed beneath it. The
caption should be no wider than the figure.
There are a number of ways of preparing figures for formal
reports, each with advantages and disadvantages.
a) Hand drawn
b) Drafted
c) Computer drafted.
d) Scanning.
Hand-drawn figures are not usually used in formal reports,
but they are fast and convenient.
Drafting involves special pens, templates, drawing boards
etc. The usual approach is to draw an oversize figure and
Xerox reduce it (that cleans it up a lot). You then manually
cut and paste it into a prepared gap in the report and Xerox
that page. This process is very labor intensive (the chem.
dept at UBC has two graphic artists for this purpose), but it
is the only way to do some types of pictures.
Computer drafting moves all the drafting accessories onto
the computer, however it can be difficult to do chemical
drafting on the computer and the results are often
unsatisfactory. It is most satisfactory if you have prepared
templates of flasks etc. (CorelDraw has a good selection) or
of rings and bonds (ChemDraw). Drawing pictures from
scratch can be a real pain. Be sure to distinguish between
CAD type programs (CorelDraw) used for drafting, and
paint type programs (CorelPaint). The latter is good for
pictures and tends to be poor for equipment figures.
Computer figures can be printed out and manually cut and
paste in or they can be electronically cut and paste in using
OLE. OLE is the best way to go, you don’t loose resolution,
but it sucks up computer resources. Also Corel has never
mastered OLE so you can’t always use it. You can cut and
paste in bitmap files from just about any program, but be
careful as their resolution is limited (or they become so big
they crash the computer). You need at least 600dpi
resolution to reproduce line drawings properly.
Introduction:11
Scanning is great – when it works. You use somebody else’s
pictures and just cut and paste them electronically into you
report. There are three problems though, one is copyright,
they are, after all, somebody else’s pictures. Resolution is
another, and color is the last. Copyright is usually not a
problem for one-off lab. reports, but for anything you sell
(such as lab. manuals) you have to get copyright permission,
which may of may not be free. Resolution is a serious
problem. Grayscale pictures may give acceptable results at
300dpi (check by printing a rough copy out), but even then
they will be huge (on disk). Line drawings need at least
600dpi or you get jaggies. Scaling down often exacerbates
the problem. Color also creates a problem. Most reports are
in black and white with perhaps grayscale pictures. Color
does not always converts to grayscale well, and almost never
convert to good line drawings (black and white). Basically
any picture with a colored background will be unusable.
As an exercise go through this manual and see if you can
determine which figures are hand drafted and scanned,
computer drafted, scanned from other sources, bitmaps
from other programs or OLE links.
KEEPING A LABORATORY NOTEBOOK
Basically, you need to record what, with what, when, where,
how and how long, all in relation to your laboratory
activities. An outline of the information you should record
(by category) is given below (you don’t need to put such
titles in the book). The laboratory book should have
numbered duplicate pages. The duplicates should be
removed and stored in a separate place from the laboratory
book. If you have a laboratory, the laboratory book should
be locked up in the laboratory. Keep the duplicates at home
or in your office. Increasing amounts of data are kept on
computers, be sure to backup the disks and record file
names in your laboratory book. The lab. Manual contains
some ‘NOTES’ sheets, they are an artifact of production.
They are useful as scratch sheets, but anything of
significance should be written in the lab. notebook, only.
Incidentally, the examples given are real, not made up for
your entertainment.
General
a) Each page should be dated and titled. Start each new
date on a new page, unless the entries are less than ¼ of
a page. The title should be short, but descriptive and
placed in an index at the front of the book.
b) Entries should be neat and in water insoluble pen.
c) Entries should be organized – start new topics on a new
line.
d) Mistakes should be deleted with one line (leaving the
mistake clear – it might not be a mistake). Do not
delete or change entries after the fact.
e) Place any literature references against appropriate
entries.
f) Note any modifications to any standard procedures.
g) Keep your notes legible. Dalton may have been a great
chemist, but his lab. notes weren’t that great as seen
below.
Pre-Laboratory Preparation.
a) Write in any directions, calculations, diagrams, flow
charts, molecular weights, cautions, weights and
volumes.
Instruments
a) Record instrument settings (scan time, resolution, scan
width, temp. etc. etc. – anything that can be varied).
Anything that doesn’t have a value, indicate any
changes. E.g. lamp height was optimized for the
standard sample.
b) State sample cells used (try and get your own). If they
break record that (different cells give different results).
c) If there are any power glitches or the signal seems very
noisy, indicate those along with the time. E.g. at UBC it
used to be impossible to work at 4.30, when everybody
was turning their instruments off. There was also
trouble with big lasers firing; recording times will help
you track these things down.
d) Record the computer file names that any data is held in.
Make them useful, have a convention. If the OS
supports long file names use them. I find it useful to
use a convention like XXYYnnnn.mmm – where XX is a
two letter month code, YY is the day (number), nnnn is
a code for the experiment/sample type, mmm is the
extension, usually you won’t have a choice about that.
E.g. JL09dx12.spc might mean a spectrum (spc) taken
July 09, of a doxyl-12 spin probe. Most computers are
pretty good about keeping the file date correct so you
may want to just use an 8-letter code instead. However,
it’s often easier to search for a file name than for a file
date. I like to use an extension nnn where nnn was 000,
001, 002 etc. for a sequence of files. It can be very
difficult to locate three month old data, especially if you
generate 100 files a day.
Preparation
a) Record the chemicals, grades, weights and volumes
used.
b) Record the order in which the chemicals were added. I
once did a preparation with three chemicals, which
gives three possible orders (assuming the order of a
given pair is irrelevant). Not only did two of the
combinations give the wrong product, the reactions
were explosive. The order was not given in the original
instructions.
c) Draw, or otherwise indicate the equipment used.
(Some reactions depend on the size and shape of the
flasks). Something a little more auspicious that the
efforts of the Greek alchemist shown below, but drafting
is not required.
Introduction:12
(almost a flash) then went pale yellow, the color before
freezing. (In this case the pale yellow turned out to be iron
contamination from the cheap stainless steel syringe
needles used to deliver into reactants to the sample). 2) Fine
white needles formed in the acetone wash bath after two
days of use. (They turned out to be acetone peroxide, a
contact explosive, even when wet).
Computers.
d) If any of the bottles have old labels, broken caps, or
discolored contents, record that. Some chemicals just
don’t work when old. Hydrogen peroxide is really bad
for that, check the bottle date.
e) Record any changes to the preparation procedures. E.g.
200mL flask used instead of recommended 50mL flask.
f) Note the course of reaction and other details. E.g. 1)
reaction proceeded smoothly and was complete in
10mins. 2) Reaction proceed rapidly and blew a bung
out (replaced rapidly). 3) Some silicone grease dripped
into the reaction vessel. 4) Reaction turned green after
30 min (instead of yellow at 45min.). Mixture
detonated after 32min. (The student who noted the
latter dropped chemistry and became a lawyer). 5)
Initial preparation showed traces of NO2. Reaction
vessel was flushed with nitrogen again to remove
oxygen. 6) Foul smell, sample stored in fume hood.
Times
Time is more important than you think. One preparation in
my laboratory, at UBC, didn’t work on sunny winter days,
but worked fine on sunny summer days. This was because
the sun would shine into the laboratory at 4pm, in winter,
just when the silver salts were added to the reaction (it was
an 8hr prep.). In the summer, the sun was to high to shine
in. Record reaction times, flushing times, reflux times, start
times, end times, just about any time you can think of.
Results
a) Record basic physical data; total mass, state, % yield,
m.p.t. etc.
b) Record any other data including program and version
number, if the result is produced by a computer. Be sure
to record any file names.
Miscellany
Record anything else you notice. e.g. 1) samples were yellow
when removed from freezer, but turned a transient red
Introduction:13
REMEMBER TO BACK UP ALL YOUR COMPUTER
DATA IMMEDIATELY. Computers generate huge amounts
of information and it’s silly to reproduce it in a notebook.
There are some exceptions, X-ray data and spectra typically
find their way into special libraries. For your work, you can
restrict yourself to the following items.
a) Record filenames used in a given experiment. Record
any data that the instrument doesn’t put into it’s files.
b) If doing simulations setup a table of filenames, input
parameters and comments on success or whatever.
c) Computers are finicky, record any difficult to remember
procedures (say for importing data) into your book.
d) Paste in things like ASCII tables or program procedures
into the lab. book.
e) Record the computer type and program version nos.
Bugs are often undetected for a long time, this data will
help you decide their relevance.
f) Make sure you indicate the algorithms used for doing
calculations, particularly if you used a computer.
PLAGIARISM
You cheat,
You’re dead meat.
For a detailed discussion of plagiarism see the OUC Guide to Plagiarism available from the bookstore. The policy is
basically one of zero tolerance. The penalty for plagiarism is usually a zero for the work involved and a letter of
reprimand. Penalties for theft of papers or repeated plagiarism may be expulsion.
Avoiding plagiarism in chemistry labs. is quite simple; don’t copy other peoples work ! That is, do not copy
or read the whole or sections of another person laboratory report, draft or final.
There are cases where it is acceptable to copy other peoples work, in which case you should note the following:
a) If you wish to copy blocks of text from some source, put it in quotes and reference the source. You should not do this a
lot or you will be penalized for poor style. The source of material must not be another students lab. report or from a
‘tutoring service’.
b) If you use any source to assist in writing your labs. make sure you reference those sources in your write up. If you
paraphrase the text from these sources, try to do it as loosely as possible (i.e. keep it close to your personal style). If the
paraphrasing is too similar to the original you may be open yourself to a plagiarism charge. I find it best to read two or
more sources, close those sources and then write out what I understand of what I’ve just read. Again, the sources must
not be other students lab. reports, profs. notes etc.
c) You may discuss labs. with other students and you may compare original data and graphs. At a pinch, you can
compare calculations to track down errors. Under no circumstances should you read or copy other students lab. reports
(final or draft), that is considered plagiarism. If you read another students report (but not necessarily copy) it will taint
the style of your write up. It is quite shocking how easy that is to detect, particularly is small classes – so don’t do it!
d) Do not copy other students graphs or tables either electronically or by Xeroxing. Producing your own graphs and
tables is an important part of this course. (This may be acceptable in other courses, but not this one).
See the supplementary information on others marks penalties.
HOUSE KEEPING
Before starting an experiment, wash, and if necessary dry, any glassware, before use. Remember, the last person to use
the glassware was a student.
At the end of the experiment be sure to clean and wash any glassware. If you found it on the bench, in the cupboard, the
draws, the outside and return it there. If it came from a stock cupboard , put it on the drying rack. Make sure you leave
the balances clean. If any equipment was disassembled when you got it, disassemble it again and return to where you
found it. Leave any equipment or chemicals that the instructor/technician gave you on the bench. Clean up any spills,
paper towels, or any other mess you make. Report any breakages or depleted reagents so we can make replacements.
Failure to do this housekeeping may result in marks being deducted.
INTRODUCTION:14
© P.S.Phillips 2011 October 31, 2011
INTRODUCTION TO ERROR ANALYSIS
INTRODUCTION. There is a hierarchy of error analysis.
Each step being successively more rigorous.
i) sigs figs
ii) simple addition of errors
ii) addition of squares of errors
iv) series expansions to estimate errors
v) calculus
Although each step is more rigorous, they are less
conservative. i.e. sig. figs always overestimates the errors.
Note that each case requires a prior estimate of the error. If
you have to estimate the error from your data set (typical in
the earth, life and social sciences) then you must resort to
statistics. All quantitative chemistry experiments should
incorporate a check using significant figures. For error
analysis usually simple addition of errors will suffice,
although one may have to resort to series expansion of
functions to do that.
I. SHORT CUTS IN ERROR ANALYSIS: A NOTE
ON SIGNIFICANT FIGURES. Error analysis is a pain
so if we assume all the errors are +1 in the last reported
figure of the data, then the error analysis is greatly
simplified: One just counts significant figures or decimal
places and propagates those according to the rules familiar
to you from first year chemistry and physics. At this stage of
life, you should do significant figures instinctively. However,
the glowing display on your calculators seems to interfere
with this process so here are a couple of rules to stop you
going too far wrong.
1) Never, ever write down all 10-12 figures off the
calculator, but feel free to carry that number in your
calculations.
2) Computers/calculators often do not do calculations to
more than 5-6 sig. figs. for functions Even though they may
print out more.
Never quote errors to more than two sig. figs. One sig. fig.
will often suffice. e.g. 56.74+1.32 becomes 57+1,
1032.4+1.3% becomes 1.03x103+1%. Also you must get
the sig. figs. right. An error is a + quantity so follows the
rules for addition/subtraction; that is the number of
decimal places in your error must match those of the error.
3) If your using volumes in calculations you will never
have more than four sig. figs. Usually three after
subtractions.
4) If your using weights (in our labs.) you will never have
more than six sig. figs. Usually only five after subtractions.
© P.S.Phillips October 31, 2011
5) Atomic masses are often only good to three sig. figs.
due to variations in isotopic composition.
6) If you worry about how many sig. figs. to carry in
calculations, carry six, although four is often adequate. (In
general, carry one more sig. fig. than you know the answer
will generate).
7) Significant figures underestimate the true error so
beware that reasonable significant figures may hide a gross
error. If you’re down to 2 sig. figs. you should consider
doing an error analysis to see if the data actually means
anything.
8) Remember sig. figs. only apply to simple math
operations. If functions are involved you will have to resort
to proper error analysis, at least for that step in the
calculation. Watch polynomials in x, in particular, if x<1
then the high order coefficients. need less sig. figs than the
lower order ones. If x>1 then the high order coefficients
need more sig. figs. Both Excel and Origin have a bad habit
of reporting polynomial coefficients with insufficient
significant figures. Work out how to reset that.
9) One notable exception to sig. figs, of functions are logs.
The leading number carries the exponent so has now error.
Thus, the log, 3.13 has two sig. figs., the 3 just tells you to
multiply by 1000.
10) Soooooo, unless you have a very good reason (e.g. you
are measuring frequencies) never write numbers down to
more than 6 sig. figs. In addition, you never write a final
answer down to more than four sig. figs, in fact three will do
in many cases. IN ADDITION, do the proper sig. figs, don’t
just blindly write down three or four sig. figs at each step
and don’t give errors more than two (preferably one) sig. fig.
A short cut, but one that requires a fair amount of
competence and experience in error analysis, is to break the
calculations down into small steps and try to identify where
the largest error occurs (Actually it’s always a good idea to
do this before the experiment then you know where to focus
your attention). Often this error will be so much larger than
all the other errors that you can ignore them, i.e. you only
need propagate the one error. The most common example
of this is where you mix volumes and weights in a
calculation. Weights are 2-3 orders of magnitude more
precise than volume so you often only need propagate the
volume errors.
II. ERRORS. All measurements are associated with some
kind of error or uncertainty. We never know exactly how big
ERROR ANALYSIS:1
the error is, nor even, exactly, what range a quantity we are
trying to measure lies in. Much error analysis consists of
educated guesses.
Statistical analysis and formal
computational procedures can help, but to use them
properly we must understand that they do not remove
uncertainty, but merely let us express, more clearly, what the
uncertainty is. For instance the statement
[Mn2+] = (1.56 +0.03) x 104 g/ml
This means: "I think there are 19 chances out of 20 that
[Mn2+] lies between 1.53 and 1.59 x 10-4 g/ml". The
various conventions are discussed later.
the flask now systematic or random? This depends on what
was going on in the factory where the flasks were made. The
manufacturer may or may not have done something which
made all the flasks consistently too big. One can only guess
about this kind of thing unless one has a lot of information
about how equipment was made and calibrated, right back
to the primary standards of mass, length, time, temperature,
etc. Fortunately, when experiments are being done to about
three-figure accuracy, the expected range of error in
calibrations of volumetric equipment, or of the weights built
into analytical balances is usually very small in comparison
to other sources of error (table 1). The purpose of the above
example was not to get you locked in to worrying about
volumes, but to encourage you to be wide-ranging in your
thoughts about what could have gone wrong in your attempt
to measure something quantitatively. A large part of an
error analysis should consist of your assessment, in words,
of the most likely sources of large error.
III. SYSTEMATIC AND RANDOM ERRORS.
IV. ACCURACY, PRECISION, ACCEPTED VALUE,
TRUE VALUE. One never knows the true value of any
does not mean that [Mn2+] lies, for sure, between 1.53 and
1.59 x 10-4 g/ml. It may mean several things, according to
the convention used by the particular writer for the meaning
of +0.03. To avoid ambiguity, state your convention along
with the numerical result, for example,
[Mn2+] = (1.56+0.03) x 10-4 g/ml (95% conf. limits)
Errors are usually divided into two categories. Systematic
errors and random errors.
RANDOM error is just that, random - that is it’s origin and
magnitude are unknown, but are equally likely to be +ve or
–ve and for a given measure, average to zero. (Note though
in practice errors cannot add in a simple fashion and thus
do not cancel to zero). The probability of a given error
arising is usually assumed to follow a Gaussian distribution.
Usually random errors are estimated from the standard
deviation of a set repeat tests. This is discussed below..
SYSTEMATIC errors can arise in many ways, some of which
may not come to mind very easily. For example, the volume
of a given flask might not be exactly l00mL or the balance
may not be exactly zero. Systematic errors occur in a fixed
direction only (e.g. the flask is too big, or balance not
zeroed) and for a given source do not average to zero, ever.
We cope with systematic error by using common sense and
scientific experience to list the likely sources of it and devise
procedures to eliminate as many as possible. For what
sources remain, we have to make educated guesses although
they and will show up as apparent random errors in a
statistical analysis. Experiments should always be checked
with a known sample to help identify such errors, but often
these errors are assumed negligible as an act of faith (aka
from experience).
Suppose, for example, that one had a couple of dozen
volumetric flasks, and took a different one off the shelf for
each repeat of the experiment. Is the error in the volume of
ERROR ANALYSIS: 2
quantity; but for many quantities there is an "accepted
value", which is the result obtained in the experiment, which
is generally judged to have been the best performed to
determine this quantity. Alternatively, the result may be
compared to a standard – an item that is defined as having
an accepted value. The ACCURACY of any determination
means the closeness with which the determination matches
the accepted value, or, the closeness you think it has to the
true value. This may again be expressed in terms of "19
chances out of 20...", etc., but it includes the effects of both
random and systematic errors. The PRECISION, also called
reproducibility, relates only to random errors. The better the
precision the lower the random error (and, probably, the
better the experimenter).
Process
Error
Total titer by burette (50mL)
Total titer by burette (10ml)
End point detection
Volumetric flask (50mL)
Volumetric flask (100mL)
Volumetric flask (200mL)
Volumetric flask (250mL)
Pipetting (10mL)
Pipetting (25mL)
Weighing on an analytical balance
+0.03mL
+0.01mL
+0.01mL
+0.02mL
+0.08mL
+0.10mL
+0.10mL
+0.01mL
+0.02mL
+0.0002g
Table 1. Examples of Reasonable Error Limits
© P.S.Phillips October 31, 2011
V. USING OF STANDARD DEVIATION AS THE
ERROR. The most common way of characterizing random
error in a data set is the standard deviation. The true
standard deviation for a population is of n observations of a
variable x is
1
2
s x2 = lim å (xi - mx )
n®¥ n
where µx is the true or population mean. This is sometimes
written
1
2
s x2 = å (xi - x )
N
where it’s understood that N (as opposed to n) is the true
population size and not the sample set size, and x is the
mean (equals the population mean as N is the population
size). In practice, µx is unknown and is calculated for the
data; the limit on n ensures that x approaches µx, the true
(population) mean. If n is small, then the standard
deviation and average are no longer independent as, given
n-1 data points and x , the nth data point can be calculated,
we have lost a degree of freedom. To account for this we
must reduce the sample size by one so
n
(x - x )2
sd x2 = å i
n -1
i=1
Here n is the sample size, x is the mean of the sample set
(an estimate of µx) and sd the standard deviation (an
estimate of σx).
If n is large and we know µx then any difference between µx
and x can be attributed to a systematic error. If n is small
then x is inherently unreliable. We can estimate the
reliability of the mean by using the standard error on the
mean, σm, which is given by
σm = σ / n ½
σm tends to zero for large n. i.e. we can thus improve our
estimate of the average by collecting more data points. Do
not confuse the standard error on the mean with the
standard deviation. The former is a measure of the error of
estimating of the mean (i.e. accounts for the fact that the
sample size and population size differ); the latter is a
measure of the spread (or error) of the data
CALCULATING STANDARD DEVIATION. For the
purpose of calculation, it’s convenient to make the following
assignments
S
Sxx = å (xi - x )2
Vx = xx
n -1
© P.S.Phillips October 31, 2011
sd x = Vx
and
However, it’s inconvenient to calculate Sxx using the above
formula so it’s often calculated using the mathematically
equivalent formula
2
1
Sxx = å xi2 - (å xi )
n
While this is algebraically equivalent, it’s not
computationally equivalent. The former method requires
lots of storage memory so the latter method tends to be
used on calculators. However, the latter method is subject to
round-off errors so you can get quite wildly different vales
for the standard deviation with different calculators so be
warned.
An interesting variation in calculating the standard
deviation is as follows
sd x2 =
1 n-1
2
( xi)1 - xi )
å
2(n -1) i=1
In the absence of systematic errors (such as drift or rolling
baseline), this reduces to the normal value for the sd.
However, in the presence of drift (low frequency noise) it
gives the sd. associated with high frequency noise. (i.e. it is
robust wrt. to drift). This is useful for identifying ‘noise’ in
the presence of drift. Furthermore, this is a running
measure, that is, it can be easily calculated as the data is
acquired. The usual sd. requires you to constantly
recalculate the mean.
CONFIDENCE LIMITS. If the data is normally distributed,
then the standard deviation is just the half-width of the
normal curve at half-height. While this is a convenient
measure of the normal curve, much of the data lays in the
tails of the curve. Roughly, one in three points lay outside
the +1sd limit of the curve or to put it another way, there’s
only a 2 in 3 chance that the true mean lies within the
quoted limits. For some reason, this bothers some people
and they prefer to use wider error limits, for instance +2sd.
That is, limits such there are 19 chances out of 20 that the
true value of the mean lies within the limits. Occasionally
you will see +3sd, or 99 chances out of hundred. Because
of this, it is necessary to state the so-called confidence
limits for your error so
3.5+1.0
(68%
confidence limits)
3.5+1.0
(95%
confidence limits)
3.5+1.0
(99%
confidence limits)
means 3.5 with a standard
deviation of 1.0
means 3.5 with a standard
deviation of 0.5
means 3.5 with a standard
deviation of 0.33
ERROR ANALYSIS:3
For our purposes, we will just use first method, i.e. one
standard deviation and the limits not explicitly stated. A
more rigorous approach is recognize that for small data sets
the errors are not normally distributed, they are distributed
according to the Student-t distribution. The confidence
limits should then be written x ± t dc sd x where t dc is the t
value for a confidence limit of c (0.1 for 90%, 0.05 for 95%
etc.) and d degrees of freedom (number of data points –2,
which you should quote in your results).
OUTLIERS. Sometimes you obtain data that’s way outside
the expected range of values. Such data points are called
outliers. There are three reasons for spurious data i) It’ s real:
While the probability of a data point beyond the five s.d.
limit is small, it is still finite so occasionally you can expect
an odd point. ii) It is real: The data distribution is not
normal. For example, the data may be distributed with a
Poisson or Lorentzian distribution, both of which have long
tails. Under such circumstances, outliers can be quite
common. iii) It is due an error, e.g. contamination, power
bumps. The last case is the most common cause of outliers
and for that reason outliers are often just thrown out. The
problem is that it is not always clear that the data is a glitch
or that it is even an outlier. For highly scattered data, one
should always do an outlier test before rejecting a point.
Also, remember that it may be real data. Although it may be
necessary to throw the point out to keep your statistical
analysis valid, that data point may contain information. For
instance in soil sampling that point may represent an ore
deposit (in fact ore deposit are detected by looking for
outliers). In medicine, the data point may be due to a
diseased specimen, in which case your analysis may provide
a diagnostic for that disease.
My personal preference is to leave outliers in and use robust
estimation methods, which are, by definition, insensitive to
outliers. If your analysis methods are automated in any way
you should use robust methods, because it is very difficult to
automate outlier rejection in noisy data.
from a sample population that is sufficiently large to be
reliable and is representative.
Error analysis usually refers to analysis the effect of random
errors, not systematic errors. While it is useful to ask
questions such as “If the flask was to big, how will that affect
the measured density”, it’s not useful to ask such questions
in a quantitative fashion. After all, if you know how big a
systematic error is, it has ceased to be an error.
ERROR PROPAGATION FOR A PRODUCT OF TWO
FUNCTIONS. Consider two functions f(x) and f(y) each
with small errors associated with the variables, i.e. f(x+δx)
and f(y+δy). What is the error for the product of the two
functions? If the errors are small, and the functions well
behaved, then we can expand them about the average value
of x and y using the Taylor series. So for f(x)
f ''(x )
f (x ± d x ) = f (x ) ± d x. f '(x ) ± d x 2
)
2
If the function is smooth then f ’’(x) will be small and if the
error is small so will be δx so we can ignore higher order
terms so
f (x ± d x ) » f (x ) ± d x. f '(x )
Thus for the product of f(x) and f(y), w= f(x) f(y), we get
(including the errors)
w + d w =f ( x ± d x ) f ( y ± d y )
» ( f ( x ) ± d x. f '( x ))( f ( y ) ± d y. f '( y ))
= f (x ) f ( y ) ± f (x ) f '( y )d y ±
f ( y ) f '( x )d x ± f '( y ) f '( x )d xd y
Again, for small errors and a smooth function we can drop
the last term.
æ
f '( y )d y f '(x )d x ö÷
÷
» f (x ) f ( y )çç1 ±
±
çè
f ( y)
f (x ) ø÷÷
thus
dw »
VI. ERROR ANALYSIS. Although the following is a
more rigorous approach to error analysis than you will see
in first year chemistry texts and will suffice for our needs,
you should be aware that there are still a number of
approximations made. Briefly, they are as follows: It is
assumed that the errors are random and distributed in a
normal fashion (this will usually be true if outliers are
rejected). It is assumed that the errors are small ~1% (and
certainly <10%. If not then the error will be generally larger
than calculated). It is assumed that the errors are derived
ERROR ANALYSIS: 4
f '( y )d y f '( x )d x
±
f ( y)
f (x )
For the simple functions f(x)=x and f(y)=y this reduces to
the simple rule that the error is the sum of the fractional
errors. i.e.
æ d y dx ö
» f (x ) f ( y )çç1 ± ± ÷÷÷
çè
y
x ø÷
thus
dw »±
d y dx
±
y
x
© P.S.Phillips October 31, 2011
The + implies that the errors could mysteriously cancel out
which is not the case so it’s usual to ignore the signs of the
errors and write
d y dx
dw » +
y
x
This overestimates the error, but will be dealt with more
rigorously below. For more complex functions we need to
incorporate the derivative, this will also be dealt with below.
For basic error propagation the formula below suffice.
ve they will tend to cancel, but not completely, as that would
require all the errors to have their signs anti-correlated, not
a very likely event. To take this into account we proceed as
follows: Consider that we want to determine quantity w,
that is a function of at least two variables, so that
w=f(x,y…..). We can determine a value of wi for each
measured set of values so that wi=f(xi,yi,…). Now we wish
to get the standard deviation of w
1
2
sw2 = å (wi - w )
N
Operations and Errors
Addition or Subtraction Z = A + B + C+.…
xi-x is the error for a given measurement so assuming it’s
small we can expand the error in w via the chain rule so that
æ ¶w ö
æ ¶w ö
wi - w  (xi - x )ççç ÷÷÷) ( yi - y )çç ÷÷÷)
çè ¶y ÷ø
è ¶x ø
∆Z =| ∆A| + |∆B| + |∆C|+….
Multiplication or Division Z = A.B.C….
|∆Z/Z| = |∆A/A| + |∆B/B| + |∆C/C|+….
General Z = f(A,B,C….)
|∆Z| = |∆A.df/dA| + |∆B.df/dB| + |∆C.df/dC|+….
ERROR PROPAGATION FOR MULTIDIMENSIONAL
FUNCTIONS. We could proceed as above, but it slightly
clearer to use the chain rule. To calculate the effect of a
small error we need to examine the effect of the error on
(i.e. small changes in) the function, which is the same
questions as what is the size of the derivative of the function
with respect to each of it’s variables. For a function
w=f(x,y,z) we have that
¶f (x , y , z ) ÷ö
¶f (x , y , z ) ÷ö
¶f (x , y , z ) ÷ö
÷÷ dy )
dw =
÷÷ dx )
÷ dz
¶ x ø y ,z
¶y ø÷x ,z
¶z ÷ø y ,x
If the errors are small, we can approximate dx to δx etc.
This is equivalent to dropping the high order terms in the
Taylor expansion. It’s thus straightforward to get the error
for such function. Also, if we recognize that the product, xy,
is a multidimensional function, f(x,y), it’s easy to see how to
get the error for a product.
VII. USING THE STANDARD DEVIATION AS
THE ERROR.
The error is not a simple number, it can have any number of
values, it is in fact a characteristic parameter for a
probability distribution of possible errors, it is not the error
itself. Assuming the errors are normally distributed and
that sufficient data has been collected, the standard
deviation of the data will be width of the normal
distribution. Since the errors for each term maybe +ve or © P.S.Phillips October 31, 2011
hence
sw2 
é
ù2
æ ¶w ÷ö
æ ¶w ÷ö
1
ç
ê
ú
ç
å ê(xi - x )çèç ¶x ø÷÷) ( yi - y )çèç ¶y ÷÷÷ø)ú
N
ë
û
2
2
1
2 çæ ¶w ÷ö
2 çæ ¶w ÷ö
= å (xi - x ) çç ÷÷ ) ( yi - y ) ç ÷÷ )
çè ¶y ÷ø
è ¶x ø
N
æ ¶w öæ ¶w ö
2( xi - x )( yi - y )ççç ÷÷÷çç ÷÷÷)
è ¶x øçè ¶y ÷ø
If we now define a covariance between x and y, σxy, as
1
å(xi - x )( yi - y )
N
so we get for the error propagation function
2

s xy
2
2
2
2 çæ ¶w ÷ö
2 æç ¶w ö÷
sw  s x çç ÷÷ ++
s y ç ÷÷
ç ÷
è ¶x ø
è ¶y ø
2 çæ ¶w ÷öæç ¶w ö÷
++
2s xy
ççè ÷÷øçç ÷÷÷ 
¶x è ¶y ø
If x and y are uncorrelated then we expect that, on average,
the covariance will be zero (there will be an equal number of
+ve and –ve values in the sum) and we may neglect the last
term giving us
2
2
2
2 çæ ¶w ÷ö
2 çæ ¶w ÷ö
sw  s x çç ÷÷ ++
s y ç ÷÷ 
ç ÷
è ¶x ø
è ¶y ø
Which for the simple case of the product of x and y (w = xy)
this reduces to
sw2  s x2 ++
s 2y 
i.e. we sum the squares of the errors, to get the total error.
ERROR ANALYSIS:5
We thus need to modify the formula above to account for the
fact that the errors do not add linearly.
should clearly be a very good fit to the points. b) The words
"should be a straight line" in the first sentence above don't
really mean very much. You may find that the plotted points
Z=f(x,y)
2
Error in Z sz
Relative Error in Z
x+a
s x2
sz / z = s x / x
ax+by
2
a2s x2 + b 2s 2y ± 2abs xy
-
Multiplication
+axy
(ays x )2 ) (axs y )2 ) 2 xy(as xy )2
2
(sz / z )2 = (s x / x )2 ) (s y / y )2 ) 2s xy
/ xy
Division
+ax/y
(ays x )2 ) (axs y )2 - 2 xy(as xy )2
2
(sz / z ) = (s x / x )2 ) (s y / y )2 - 2s xy
/ xy
Powers
Exponentials
ax+b
ae+bx
-
sz / z =±s x / x
sz / z =±bs x / x
Logarithms
aln(bx)
(as x / x )2
-
Operation
Simple sums and
differences
Weighted sums
and differences
Table 3. Error propagation formula. It is common to ignore the covariance term if x and y are uncorrelated.
If x and y are correlated, as happens when we do linear
regression, then we must consider the covariance. This is
discussed in the section below.
ERROR PROPAGATION FOR SOME SPECIFIC CASES. As
an exercise, you should derive these formulae. The formula
are for a function Z=f(x,y), which a and b are constants. In
most cases, the covariance term can be ignored.
Other functions can be dealt with by using the error
propagation formula above, but another approach is to
expand the functions directly as a series and work from
there. e.g. ln(x+δx)=ln(x)+ln(1+δx/x)~ln(x)+δx/x as
ln(1+x) = x+….. etc. so for small x the error on ln(x) is
+δx/x. Similarly, using the binomial expansion, the error on
1/x is also +δx/x. I’ll leave it as an exercise for the student to
show that the error on the nth root is +δx/n, i.e. it gets less!.
Conversely it rises rapidly with powers of n.
VIII. ERRORS IN LINEAR REGRESSION FOR
STRAIGHT LINES. Often, student data is so bad that do
a proper error analysis of a linear regression is overkill.
Simpler procedures for extracting the data and their errors
will suffice. That is discussed here; a full error analysis is
given below.
When a graph of y versus x should be a straight line, it is
common to calculate its slope m and intercept b in the
equation y = mx + b statistically, by the method of least
squares. This is a good procedure, but it has some pitfalls,
which should always be borne in mind: 1) Always draw the graph, for two reasons: a) Plotting the
least squares line on the graph is a good check against
numerical error in putting data into the calculator. The line
ERROR ANALYSIS: 6
clearly fit a curve, and that you shouldn't be looking for a
straight line.
2) In some experiments, only part of the data fit a straight
line, and there is curvature in some other region. In this
case, you make a visual choice from your graph of which
points to take into account in drawing the line. There is
then no point in using anything other than a visual
procedure for drawing the best line.
3) The usual method of doing the least squares calculation
assumes no error in x, and random scatter in y. For
example, if you are constructing a calibration curve of
spectroscopic absorbance against concentration of a colored
solute, the absorbance commonly has errors amounting to
at least +1%, which the standard solutions can be made up
to an accuracy of 0.1% or better. In a plot of absorbance as y
versus concentration as x, the usual assumption is
legitimate. Hence: a) Always tabulate as y the quantity
which has the larger expected random scatter. b) If both x
and y have large scatter, recognize that a more complicated
statistical analysis is called for. This will not be done in
these laboratories.
SLOPE AND INTERPOLATION ERRORS. In the
instrument room, computer programs are available which,
in addition to giving the slope of a line, will give its standard
deviation. Treat this just like the standard deviation of a
mean. There is a 68% chance that the slope lies within +
one standard deviation of the calculated value. Double
those limits for 95% confidence. Often, having calculated
the line, one wants to take a particular y value (e.g.
absorbance of an unknown solution) and read the
corresponding x (concentration) from the graph. The
© P.S.Phillips October 31, 2011
programs again give an error limit, which should be treated
as standard deviation and doubled for 95% confidence.
If there are large errors or outliers in the data, it is better to
use a robust linear regression (e.g. a least median squares).
However, such programs are not widely available. Also, if
there is significant error in both x and y, it’s often simpler to
abandon statistical procedures. Instead plot the graph, draw
around each point a rectangle representing error limits of
both x and y, draw the best line through the points, then
draw two other lines, passing through the boxes with
maximum and minimum slope. If the line can be clearly
drawn through all boxes except one, and cannot be adjusted
to pass through that one, then there is some error in that
one point which has not been taken into account in drawing
the box. Such a point is called an outlier. (See figure.1)
mmax ~-0.70, mmin ~ -0.36, and m~-0.50
uncertainty in m = (0.70 - 0.36)/2 = 0.17
so m = -0.45+0.17, similarly b = 5.0+0.8
Figure 1. Choosing a best line fit and the error.
RIGOROUS ESTIMATION OF ERRORS IN AN L.S.F . A
rigorous derivation of an l.s.f. is tedious so we will focus on
some of the pitfalls and the correct way to estimate errors.
Most l.s.f.’s for a fit of y to x make the following
assumptions;
a) The errors are independent of x and y.
b) The errors are all the same. (You can circumvent this by
using a weighted linear regression).
c) The data contains no outliers. (You can partially
circumvent this by using least median squares.)
d) The x data contains no errors. (There are routines for
allowing for this, but they are difficult to find.)
e) The errors are distributed normally. (Outliers violate
this, but some errors e.g. counting statistics are distributed
as a Poisson curve. There are routine to allow for this, but
they are difficult to find.)
f) Most importantly, the underlying data is in fact linear!
© P.S.Phillips October 31, 2011
Given that these criteria are met then we need to worry
about how good the fit is, how to compare the fitted
parameters with other data sets and what the errors are for
values calculated from the parameters
HOW GOOD IS AN L.S.F. The usual criterion is to look at
how close the regression coefficient, r, is to one. Regression
coefficients are not only misleading they are evil. DO NOT
USE THEM. The more normal approach is to use the chisquare parameter, but for our purposes that is usually
unnecessary and will not be discussed here. Looking at the
errors on the fitted parameters is usually adequate.
However, if the data is far from the origin the error on the
intercept will be large and one may need to do a chi-square
test to reassure oneself that all is ok., although that won’t
change the fact that the error really is large. Generally, one is
more interested in the errors on values calculated from the
parameters. (See below).
COMPARING FITTED PARAMETERS. Often we need to
know whether two fits give lines with the same slope or
intercept. We will not discuss that further here other than to
say that a t-test on the parameters will usually work.
ERRORS ON CALCULATED VALUES. To properly calculate
the errors for values calculated for the parameters one needs
the covariance so one should be sure to use a program that
returns this value. For a linear fit, y = ax+b, derived from
data points each with an individual error of σi, the errors on
the parameters a and b, σa and σb respectively, and the
2
covariance of a and b, σab
are given by
sa2 = Sxx / D
sb2 = S / D
where
2
sab
=-Sx / D
D = SSxx -(Sx )2
and
n 2
x
Sxx = å i2
i=1 si
n
1
S=å 2
i=1 si
n
x
S x = å i2
i=1 si
If all the σi are the same and equal σ, this simplifies to
¢ / D¢
sa2 = Sxx
sb2 = S ¢ / D¢
where
2
sab
=-Sx¢ / D¢
ERROR ANALYSIS:7
D¢ =
¢ -(Sx¢ )2
nSxx
and
n
¢ = å xi2
Sxx
i=1
s2
n
Sx¢ = å xi
i=1
The error σ may be estimate from the scatter of the y values,
i.e.
1
2
( yi - ˆy )
s2 =
å
n-2
where ŷ is the fitted y value i.e.
ˆyi = axi + b
The n-2 arises because we use a and b to estimate ŷ . Some
programs simply assume σ is one, in which case the error
estimates on a and b (if given) are highly suspect.
The various sums are often provided by the program along
with other data. However, what we want is the error in a
ERROR ANALYSIS: 8
predicted y for a given x. Normally we would simply sum
the errors for a and b, i.e. σ2y = (σa x )2 + σb2 , however, in
this case we must include the covariance à la Table 3 as σa
and σb are derived from the same data set so are correlated
(or more explicitly x and y are correlated by the definition of
a straight line). The desired error is thus
s 2y = (xsa )2 ) sb2 ) 2ab(xsab )2
You should note that the covariance term is generally
negative so it may partially cancel the other terms. This is
expected as a= (y-b)/x so any shift in a, will also shift b.
However, y is usually our measured parameter and we are
more interested in the spread of the corresponding x value,
in which case the error can be deduced by application of the
formula in table 3.
2
s x2 = ( ysa )2 ) (bsa )2 ) (asb )2 - 2absab
A more common approach is to use confidence intervals for
the fit. This is discussed in your anal. chem. course.
© P.S.Phillips October 31, 2011
Measure
Error
Measure
Error
Total titer by burette (50mL)
Total titer by burette (10ml)
End point detection
Volumetric flask (1mL)
Volumetric flask (2mL)
Volumetric flask (5mL)
Volumetric flask (10mL)
Volumetric flask (25mL)
Volumetric flask (50mL)
Volumetric flask (100mL)
Volumetric flask (200mL)
Volumetric flask (250mL)
Volumetric flask (500mL)
Volumetric flask (1000mL)
Volumetric flask (2000mL)
Pipetting (micro pipets)
Pipetting (GC syringe)
Pipetting (adjustable-typical)
Pipetting (1mL max., calibrated)
Pipetting (5mL max., calibrated)
Pipetting (10mL max., calibrated)
Pipetting (1mL)
Pipetting (2mL)
Pipetting (3mL)
Pipetting (4mL)
Pipetting (5mL)
Pipetting (10mL)
Pipetting (15mL)
Pipetting (20mL)
Pipetting (25mL)
Pipetting (50mL)
Pipetting (100mL)
+0.03mL
+0.01mL
+0.01mL
+0.01mL
+0.015mL
+0.02mL
+0.02mL
+0.03mL
+0.05mL
+0.08mL
+0.10mL
+0.12mL
+0.20mL
+0.30mL
+0.50mL
all +1%
all +1%
+0.5%
+0.03mL
+0.05mL
+0.07mL
+0.008mL
+0.01mL
+0.01mL
+0.013mL
+0.015mL
+0.02mL
+0.025mL
+0.03mL
+0.03mL
+0.05mL
+0.08mL
pH meter
Thermometer (0.1C graduation)
Thermometer (1C graduation)
Thermometer (bomb)
Thermometer (digital-absolute)
Thermometer (digital-relative)
Thermometer (thermocouple)
Time interval (manual)
Time interval (computer)
Weighing on a top-loader balance
Weighing on an analytical balance
Viscometer (Canon-Fenske)
UV spectrometer wavelength
UV spectrometer absorbance
+0.1 pH units
+0.02C
+0.1C
+0.01C
+0.1C-1.0C
+0.001C
+0.01C
+0.1s
+0.01s
+1 in last figure
+0.0002g
+0.2%
+1nm
+0.003A or 1%
Table 1. Examples of reasonable error limits for various
pieces of equipment (check manufacturers manuals for
exact numbers).
Be sure to distinguish between
manufacturer tolerances and precision of measure.
Manufacturer tolerances are the accuracy of the calibration
of the equipment, which translate to a precision when
mixing equipment. It is irrelevant if calibrations are done
and standard solutions are used.
© P.S.Phillips October 31, 2011
If you do repeated measures with a single item of equipment
your precision should approach the manufacturers
precision, but in general will be more.
ERROR ANALYSIS:9
NOTES
ERROR ANALYSIS: 10
2011
© P.S.Phillips October 31,
Exp. E.
ENZYME CATALYZED REACTION KINETICS
INTRODUCTION. Many chemical reactions are very
slow at ambient temperature, usually because they have high
activation energies. One way we can increase the speed of a
reaction is to carry it out at higher temperatures. One
serious drawback to this approach, however, is that, aside
from intrinsic experimental difficulties that might arise,
undesirable competing reactions (such as decomposition)
also begin to take place faster at higher temperatures. These
complications may also decrease the efficiency of the
desired reaction.
Increasing the temperature is obviously not an option for
biological reactions under physiological (native) conditions;
~37C and pH 7. However, many reactions that are
ordinarily very slow at this temperature are nevertheless
found to occur very rapidly in natural systems due to the
action of catalysts. A catalyst is an agent that increases the
rate of a reaction by effecting a decrease in the activation
energy of the process. One example of a catalyzed reaction is
the breaking up, or digestion, of a protein into amino acid
residues. A protein is a macromolecule consisting of many,
often hundreds of, amino acids linked together by peptide,
or amide, bonds. In order to be useful to an organism, a
protein molecule must be broken down into its amino acid
constituents for further, specific polypeptide synthesis. A
particular example is α-chymotrypsin, which cleaves
polypeptides (or esters) at points adjacent to aromatic
groups (see reaction below). This enzyme has the particular
advantage that its own aromatic groups are buried deep in
the structure so it does not digest itself, which would
complicate interpretation of experiment.
A molecule that catalyses a biologically relevant reaction is
called an enzyme. Enzymes are, themselves, usually large
polypeptides having high molecular weights (ca.104-106
g/mol). They are remarkable because of their catalytic power
and specificity; only certain, narrowly characterized
reactions are catalyzed by a given enzyme, and often only
under specific conditions (e.g., ionic strength, pH, and
temperature). In some single-celled organisms, as many as
3000 different enzymes can be found. Generally, an enzyme
derives its catalytic and reaction-specific properties
because of a unique structural property called an active site.
The shape of the active site, along with other structural
features, orients molecules onto (or into) the site, enabling
the reaction to take place. The active site often contains
groups that affect the reactant molecule's conformation,
thereby speeding up the reaction. In essence, an enzyme can
catalyze a reaction by stabilizing the transition state and
© P.S.Phillips 31/10/2011
may be compared with the catalytic site of specially
prepared solid surfaces. In general, the rate of a reaction is
equal to the sum of the intrinsic (or uncatalyzed) and the
catalyzed rates. This assumes that the two processes occur
independently of each other. Thus the observed rate
constant, kobs is
kobs = ko + kcat
where ko and kcat are the rate constants of the uncatalyzed
and catalyzed processes, respectively.
If the molecular structure of an enzyme, i.e., the
conformation that creates the active site, is changed (even
subtly), catalytic activity is diminished or even lost. This
denaturation of the enzyme can be brought about by
subjecting it to extremes in temperature, pH, or ionic
strength, i.e., non-physiological conditions. Sometimes an
enzyme has more than one binding site and binding of an
inappropriate species to the second site will distort and
deactivate the first site (However, in some cases binding at
the second site is requires to activate the first site).
Sometimes denaturation is reversible, and enzymatic
activity can be restored by returning the system to
appropriate conditions. In other instances, enzymatic
activity can be permanently lost.
In this experiment, we will study the hydrolysis of an ester
catalyzed by the enzyme α-chymotrypsin. The reaction is
studied in buffered aqueous solution and is an example of
homogeneous catalysis because it is a one-phase system; all
components are soluble. α-chymotrypsin is a wellcharacterized enzyme (denoted hereafter by E). It is a
protein having a molecular weight of 24,800 D and is known
to have one active site per molecule. In fact, the
determination of this enzyme's purity is based on the fact
that it reacts stoichiometrically with certain esters. It is also
a particularly convenient enzyme to study because it is
inexpensive and can be obtained in high purity; it is
generally isolated from bovine pancreas extract.
The reactant that undergoes conversion to a product (or
products) in an enzyme-catalyzed reaction is called the
substrate. In this experiment, the substrate that reacts with
α-chymotrypsin is an ester of 4-nitrophenol, specifically,
4-nitrophenyl trimethylacetate (S). The overall reaction can
be expressed as follows:
E + S + H2O [ P1 + P2 + E
where P1 and P2 are the two products of the ester hydrolysis,
in this case, 4-nitrophenol and trimethyl-acetic acid,
respectively.
Exp. E. Enzyme Kinetics:1
Because the reaction will be carried out at a pH 8.5, both
products exist in their conjugate base forms,
trimethylacetate ion and 4-nitrophenoxide ion. In principle,
any ester can be used to study α-chymotrypsin catalyzed
hydrolysis. By using 4-nitrophenyl trimethylacetate,
however, we exploit the facts that a) the bulky alkyl group
slows the reaction down to a convenient time scale for
simple real-time analysis, and b) the aromatic product
absorbs visible light (it has a yellow appearance). The latter
property allows the course of reaction to be followed
spectrophotometrically. All other species involved in this
reaction are colorless.
The kinetics of this reaction are particularly interesting
because when the enzyme and substrate are combined, there
is an initial "burst" of nitrophenol (P1 formation, which is
then followed by a gradual increase in P2 concentration. In
an attempt to explain this behavior, we really need to
consider several mechanisms of enzyme kinetics.
Mechanism I. The simplest scheme (the so called
Michaelis-Menten mechanism) involves the reversible
binding of the enzyme to the substrate, followed by the
dissociation of this complex to form product:
k1
k2
E + S]ES+P + E
k-1
This is a three-parameter mechanism (rate constants k1, k1, and k2). Because we intend to follow the time evolution of
product, the relevant differential equation is
d[P]
(1)
= k2[ES]
dt
We must obtain a relationship between the measurable
quantity, [P], and [ES]. To do this, we first write the material
balance for enzyme, i.e.,
(2)
[E]o =[E] + [ES]
where [E]o is the total (or bulk) enzyme molarity. Equation
(2) states that the enzyme must be present either in its free
form, E, or in its substrate-bound form, ES. Notice that
[E]o is a measurable (and controllable) quantity.
Next, we make the assumption that the dissociation of the
enzyme-substrate complex into free enzyme and
unchanged substrate is faster than the reaction to form
product (and enzyme). This is equivalent to saying that
Exp. E. Enzyme Kinetics:2
k1>>k2..The consequence of this assumption is that the
concentration of enzyme-substrate complex can be
approximated by the equilibrium expression
[ES] ~ [E][S]/K
(3)
Where K is the equilibrium constant defined for the
dissociation reaction of the ES complex, ES]E + S;
i.e., K = k-1/ k1. (K is often written as Km). By combining
equations (2) and (3), we can express the concentration of
complex as
[E]o
(4)
[ES] ≈
(1 + K /[S])
Finally, we exploit a common experimental simplification,
namely, that of the initial rate approximation. This
condition, which is often used in kinetic studies means that
the substrate concentration is nearly constant for short
reaction times, i.e., as long as the reaction only proceeds to a
small degree of conversion. With this restriction, equation
(4) becomes
[E]o
(5)
[ES] ≈
(1 + K /[S]o )
which means enzyme-substrate complex concentration is
constant. Incorporating this result in equation (1) allows us
to express the time dependence of [P] by using the
boundary condition that at t=0, [P]=0
d[P]
k2[E]o
(6)
≈
dt (1 + K/[S]o )
This result predicts that the product concentration initially
rises linearly (when [S]~[S]o) with time and the reaction
velocity is constant and thus is zero order. Catalyzed
reactions often exhibit zero-order characteristics at the
start of the reaction.
The rate of production of P is, of course, the velocity of the
reaction, v. The maximum reaction velocity, vmax is thus
given by vmax=k2[E]0 (i.e. when [S]o is large). Eqn.6 is
often written as
vmax
(7)
v=
(1 + K /[S])
From which it is clear that a plot of 1/v vs. [S] will be linear
with slope K/vmax, intercept (on the y-axis) of 1/vmax and
intercept (on the x-axis) of –1/K. Such linearised plots are
called Lineweaver-Burk plots. (Note that it not only took
four biologists to achieve this simple result, but they also
had the audacity to confuse everything by naming the
equations after themselves).
rate of production of P,
Inhibition. Some chemicals reduce or destroy (inhibit) the
catalytic activity of an enzyme (without actually destroying
© P.S.Phillips 31/10/2011
the enzyme). This occurs by two mechanisms i)
competitive inhibition ii) non-competitive inhibition:
Competitive inhibition occurs because enzymes are usually
specific to molecular shape, not the molecule itself. The
result of this is that any molecule, of similar shape to the
substrate, can occupy the active site and prevent it from
reacting with the substrate. Non-competitive inhibition
occurs when a molecule binds to the enzyme site at some
position other than the active site, but results in the active
site becoming distorted thus reducing it’s efficiency.
Inhibition can be readily incorporated into the mechanism
above as follows: We will deal with competitive inhibition
first. Firstly we modify the mass balance equation (2) to
account for the fact that some of the enzyme is bound by the
inhibitor [I],
(8)
[E]o =[E] + [ES] + [EI]
Next we recognize that EI will be in equilibrium with E and
I, i.e.
EI]E + I
with equilibrium constant
(9)
K I = [E][I]/[EI]
we then proceed as before making use of (7) and (8) and we
get
d[P]
k 2[S][E]o
(10)
≈
dt [S] + K (1 + [I]/ K I )
or, in more traditional notation
vmax [S]
(11)
v=
[S] + K (1 + [I]/ K I )
In this case the Lineweaver-Burk plot will yield a slope and
x-axis intercept that depends on the inhibitor
concentration, but the y-axis intercept will be 1/vmax,
independent of inhibitor concentration (why?).
The case for non-competitive inhibition is developed as
above. However, we have one further species to consider, IES.
That is the species where the inhibitor is bound to the
enzyme-substrate complex. Once again we modify the
material balance equation and introduce a new equilibrium
constant K I′ for the dissociation of the complex IES to IE
and S. If we (reasonably) assume that the binding of the
inhibitor to the enzyme is unaffected by the presence of the
substrate on the enzyme so that KI= K I′ then we get
vmax [S]
(12)
v=
([S] + K )(1 + [I]/ K I )
In this case the Lineweaver-Burk plot will yield a slope and
x-axis intercept that depends on the inhibitor
© P.S.Phillips 31/10/2011
concentration, but the y-axis intercept will be –1/K. The
plots for the three cases are shown in figure 1 overleaf.
As we mentioned earlier, the time dependence of the 4nitrophenoxide ion concentration in the α-chymotrypsincatalyzed hydrolysis of the ester precursor is not linear, as
predicted in equation (1); hence, Mechanism I cannot be
acceptable and must be modified.
Modification of Mechanism I. We will now consider a
refinement of Mechanism I in which the pre-equilibrium
assumption, eq.(3), is relaxed, and see whether this
modification brings the predicted rate law into conformity
with the observed one. We will retain, however, the isolation
condition assumption, [S]o>[E]o. We proceed by writing
the differential equation for the formation of complex,
d[ES]
= k1[E][S]-k-1[ES]-k2[ES]
dt
(13)
After using equation (2) and replacing [S] by [S]o, we
obtain, after combining terms,
d[ES]
= k1[E]o[S]o-(k-1 +k2 +k1[S]o )[ES]
dt
(14)
Using the definitions
X = k1[E]o[S]o and Y = k-1 +k2 +k1[S]o
and integrating equation (14) with [ES]=0 at t=0, provides
the time dependence
æ X -Y [ES]ö÷
(15)
lnççç
÷÷ =-Yt
è
ø
X
or more explicitly,
æXö
(16)
[ES(t )] = ççç ÷÷÷(1- exp(-Yt ))
èY ø
The rate equation for product formation is obtained by
combining equations (1) and (15). We get for the reaction
velocity,
d[P] æç k2 X ö÷
(17)
=ç
÷(1- exp(-Yt ))
dt çè Y ø÷
and after integrating this equation and simplifying the
result, we see that the time dependence of product is
æk X ö æk X ö
[P(t )] = ççç 2 ÷÷÷t -çç 2 2 ÷÷(1- exp(-Yt ))
è Y ø çè Y ÷ø
(18)
Predictably, perhaps, this result is more complex than that in
equation (6). Inspection of equation (18) reveals that after a
certain time, the second term becomes constant (-k2/Y2),
and the product formation, [P] vs. t, is (again) zero order,
Exp. E. Enzyme Kinetics:3
i.e., linear with time. A plot of [P] vs. t resembles
qualitatively the curve shown in Figure 1.
Figure 1. A plot of P(t) for a set of arbitrary rate
constants as predicted by equation (12).
The reaction starts out slowly and then increases to a
constant rate (zero-order conditions). Notice that the
intercept of the zero-order part of the reaction is -k2/Y2.
(You should confirm that the limiting slope of P(t) as t → 0
is zero.) Abandoning the pre-equilibrium constraint has
restored the scheme to a three-parameter problem, and we
can extract the three rate constants, k1, k-1, and k2 from the
nonlinear [P] vs. t curves by using some appropriate
strategy.
We can see from equation (17) that the reaction reaches a
condition of constant velocity, v., which is
k X
k k [E] [S]
vc = 2 = 1 2 o o
Y
k1[S]o + k-1 + k2
or
vc =
d[P] k2[E]o[S]
=
dt
K M +[S]o
(19)
Equation (19) is known as the Michaelis-Menten equation,
and it is frequently used to characterize enzyme-catalyzed
reactions; KM is called the Michaelis constant and is equal to
(k-1+k2)/k1. (Notice that KM is slightly different from the
equilibrium constant, K, introduced above. Notice also that
the right-hand side of equation (19) is the zero-order rate
constant of the more complete integrated rate law; see
equation (18). This result can also be obtained by using the
steady-state approximation in [ES]; i.e., [ES]ss, =
kl[E][S]oJ/(k2 + k-1); see equation (13).
We must now face the problem that the buildup of the 4nitrophenol product is not observed to start out slowly and
then speed up to constant velocity as predicted by equation
(18). Instead, the product is formed rapidly at first, and then
Exp. E. Enzyme Kinetics:4
the reaction slows down to a zero-order (constant velocity)
behavior. These kinetic observations have been studied in
detail by Bender and co-workers. The initial burst of
product followed by the slower zero-order reaction has
been interpreted in terms of Mechanism II, which is a
modified version of Michaelis-Menten kinetics.
Inhibition. Some chemicals reduce or destroy (inhibit) the
catalytic activity of an enzyme (without actually destroying
the enzyme). This occurs by two mechanisms i)
competitive inhibition ii) non-competitive inhibition:
Competitive inhibition occurs because enzymes are usually
specific to molecular shape, not the molecule itself. The
result of this is that any molecule, of similar shape to the
substrate, can occupy the active site and prevent it from
reacting with the substrate. Non-competitive inhibition
occurs when a molecule binds to the enzyme site at some
position other than the active site, but results in the active
site becoming distorted thus reducing it’s efficiency.
Inhibition can be readily incorporated into the mechanism
above as follows: We will deal with competitive inhibition
first. Firstly, we modify the mass balance equation (2) to
account for the fact that some of the enzyme is bound by the
inhibitor [I],
(20)
[E]o =[E] + [ES] + [EI]
Next, we recognize that EI will be in equilibrium with E and
I, i.e.
EI]E + I
with equilibrium constant
(21)
K I = [E][I]/[EI]
we then proceed as before making use of (13) and (14) and
we get
d[P]
k 2[S][E]o
(22)
≈
dt [S] + K (1 + [I]/ K I )
or, in more traditional notation
vmax [S]
(23)
v=
[S] + K (1 + [I]/ K I )
In this case the Lineweaver-Burk plot will yield a slope and
x-axis intercept that depends on the inhibitor
concentration, but the y-axis intercept will be 1/vmax,
independent of inhibitor concentration (why?).
The case for non-competitive inhibition is developed as
above. However, we have one further species to consider, IES.
That is the species where the inhibitor is bound to the
enzyme-substrate complex. Once again, we modify the
material balance equation and introduce a new equilibrium
constant K I′ for the dissociation of the complex IES to IE
© P.S.Phillips 31/10/2011
and S. If we (reasonably) assume that the binding of the
inhibitor to the enzyme is unaffected by the presence of the
substrate on the enzyme so that KI= K I′ then we get
vmax [S]
(24)
v=
([S] + K )(1 + [I]/ K I )
In this case, the Lineweaver-Burk plot will yield a slope and
x-axis intercept that depends on the inhibitor
concentration, but the y-axis intercept will be –1/K. The
plots for the three cases are shown in figure 2 overleaf.
Mechanism II
The basic assumptions underlying this mechanism are:
1. The ester and enzyme form a reversible complex that is in
a rapid pre-equilibrium.
2. The ester binds to the active site of the enzyme causing
the acylation of the enzyme (attachment of the RCOgroup) and the release of 4-nitrophenoxide ion (P1).
3. The acylenzyme is then deacylated, releasing the
trimethylacetate ion, P2, thereby restoring the active
enzyme, which can catalyze the hydrolysis of another ester
molecule. The following reaction scheme portrays this
mechanism:
The mechanism can be expressed kinetically, as follows:
k1
E + S]ES
reversible enzyme -substrate binding
k-1
k2
ES+P1 + AE enzyme acylation
k3
AES+P2 + E enzyme deacylation
where AE is the acylenzyme (see the scheme). Notice that
although P1, which is monitored in this experiment, is
released before P2 is produced, the last step is nevertheless
important kinetically because it produces the active enzyme,
which can then "recycle" and thus react with another
substrate.
© P.S.Phillips 31/10/2011
The scheme described by Mechanism II now contains four
parameters, k1 k-1, k2, and k3, but by invoking the preequilibrium condition, we can reduce the number of
unknowns to three, because K= k-1/k1,. We again assume
that [S]o > [E]o. Our objective, as before, is to obtain the
time dependence of the observed product, P,. We start by
writing the differential rate laws for [P1] and [ES]
d[P1]
= k2[ES]
dt
and
d[ES]
= k1[E][S]- k-1[ES]- k2[ES]
dt
The mass balance equation for enzyme gives
[E]o = [E] +[ES] + [AE]
(25)
(26)
(27)
In addition, the equilibrium assumption gives us
k
[E][S] [E][S]o
K º -1 =
»
k1
[ES]
[ES]
(28)
By combining equations (27) and (28), we can express [ES]
in terms of [AE]
[E] -[AE]
(29)
[ES] = o
1+K/[S]o
We will now have to determine the time dependence of the
acylenzyme, AE. This step is necessary in order express ES
as a function of time. We will then use that result in equation
(25) to arrive at the desired result. We proceed by writing the
rate law for [AE]:
d[AE]
(30)
= k2[ES]- k2[AE]
dt
and using [ES] from equation (29) to obtain, after collecting
terms,
æ k2
ö
d[AE]
k [E]
= 2 o +çç
+ k3 ÷÷÷[AE]
÷ø
dt
1+K/[S]o çè1+K/[S]o
For convenience, we use the definitions
A=
k2[E]o
1+K/[S]o
B=
k2
+ k3
1+K/[S]o
(31)
(32)
The solution of the differential equation d[AE]/dt = AB[AE] with the boundary condition t = 0, [AE] = 0 is
æ A - B[AE]÷ö
lnççç
÷÷ =-Bt
è
ø
A
or, explicitly,
A
[AE] = (1- exp(-Bt ))
B
(33)
Exp. E. Enzyme Kinetics:5
Figure 2. From left to right. Lineweaver-Burk plots a reaction with no inhibitor at various concentrations of a
competitive (middle) and non-competitive inhibitor (right)
After substituting this expression for [AE] in equation (29),
we get, after rearranging,
[ES] =
[E]o + A / B
A/ B
)+
exp( Bt )
1+K/[S]o 1+K/[S]o
(34)
Notice that according to eq.(34) the ES adduct has a finite
concentration at t=0; this physically unreasonable result is a
consequence of the pre-equilibrium assumption. Eq.(34)
clears the way to expressing the needed time dependence of
P,; by combining equations (34) and (25), we find,
æ[E] + A / B ÷ö æ k2 ( A / B) ÷ö
d[P1]
çç
÷÷)+
÷÷exp( Bt ) (35)
= k2 çç o
÷
ç
dt
è 1+K/[S]o ø çè1+K/[S]o ÷ø
We can integrate this equation to obtain the direct time
dependence of P1. The result appears in the form
P1(t ) = X (t ) )Y (1- exp(-Bt ))
takes place exponentially (with an apparent rate constant B).
Thus for a given set of [E]o and [S]o values, the analysis of
curves like that shown in Figure 2 provides three pieces of
information, X, Y, and B. We now face the challenge of
extracting the three specific system parameters, K, k2, and
k3, from this information. In principle, all we need to do is
evaluate X, Y, and B from one kinetic experiment of [P1] vs.
t, and to solve equations (37) and (38), with the definitions
in (32), to obtain K, k2, and k3. In practice, this is not a
practical way to proceed because the transformations are
too mathematically obtuse. In concept, and we would have
to measure X, Y and B at different [E]o and [S]o values, and
to use appropriate mathematical transformations of
equations (37-39) to extract the rate parameters. Some
simplified approaches are presented next.
(36)
in which B is defined in (32), and X and Y are expressions
that contain rate constants and initial enzyme and substrate
concentrations, i.e.,
æ[E] + A / B ö÷
÷
X = k2 çç o
(37)
çè 1+K/[S]o ø÷÷
k A
Y= 2 2
B (1+K/[S]o )
(38)
Eq.(36) is sketched in Figure 2. This P vs. t curve now
conforms to the observation of an initial burst of product
followed by a constant rate of product formation. Notice that
according to eq.(36), the approach to zero-order kinetics
Exp. E. Enzyme Kinetics:6
Figure 3. Plot of P(t) eq.(36) for an arbitrary set of
rate constants.
At this point, remember that the substrate in this reaction
undergoes spontaneous, or uncatalyzed, hydrolysis in
© P.S.Phillips 31/10/2011
parallel with the enzyme-catalyzed reaction. Each process
forms the same species, P1, that is followed
spectrometrically. Thus, hence you must subtract the
uncatalyzed "blank" kinetic run from the experimentally
acquired data file to obtain the actual time dependence of
the catalyzed reaction that is modeled in eq. (36).
In the case of the α-chymotrypsin-4-nitrophenyl
trimethylacetate system studied in this experiment, one
important point is that the enzyme used is not pure αchymotrypsin; the material contains some impurities
(including water of hydration). Thus, its bulk concentration
is not equal to the enzyme molarity. Instead, we may write
[E]o act = p[E]o bulk
where [E]o act is the initial concentration of active (i.e.,
pure) enzyme, and [E]o bulk is the initial bulk concentration
of the enzyme (i.e., as weighed out in the experiment), and p
is the purity factor of the raw enzyme; thus the activity of
the enzyme (expressed as a percent) is 100p. We will show
next how it is possible to estimate p from the kinetic data.
We will assume that values of X, Y, and B have been obtained
from a kinetic run at known [E]o bulk and [S]o. Preferably
these values have been determined from several different
runs at fixed [E]o bulk and various initial substrate
concentrations, [S]o. First, we consider X (eq.(37)). With a
little work, we may recast X to read
k2k3
[E]o act [S]o
k2 + k3
X=
k3
[S]o + K
k2 + k3
(39)
(We emphasize that the enzyme concentration corresponds
to the active enzyme.) The reason we present equation (39)
is that it has the form of a Michaelis-Menten, (19). Notice
that X has units of M s-1, i.e., a rate. This point is clarified
by rewriting (39) as
k [E] [S]
(40)
X = cat o act o
[S]o + K M
in which kcat = k2k3/(k2 + k3) and KM, an apparent
Michaelis constant, is k3K/(k2 + k3). In its recast form, we
can conveniently transform X to the linear equation
KM
1
1
=
+
X kcat [E]o act kcat [E]o act [S]o
(41)
which we may use to obtain kcat and KM by plotting 1/X vs.
1/[S]o (if we know [E]o act ). Alternatively, we may apply a
nonlinear regression analysis of (X[S]o) data to equation
(41). We may invoke an approximation that is justified by
© P.S.Phillips 31/10/2011
prior knowledge of the α-chymotrypsin-p-nitrophenyl
trimethylacetate system, namely, that we can choose [S]o
values such that [S]o> KM. With this inequality, equation
(41) simplifies to
X = kcat[E]o act
(42)
and we can obtain kcat, as long as we know [E]o act . But as
we pointed out above, the experimental [E]o is the bulk
concentration of enzyme. We need to know p, the actual
enzyme activity, in order to obtain [E]o act . To obtain p, we
examine the kinetic parameter Y, which we may recast as
æ
ö2
çç k2 ÷÷
ç k + k3 ÷÷
÷
Y = [E]o act çç 2
çç
K M ÷÷÷
÷÷
ç1 +
èç [S]o ø÷
(43)
Again, using prior knowledge of the system studied here, we
add to the inequality [S]o>KM the approximation that k2
> k3. These statements greatly simplify equation (43), so
that
(44)
Y »[E]o act
and we may obtain [E]o act directly from the rate parameter
Y. Once we know [E]o act equation (42) immediately
furnishes a value of kcat, which, considering the inequality
k2>k3, is approximately equal to k3, the enzyme
deacylation rate constant.
If the inequalities are not justified, we can, with some effort,
transform equation (43) to read
k3 ö÷ 1
K (k k )
1 æç k2 ))
÷÷
(45)
=ç
) M 2 3
ç
Y è k2 ø÷ [E]o act
k2 [E]o act
and we can use a plot of 1/ Y vs. 1/[S]o to obtain KM and
k2/(k2 + k3).
Finally, we may recast B, see (32), into a more convenient
form (using the approximation that k3K < (k2 + k3)[S]o;
i.e., KM< [S]o ):
æ K ÷ö 1
1
1
÷
=
+çç
B k2 + k3 çè k2 + k3 ÷÷ø[S]o
(46)
in which a double-reciprocal plot of B and [S]o will yield K
and k2 + k3. If B is not determined at different substrate
concentrations, the approximations [S]o<K and k2>k3
may be made, in which case,
k [S]
(47)
B= 2 o
K
Exp. E. Enzyme Kinetics:7
PROCEDURE.
Solutions Needed. Prepare the following solutions.
1. Solution #1. Prepare (or obtain) about 60mL of a TRIS
buffer with pH = 8.5 (0.01 M). You will use this solution as
the reaction medium and also as a solvent blank.
2. Solution #2. Prepare a 3.4 x 10-3 M solution of the
substrate, 4-nitrophenyl trimethylacetate, in acetonitrile.
About 10mL is sufficient for one experiment, although
25mL may be more convenient to prepare. (Use appropriate
caution when using acetonitrile. Wear protective gloves and
work in a fume hood.)
3. Solution #3. Obtain α-chymotrypsin solution (about
50mg of α-chymotrypsin in 1.0mL of the pH 4.6 acetate
buffer). You will use this directly in the kinetic run.
4. Solution #4. Make up 5 or 10mL of a 2.8 × 10-5M solution
of 4-nitrophenol solution in the TRIS buffer. You will use
this solution to determine the molar absorptivity of the
product, P1. Note that since the pKa of 4-nitrophenol is
about 7.0, the predominant species in the pH 8.5 TRIS
buffer is the 4-nitrophenoxide ion.
5. Solution #5. Make up 100mL of a 3.0x10-3M solution of
Malthion (MW=330) in acetone from the stock solution of
commercial Malthion (1.5M). Note that Malthion smells
and, more importantly, inhibits the enzyme acetylocholinase; the enzyme that plays a key role in nerve signal
transmission. This is a characteristic of nerve gases and
many modern pesticides; breathing them in or splashing
them on the skin results in central nervous system failure
(a.k.a. death). Be sure to use gloves, make up the solutions
in the fume hood and keep them stoppered when not in use.
Determination of the Molar Absorptivity of 4Nitrophenol. Set the spectrophotometer wavelength to 400
nm, the position at which the hydrolysis product, P1 is
measured. Use two matched, 1cm spectrophotometer cells.
Preferably these should be constructed of fused silica, but
Pyrex cells are acceptable at this wavelength. Add TRIS
buffer to both cells, place them in the spectrophotometer
cavity, and zero the instrument. Remove the sample cell and
rinse and fill it with the 2.8 × 10-5M 4-nitrophenol
solution in the sample cell (solution #4). Replace the cell in
the spectrophotometer, and record the absorbance.
Determination of the Spontaneous Hydrolysis Rate of
the Substrate. To determine the rate constant of the
uncatalyzed (i.e., spontaneous) hydrolysis of 4-nitrophenyl
trimethyl-acetate, fill a clean sample cell with precisely
3mL of TRIS buffer. Add 100uL of the 3.4 x 10-3M 4nitrophenyl trimethylacetate/acetonitrile solution (solution
#2). Stopper (or cap) the cell, invert it a few times, and place
Exp. E. Enzyme Kinetics:8
it in the spectrophotometer cavity (make sure a reference
cell containing TRIS buffer is in place), and record the
absorbance at 400nm for at least 2 min., every 5s. In this and
the enzyme kinetic runs, thermostat the cell if possible.
Record the temperature in your notebook. Save the data file
in ASCII format. Do not keep this run on the screen, clear it
off the instrument.
Run the Reaction. Add 3.0mL of TRIS buffer to the
reaction cell (use a pipetter). Place it in the
spectrophotometer cavity and zero the instrument at
400nm. Make sure the reference cell contains the same
buffer solution. Now, add between 10 and 100µL of the
substrate stock solution (solution #2) depending on which
sample (samples 1-5) you intend to run (see table 1, use a
GC syringe to measure the solutions). Mix thoroughly.
Sample No.
Reference
1
2
3
4
5
6
7
8
9
10
Substrate
volume (µL)
0
20
25
30
50
100
20
25
30
50
100
Inhibitor
volume (µL)
0
0
0
0
0
0
40
40
40
40
40
Table 1. Solutions to run. All samples
are made up in 3.0mL of TRIS buffer.
Next add the enzyme to the reaction solution. Use 40µL of
the enzyme stock solution (solution #3 above). There are
several possible techniques for introducing the enzyme: a)
Directly inject the appropriate volume of the enzyme stock
solution into the reaction cell; quickly cap the cell, invert it
several times (do not shake), place it in the
spectrophotometer, and immediately begin data acquisition
(remember you want the initial rate). b) Alternatively, you
can deposit the enzyme solution onto the tip of a clean,
small stirring rod that you then immerse in the cell and use
to stir the reaction mixture. Place the cell in the
spectrophotometer and begin data acquisition. (Experiment
with this technique beforehand; it may be useful to wet the
tip of the stirring rod sparingly with buffer solvent.)
Collection time should be about 2 min. with data points
every 5s (we are only interested in the initial rate). Save the
© P.S.Phillips 31/10/2011
data file in ASCII format. Repeat until all five solutions have
been run. Once you have the data saved, clear it, do not
accumulate the inhibited runs on top of it. You can run out
of memory if you do (the spectrometer can save 10 spectra
only).
Testing an inhibitor. Repeat the runs above, but in addition
add some Malathion inhibitor (solution #6) as indicated in
table 1 (samples 6-10). Again, remember to save the data
file in ASCII format.
Lineweaver-Burk plot. However, Malthion will affect the
enzyme the same way so it should be possible to deduce the
effect on the kinetic runs and consequently (with luck)
which it actually is.
2) You were told to invert the UV-cell several times to mix
the enzyme, not to shake it. Explain why. (Assume the cell
is properly capped so that spillage is not a problem).
3) The spacing of the substrate volume added is not
uniform. Why did we do that ?
Data Analysis. Import the data files to Excel. You will also
need a program that is capable of performing nonlinear
regression analysis on user-defined functions (Origin). We
furthermore assume that each data file (including the
spontaneous substrate hydrolysis blank) has the same time
interval between data points, and the total acquisition times
are nominally equal.
REFERENCES.
Subtract the spontaneous hydrolysis blank from each of the
kinetic runs. However, before doing this, multiply the
absorbance values of the blank file by an appropriate factor
that reflects the different substrate concentrations used. For
example, if you used 100µL in the blank and 80µL for the
kinetic run, multiply the absorbances of the blank file by 0.8
before subtracting them from the kinetic data file. (This
assumes that the spontaneous hydrolysis constant, ko, is
independent of concentration.) Then, convert absorbance to
concentration using the molar absorptivity of the product
(4-nitrophenoxide ion) determined in this experiment.
Perform a nonlinear regression analysis (you’ll need help
with this - using Origin’s non-linear fitting routines - you
can download a demo version off the net) on the acquired
P1 vs. t data sets according to equation (36), and thus obtain
in each case X, Y, and B. From equation (42), obtain kcat [E]o
act and KM by regressing 1/X vs. 1/[S]o. Also, find the purity
factor, p, from the known bulk concentration of enzyme.
R. A. Alberty and R. J. Silbey, Physical Chemistry, 2nd ed., pp.
730-736, Wiley (New York), 1997.
P. W. Atkins, Physical Chemistry, 5th ed., pp. 890-891, W. H.
Freeman (New York), 1994.
P. W. Atkins, The Elements of Physical Chemistry, 1st ed.
pp270-277, Oxford (Oxford), 1992.
M. L. Bender, F. J. Kezdy and F. C. Wedler, J. Chem. Educ.,
44:84 (1967).
M. L. Bender and F. J. Kezdy, J. Amer. Chem. Soc., 86:3704
(1964).
I. N. Levine, Physical Chemistry, 4th ed., pp. 542-545,
McGraw-Hill (New York), 1995.
J. B. Milslien and T. H. Fyfe, Biochemistry, 8:23 (1969).
J. H. Noggle, Physical Chemistry, 3rd ed., pp. 576-582, Harper
Collins (New York), 1996.
T. W. G. Solomons, Organic Chemistry, 5th ed., pp. 11811184, Wiley (New York) 1996.
L. Stryer, Biochemistry, 4th ed., pp. 222-227, W. H. Freeman
(New York) 1995.
I. Tinoco, Jr., K. Sauer, and J. C. Wang, Physical Chemistry:
Principles and Applications in Biological Sciences, pp. 418441, Prentice Hall (Englewood Cliffs, N. J.), 1995
From equation (47) determine the quotient k2/K. If you have
obtained X, Y, and B at several substrate concentrations, use
equation (41) to find kcat and KM. Compare these values
with those obtained from equation (45). Finally, determine
k2 + k3 and K from the double-reciprocal plot displayed in
equation (46).
Test the inequalities used in some of the derivations, namely,
[S]o > KM and k2 > k3.
QUESTIONS.
1) The mechanism is more complex than the simple
Michaelis-Menten one so we cannot determine if the
Malathion is competitive or non-competitive using a
© P.S.Phillips 31/10/2011
Exp. E. Enzyme Kinetics:9
NOTES
Exp. E. Enzyme Kinetics:10
© P.S.Phillips 31/10/2011
Suite G.
INTRODUCTION. Want to know the heat of solution of
glycine? You just pickup Lange or the CRC and look it up.
However, what if you wanted to know the heat of solution of
glycine in something that approximates blood plasma, then
what? You will have to spend a lot of time in the literature or,
you will have measure it. Here we will explore the
measurement of some thermodynamic parameters for
glycine, the simplest of the amino acids. The experiment
should give you some insight into doing these
measurements under non-standard conditions, and how to
do them rigorously.
In part I, we will simply measure the two pKa values for
glycine and explore some numerical tools, including
programming Maple, to assist us in getting a reliable value.
In part 2 we explore the enthalpy of proton transfer for
glycine and pay attention to activity effects. If part 3 we will
find the enthalpy of formation of glycine and pay particular
attention to error analysis.
Part 1. ACID BASE TITRIMETRY
INTRODUCTION. This is a simple pH/conductiometry
titration. Glycine has to pK a s so the experiment has to be
modified accordingly.
THEORY. The theory of strong acids and bases is
sufficiently simple to need no further elaboration here.
However, the theory for titration of weak acids is messy and
is developed in appendix I, from which we can show that the
concentration of hydrogen ion during the titration of a weak
acid with a strong base is;
[H+]3+α[H+]2-β [H+]-KaKw = 0
(1.1)
where Vao is the initial volume of the analyte, cbo is the initial
concentration of analyte, Vb is the volume of titrant added,
cbo is the concentration of titrant and
co f
a = a ) Ka
1) rf
c o K (1- f )
b= a a
) Kw
1) rf
where r = cao / cbo , and the fraction of analyte titrated, f, is
f = Vb cbo / Vaocao . These equations enable us to extract Ka
using the whole titration curve rather than just the one illdefined end-point.
PROCEDURE. This is a simple pH titration. First, you
need to calibrate the pH meter, using the provided standard
buffers (pH 4.00, pH 7.00 and pH 9.00 or 10.00). You will be
shown how to do this. Make sure you don’t get cross
© P.S.Phillips October 31, 2011
THERMODYNAMICS OF GLYCINE
contamination between the standard buffers, and swish the
electrode around. Remember to let the reading stabilize.
Glycine has two pKa’s so we are going to start with a
solution of glycine hydrochloride (you make). You will be
provided with your titrant; accurately made KOH solution
(exact value on the bottle).
We will titrate glycine hydrochloride with KOH over a
pH range of about 2 to 13, and record the pH as a function
of volume of KOH added. You will need to do a rough
titration first to get the two approximate end-points. This
will give you the two pK a values for glycine.
Proceed as follows. Makeup 100 mL of 0.1M glycine HCl
(it need not be exactly 0.1, but you should know what it is
accurately.) Take a 25.0 mL aliquot and adjust the pH < 2.0,
if necessary, with a few drops of the supplied standard 0.1M
HCl (corrosive!). Titrate this solution with the 0.25M KOH
solution provided
Collect data about every 0.5 mL except near the endpoint where the pH changes rapidly. At that point change to
0.1ml increments. The increments can be approximate but
you must know what the increment is to within 0.005mL, or
whatever you can be read the burette to. You may have to let
the pH meter stabilize between readings.
Repeat the titration using 0.1 mL increments either side
of the first end point and about 0.2mL around the second
endpoint. You will need to plot your first data set to establish
what “around the endpoint” means.
Ask the instructor if they want you to repeat the
experiment with glutamic acid. In that case you make need
to run to pH 8, or do an intermediate titration with 0.2M or
0.5M acid. Discuss your observations in your report.
CALCULATIONS.
Do the following calculations for both the titrations.
1) Determine the end-point and hence the pKa‘s of both
the acids directly from a plot of pH vs. VNaOH.
2) Determine the pKa of both the acids from a plot of
dpH/dV vs. VNaOH. That is, setup Excel to do a simple
derivative using dy / dx » ( yi)1 - yi )/(xi)1 - xi ) . You may
have to drop the first few points of the amino acid titration.
Typical results are shown in figure 1.1 below.
3) Repeat the two plots of the titration curve using
CurveFit (if provided by the instructor) with the cubic spline
(with and without tension) and Akima spline. One method
works better than the other.
EXPERIMENT G:1
4) Fit the titration curve to a cubic (in the vicinity of each
pKa and get α and β in (1.1) and hence the pKa’s.
5) If you were asked to do a titration using conductivity,
repeat the process with the conductivity data using the
method of broken lines and the derivative method.
glycine. This lab. illustrates the complexity of such
apparently simple experiments. In fact, we will have to take
some short cuts and make use of literature values or we
wouldn’t have time to do it all.
THEORY. Here, we are interested in the enthalpy of
protonation ( DH proton of glycine, HGly) in aqueous
solution, that is
H+(aq) + HGly (aq) ] H2Gly+(aq)
Figure 1.1 Typical titration curve and the
differential. The weaker the acid (or base) the less
well defined the inflection point becomes.
5) Get the pKa using a Gran plot. That is, plot [H+]VNaOH
vs. VNaOH. The slope of the line is –Ka and the x-axis
intercept is the equivalence point. Compare those values
with those obtained by the other methods. You may want to
use the robust LSF to fit the data (CurveFit again). At the
very least, you may have to eliminate points from the plot
ends before fitting. Note you cannot use this plot over the
whole range: select data from around the end-points
QUESTIONS.
1) Compare your data to the literature values. Does the pKa
in the 0.3M NaCl differ from water or its literature value?
2) We often talk about sharp and fuzzy to describe slope
changes or breaks. The formal terms to describe lines are
smoothness, monotonicity and continuity. Briefly, describe
the correct descriptions for the terms and support with
some math. Be sure to distinguish between the informal and
formal definitions of smooth.
3) The conductivity data will go through a minimum.
Explain this and the general structure of the titration curve.
Part 2. SOLUTION THERMODYNAMICS
INTRODUCTION. As elegant as thermodynamics is
(everything follows from the first two laws) there is no way
of predicting enthalpies or entropies; they must be
measured. Some simplification occurs because we measure
state functions so data that are not directly measurable are
accessible via what I call the cycle method (just a variation
of Hess’s Law). In this experiment, we will measure the heat
of protonation of an amino acid (glycine) in aqueous
solution via its heat of solution and heat of reaction for solid
EXPERIMENT G:2
(2.1)
This is characterized by pK a2 for glycine. Note that this
reaction is not the dissociation of glycine (or the reverse),
that is given by
HGly (aq) ] H+(aq) + Gly-(aq)
(2.2)
and characterized by the pK a1 for glycine.
I have dropped the superscript “o” from the enthalpies for
convenience, they do, however, refer to standard conditions.
We can obtain DH proton from the temperature dependence
of the pKa . Here we will obtain it from calorimetric reaction
cycles:
Reaction 1.
(Gly)
DH
HGly(s) ) H+ (aq) ¾¾ dissoln
¾¾¾¾
® HGly(aq) ) H+ (aq)

DH rx1
H2Gly + (aq)
DH proton (HGly(aq))
This is the dissolution of glycine in hydrochloric acid and it’s
subsequent protonation. The protonation is not complete
and has to be accounted for. In the presence of excess acid,
there is no significant dissociation of glycine so this is
ignored.
Reaction 2.
DH
(Gly)
¾¾¾¾
® HGly(aq)
HGly(s) ¾¾ dissoln

DH soln
DHdissoc (HGly(aq))
Gly-(aq) ) H+
This is simply the dissolution of glycine and it’s subsequent
dissociation, normally referred to as the heat of solution. The
dissociation is not complete and has to be accounted for; see
later. The protonation of glycine is not significant under
these circumstances and can be ignored. Note the
distinction between enthalpy of solution (just adding
glycine to water) and enthalpy of dissolution.
Reaction 3.
NH2CH2COOH  + NH3CH2COOThat is, dissociation to the zwitterion. It turns out that
© P.S.Phillips October 31, 2011
glycine only exists as the zwitterion in solution. This is
discussed below.
By examining these schemes above you can see that to get
the enthalpy of protonation ( DH proton ) one needs the
enthalpy of dissolution ( DH dissoln ) and the enthalpy of
dissociation ( DH dissoc , see the appendix). The enthalpy of
dissolution can then be obtained from reaction cycle 2:
DH proton = DH rx1-DH soln+ DH dissoc
There are three problems, however: The first is that the
reaction (1) is done in a 0.3M HCl solution. This is strong
enough to influence the activities, and thus the reaction
enthalpy. This is overcome by doing the enthalpy of solution
(reaction (2.2)) in a solvent of the same ionic strength, in
this case, 0.3M KCl.
The second problem is quite insidious. Neutral glycine does
not exist in solution (at least only 1 in ¼ million) it exists as
the zwitterion. However, since it’s always in this form no
parameter relating to neutral glycine appears in the
equations, so it actually doesn’t matter. However, this is not
true of other amino acids where the zwitterion may not
dominate.
The third problem is that glycine is not a very acidic so it
does not completely dissociate in solution. We thus have to
adjust for the degree of dissociation. We can get K1 for
dissociation from the appendix. For n moles of glycine we
have the ‘ICE’ calculation
HGly(aq)]H+(aq) + Gly- (aq)
n
0
0
n-α
–α
-α
and
K1 =
[H+ ][Gly-]
[HGly]
made while a sample of glycine is dissolved in the acid. The
temperature is recorded continuously throughout the course
of the experiment. The heat change is determined by
comparison with a standard run (of adding TRIS to 0.1M
HCl). Since we will be using solid glycine, we have to do a
third run to establish the heat of solution of the glycine.
You will be dealing with changes in temperature of less than
a degree so you should be definitely trying to get better than
1% accuracy for the various individual measurements. A
temperature measurement to 0.01C may look impressive to
you, but it is not much good for this experiment. The
thermocouple is precise to 0.001C, if correctly used. You
will have to be very careful to get decent results.
CALORIMETER DISASSEMBLY/ASSEMBLY. The
apparatus contains some very fragile glass bits. Be careful
when handling them, you'll need a bank balance with five
significant figures to repair them. If the calorimeter is
assembled (see Figure 2.1), disassemble as follows: If the
glass push rod is raised, push it down gently to eject the
sample dish. Disengage the drive belt if on. Then gently lift
the whole assembly out of the calorimeter and place it in the
retort ring provided. NOTE: that the thermocouple is
plugged into the back of the calorimeter so don't expect to
be able to move the assembly very far without unplugging it
first. Hold the glass plunger rod and pull off the Teflon
sample cup while twisting it and then slide out the glass rod.
Inspect the sample cell and sample dish for dirt and water.
Carefully clean and dry if necessary. Now, carefully lift out
the Dewar flask and clean and dry if necessary. Reverse the
process (including cleaning and drying) to assemble the
apparatus. If the calorimeter is already disassembled,
familiarize yourself with each of the components and the
order in which they fit.
from which we get
K1 =
α2
(n − α )0.1
Equilibrium constants are for concentrations, not moles, so
the factor of 0.1 is to correct for the 100mL solution. Hence
we get the factor, 1/α, to multiply the enthalpy of
dissociation by to correct for incomplete dissociation (1/α
should be about 500).
BASIC PROCEDURE. The calorimeter is a Dewar flask
containing a rotating sample cell and a thermocouple (see
fig.1) attached to a data processing unit. A known amount of
acid (about 100g) will be measured into it, the stirrer will be
run continuously, and calorimetric measurements will be
© P.S.Phillips October 31, 2011
Figure 2.1. Schematic of solution calorimeter.
EXPERIMENT G:3
PROCEDURE IN CHRONOLOGICAL ORDER. set for a chart speed of 2cm/min, a sensitivity of 5V and the
This experiment goes faster if you coordinate your efforts so
read all the instructions first. You may want to do a dry run
first (no solutions or glycine); in particular make sure you
can assemble the sample cell.
First, turn on the calorimeter (switch is on rear left) to check
that it's OK. The calorimeter may give a message about rebooting the RAM disk. If it does, just press the <ENTER>
button, then <ENTER> again when it prompts for the date,
then again when it prompts for the time.
PART I. Heat of reaction.
1. One partner should accurately (4dp) weigh 1.00+0.05 of
dried glycine on an analytical balance into a stoppered
weighing vial. You may want to pre-weigh the sample on a
top-loading balance. The glycine has been ground and
dried (and is stored in a desiccator) so minimize exposure
to the air! Don't weigh out any big lumps; they won't fit in
the dish. Also, prepare the standard sample (see below).
2. Meanwhile, your partner should prepare (or otherwise
obtain) a 0.30M solution of hydrochloric acid. Then put
about 120mL of the HCl solution into a flask and warm it to
25.5 to 26C, but no more, by running it under the hot tap.
When done, weigh to 2dp. about 100g of the warm solution
into the Dewar and it back into the calorimeter.
3. Carefully pour the glycine sample into the Teflon sample
dish (don't spill any or get it into the center hole, if you do,
start that sample again. The sample will nearly fill the dish).
Place the sample dish on the bench and hold the sample cell
exactly vertically above it and gently press down on the stem
of the sample cell until the dish is seated in the bell (it
should not take much pressure to do this; do not force it).
Now slip in the glass push rod and press on it firmly so it
sticks in the sample dish hole.
4. Place the assembly carefully into the Dewar and attach
the stirrer belt (at the motor first). Now press
*122<ENTER> (with your finger tip NOT your finger nail),
you will be prompted for the DAC SPAN (DAC = digital to
analog converter), press 1<ENTER> (this means that a
1C change from the offset temperature, vide infra, will
produce an output of 10V). Next press *250<ENTER>
then 5<ENTER>, wait for about 30 seconds then press
*250<ENTER> again followed by 0<ENTER>. (This
recalibrates the thermocouple). Note that this calorimeter is
very sophisticated, but unforgiving, and pressing any other
combination of the buttons will produce all sorts of weird
results. For instance it will recalibrate itself in the middle of
your runs so don't do it. Now, take a few minutes to check
that the (beige) Linear chart recorder is ready. It should be
EXPERIMENT G:4
attenuator must be switched to calibrate (this means that an
input of 5V moves the pen 10in – the paper is cm on the xaxis and inches on the y-axis). Put in record mode and
lower the pen. Make sure it is plugged into the calorimeter,
and then zero the pen to the line about 2½cm (1in) to the
right of the left side of the recorder paper. (This is
opposite to the usual way of zeroing the recorder). Make sure
that the attenuation knob is clicked over to “calib.” Be sure to
record all the DAC and recorder settings.
5. Now, start the stirrer motor by pressing the F1 button.
From the front panel read the temperature, to one decimal
place (i.e. the nearest 0.1), do not round up, and then
subtract 0.4 from that value and then round down to the 0.1
degree. This is the offset temperature. Now press
*124<ENTER>, you will be prompted for the DAC offset,
enter the offset temperature (typically 24 or 25 for the first
run) and press <ENTER>. This should return the pen to
the left side of the chart paper (if it doesn't use the zero
knob to adjust it). THIS IS VERY IMPORTANT, get it right.
The offset temperature must be lower than the final
temperature; if it's not the DAC will saturate and the
recorder pen will bottom out.
If the DAC+offset is too small the line will be dead flat when
you start (also could be the recorders not on). You can fix
that by shifting the offset up. If the offset temperature is too
high the recorder will bottom out( line goes dead flat). You
then have to estimate what the DAC span should be and start
again. See part IV for further comments.
6. Re-zero the chart recorder, as described above, if
necessary. You are now ready to start a run. Flip the chart
speed from off to cm/min. Get the instructor to check the
drift is ok. After the chart has run for 5-8cm (about 3min,
or just before it goes off-scale) gently, but rapidly, press the
push-rod down until it hits the stop. Get your partner to
note the temperature at this point. The push rod releases the
sample into the solution so the temperature will drop and
this will be tracked by the chart recorder. Let the recorder
run for about another 15cm (about 5min) after which stop
the chart. If the temperature drops slowly (it normally takes
about a minute to bottom-out) check that the push-rod is
pushed down all the way to the stop. Record the final
temperature, this will give you a rough measure of ∆Tc so
you can check your scaling factors.
7. Stop the motor by pressing <SHIFT> then <F1>.
Remove the belt and slowly lift out the assembly part way
and allow it to drain and place the assembly in the retort
ring and dry. Check the Dewar for undissolved glycine.
© P.S.Phillips October 31, 2011
8. Get the instructor to check that the run is OK.
PART II. Heat of solution.
Proceed as above with the following modifications
1. Again, one partner should accurately weigh about 1.0g of
powdered, dried, glycine on an analytical balance into a
stoppered weighing vial.
2. Meanwhile, your partner should prepare 0.30M sodium
chloride if required. Put about 120mL of the saline into a
flask, and warm it to 25.5 to 26C and then accurately weigh
about 100g of the saline solution into the Dewar.
3. Proceed as described in steps 3-8 above.
PART III. Calibration. We determine the Cp of the
calorimeter by doing a reaction with a known ∆H, in this
case the reaction of TRIS with aqueous HCl. The procedure
is as above, but with the following modifications to the steps
1. Accurately weigh out, on an analytical balance, 0.5+0.01g
of TRIS.
2. Weigh out 100.00+0.05g of 0.100M HCl, warmed to 26C,
into the Dewar using a top-loading balance.
3. Pour the TRIS into the sample dish.
4. Assemble calorimeter. Start the stirrer and wait 3-5 min.
Reset the DAC SPAN to 1.
5. Reset the DAC offset as described previously, but calculate
and enter the offset, with one decimal place, as follows:
round the temperature to the nearest 0.1 and then subtract
0.4. Now zero the pen to the line about 2½cm to the left of
the right side of the recorder paper.
CALCULATIONS. The first step is to get the Cp of the
calorimeter from the calibration run. The enthalpy of
reaction for TRIS with HCl, in joules, is given by
-m.(245.76 + 1.436(25-T0.63R))
where m is the weight of TRIS and
∆Tc = Tf - Ti
T0.63R = Ti + 0.63.∆ Tc
where the subscripts i and f are used to denote the initial
and final temperature in C. For Ti simply use the value
when the plunger was pressed, this will be slightly
erroneous, but it is only used to make a small correction.
∆Tc can be obtained directly from the graph. To do that
draw the best straight lines through the tails of the plot,
extrapolate them so they extend past the vertical portion of
the plot. Now choose a point about two thirds down the
vertical part of the plot and draw a perfectly vertical line
through this point so that it intercepts the two extrapolated
lines from the tails. (See figure 2.2, but note that it's for an
© P.S.Phillips October 31, 2011
endothermic reaction so it’s upside down for the exothermic
TRIS+HCl reaction.
The 2/3rd point is half the time is takes to get within 5% of
the baseline). The temperature change is then just the length
of the vertical line (in inches) times the appropriate scaling
factors, which depend on the DAC SPAN and recorder
sensitivity setting. To get Cp of the empty calorimeter, divide
the enthalpy of reaction by ∆Tc and then subtract off the
heat capacity of the HCl solution (specific heat for 0.1M HCl
is 4.1796J/g/K).
Figure 2.2. Finding ∆Tc The 0.190 is the drift up
from the start (baseline) and the point where Ti is
taken, which is used to estimate T0.63R
Getting the other two enthalpies is straight forward, but
remember, the solution weighs about 102g (saline or acid +
glycine). Assume that the specific heat of the solution is the
same as 0.1M HCl so
∆Hsoln = -Cp(Tf - Ti)
and
Cp = Cp (calorimeter) + Cp (solution)
The enthalpies are given by these formula, but there is one
subtle problem. In order to get the signs right you must
recall that you are measuring the temperature of the
surroundings and ∆Hsurrounding = -∆Hsystem. That’s’ where
the –ve sign comes from in the above equation. Remember
to correct the saline run for contributions from reaction (2)
(see the theory section and Appendix II) and correct the
acid run for incomplete dissociation.
QUESTIONS.
1) Compare the heat of solution and reaction from your data
with literature values (preferably at the same ionic strength).
2) What is a zwitterion and what significance does this have
for glycine? What if the zwitterions did not dominate, it was
say only 50%, how would that effect the analysis of the data.
4) There are a number of assumptions and approximations
made throughout the experiment. Can you identify them?
EXPERIMENT G:5
Part 3. BOMB CALORIMETRY.
INTRODUCTION. If you have ∆Hcomb of a compound
then by using ∆Hf(CO2) and ∆Hf(H2O) you can get the ∆Hf
of that compound. Since most organic compounds burn,
bomb calorimetry gives access to the ∆Hf of a huge number
of compounds. However, there are four problems a)
Sometimes it is difficult to get the compound to burn. It may
be difficult to form a pellet and high carbon compounds
tend to ablate or burn with a lot of soot. b) You are
measuring large numbers, which are ultimately subtracted
from other (similar) large numbers. That means you must
collect data to at least four sig. figs. no trivial feat for a
relatively complex experiment. c) Organic compounds may
or may not burn completely. d) nitrogen in the compound
or in the air can burn. Only a little bit, but it is highly
endothermic. This has to be compensated for. e)
Thermometers that we use are not perfect; they need to be
calibrated. We will not worry about that here, but you should
note the problem.
We will do it for glycine for the sake of continuity, although
we won’t actually use the value for our calculations. You have
done this experiment once or twice, but you should note the
following modifications:
i) You will make more extensive use of a computer to
analyze the results.
ii) You will do a complete error analysis.
iii) You will do duplicate runs of the sample.
iv) You will need to flush the bomb with pure oxygen
(as opposed to just filling it).
v) We will adjust for the combustion of nitrogen.
during the combustion. Hence, a strong steel bomb must be
used as a reaction vessel, and the experimental instructions
contain a large number of precautions and details which
must be carefully followed. It is important NOT to use more
than the recommended amounts of solid reactant. (A set of
instructions for bomb calorimetry, at another institution,
once contained the quantity ".5g of sugar". This was badly
copied and looked like "5g sugar". When the calorimeter was
loaded with 5g, and ignited, its lid went through the ceiling,
and a student, who is now a faculty member at UBCV,
narrowly escaped having his career terminated at that point.
Two morals to the story: a) do not exceed stated quantities;
b) people who make a fuss about putting a zero before the
decimal point aren't fooling; always write 0.5, not just .5).
APPARATUS. The Parr bomb calorimeter consists of an
oxygen bomb immersed in water contained in a bucket,
which is isolated from the surroundings by a fiberglass
jacket. The jacket lid is fitted with a calorimeter
thermometer and stirrer both of which extend into the
water. As the experiment is to determine the temperature
increase of the system under adiabatic conditions, some
calorimeters encase the bucket and bomb in a double walled
jacket containing water, the temperature of which can be
adjusted to that of the water surrounding the bomb.
However, it is easier in practice to use the system shown in
fig.3.1 in which an insulating jacket minimizes heat
THEORY. Energy changes, not enthalpy changes, are
measured directly in this experiment. This is because the
bomb calorimeter operates under constant volume
conditions, not the constant pressure conditions that most
experiments are done at. For this experiment we must
replace
∆H = Cp ∆T
with
∆E = Cv ∆T
(3.1)
The experiment to be performed consists of a calibration to
find the heat capacity at constant volume, Cv, of the
apparatus, followed by determination of the heat of
combustion of an unknown. Cv is not found by an absolute
method, but by a relative method in which a substance of
known heat of combustion is burnt in the calorimeter to
determine Cv.
Determination of the heat of combustion of a substance in
oxygen requires, in practice, a high starting pressure of
oxygen; an even higher pressure is generated transiently
EXPERIMENT G:6
Figure 3.1. The assembled bomb calorimeter.
exchange with the surroundings. The results are then
corrected for any deviation from the adiabatic condition
using a graphical method.
© P.S.Phillips October 31, 2011
PROCEDURE. NOTE! Before performing this experiment, place the wire in the furrow). Note also that there must be
become familiar with the use of the apparatus and the
procedure. Failure to do so could cause an accident resulting
in serious injury. Mount the bomb (see Fig. 3.2) in the bench
clamp and secure it with the Allen key provided.
Make sure there is no internal pressure by unscrewing the
release valve 3 or 4 turns, then remove the large screw cap
(removable bomb head). The inner bomb head is removed
by carefully working it back and forth to free the O-ring
seal. Do not apply force to the release valve as this can be
damaged. When the head is loose, lift it so that the attached
electrodes clear the bomb and place it into the bomb head
support stand (this is the smaller of two stands provided).
Check that the bomb is clean and dry and that the electrodes
are free of any residual fuse wire.
Figure 3.2. The Parr oxygen bomb.
Take a stainless steel combustion cup (clean if necessary)
and accurately weigh into it, a commercially pressed pellet
of benzoic acid (~ 1.0-1.2g. Do not touch the pellet with
your greasy paws, fat is highly caloric). If the sample weighs
more than 1.2g, use a spatula to scrape off the excess. Place
the cup into the looped electrode and tilt it slightly to one
side so that the flame will not impinge directly onto the
straight electrode. Make sure the cup is firmly seated though
so it can't shift while moving the bomb around. Use the
forceps and scissors to cut a 10.0cm length of iron fuse wire,
which is attached between the electrodes as shown in the
figure 3.
You may need help in your first attempt at this. The wire
must be bent down as far as possible so that it touches the
surface of the pellet and stays there. (If this is a problem you
may need to scrape a furrow in the pellet, reweigh it and
© P.S.Phillips October 31, 2011
no short circuit to the metal capsule.
Figure 3.3. Steps in attaching fuse wire to the electrodes
Now replace the head onto the oxygen bomb and push it
firmly into it's seat (remember the o-ring with the metal
washer on top). Do this very carefully so as not to jar the
pellet from under the fuse wire. Screw down the knurled cap
hand tight then shut off the release valve finger tight. Firmly
press the fitting of the hose from the oxygen tank into the
inlet valve on the bomb head. Once the metal shoulder of the
hose fitting contacts the valve socket, screw down the
knurled union nut. Twist the head to check that it cannot
rotate in the main body.
BEFORE PROCEEDING ANY FURTHER,
GET THE INSTRUCTOR TO COME AND WATCH!
This is a serious safety instruction, do not insert any
commas in it as some clown did one year. Check that both
the release valve and control valve of the oxygen pressure
gauge are closed. Now check that the bomb’s vent valve is
open and then open the oxygen tank valve and very slowly
let oxygen. Feel for oxygen coming from the vent and let the
bomb flush for 10min. Put your hand on the control valve
and close the bomb vent valve. Watch the gauge. It should
indicate a gradual flow of oxygen into the bomb - a pressure
increase of about 10 atmospheres per minute is about right.
If oxygen is introduced too rapidly, the sample could be
blown around inside the bomb.
UNDER NO CIRCUMSTANCES REMOVE YOUR HAND
FROM THE CONTROL VALVE UNTIL IT IS SHUT OFF.
The bomb can easily be over filled. Shut off the valve at 31
atmospheres and then wait as the pressure stabilizes out;
probably at about 30 atmospheres. After the control valve is
finally closed release the oxygen from the hose with the
release valve (an automatic valve will prevent the oxygen
flowing out of the bomb). Remove the hose from the bomb.
Place the chromium plated elliptical bucket into the
EXPERIMENT G:7
fiberglass jacket such that the three indentations in the
bucket register with the locating feet in the jacket. Fit the
wire bomb lifter into the holes in the knurled bomb screw
cap, loosen the bench clamp, then raise the bomb by a finger
inserted through the hole in the lifter. Do not hold the
outside of the lifter - this would cause it to open thus
releasing the bomb. Place the bomb onto the indentation in
the bottom of the bucket then remove the lifter. Ensure that
the ignition power supply is not plugged into the wall outlet
then plug the igniter leads into the electrode terminals on
the bomb. Attach the leads across the "10 cm fuse" terminals
on the power supply. Fill to the mark a 2000mL volumetric
flask with water using both hot and cold water taps to bring
the final temperature to between 25.5C and 25.8C. Use a
regular thermometer for this and not the calorimeter
thermometer. Transfer this quantitatively to the bucket and
check that the temperature is (25+0.5)C. Check also that
no oxygen leaking from the bomb. If there is, do not
proceed with the experiment - get help. Read carefully, so
as not to damage the calorimeter thermometer (which costs
a small fortune), lift the jacket lid from the large stand onto
the jacket so that the stirrer pulley is oriented near the
motor mounted on the jacket, then fit the drive belt between
the stirrer and the motor and plug in the motor.
Start the stirrer and wait 5 or 10 minutes to allow the
apparatus to thermally stabilize, then start a timer and take
temperature readings every 20 seconds. Although the
thermometer is calibrated in 0.02C divisions, you should be
able to estimate temperatures to about +0.003C with the
help of the thermometer magnifier. Record the temperature
until it has changed at a uniform rate (probably about 0.010.02C every 100 seconds) for 5 or 6 readings.
The Parr instruction manual gives the following warning:
"CAUTION: DO NOT HAVE THE HEAD, HANDS OR
ANY PART OF THE BODY DIRECTLY OVER THE
BOMB DURING THE FIRING PERIOD, AND DO NOT
GO NEAR THE BOMB FOR AT LEAST 20 SECONDS
AFTER FIRING."
Plug in the power supply then, noting the time, stand back
and push the firing button for 5 seconds. The red light
should normally flash on for about ¼ second. Take
approximate readings every 20 seconds as the temperature
rises then, after equilibrium is again reached, take a further
10 readings at 10 second intervals.
Unplug the power supply from the outlet and remove the
ignition leads from the supply. Unplug the motor, remove the
drive belt, then carefully remove the jacket lid and place it
onto the special stand. Unplug the leads from the bomb and
EXPERIMENT G:8
use the lifter to put the bomb into the bench clamp. Use an
aspirator to remove water from the top of the bomb then
carefully unscrew the release valve thus allowing the bomb
to slowly depressurize. Ensure that all pressure is released by
unscrewing the valve at least 5 turns then remove the screw
cap and bomb head, placing the latter in the special stand.
Check that the sample is completely combusted then
carefully remove, straighten and measure the length of the
remaining ends of the fuse wire. Do not weigh any globules
of oxidized iron. Meanwhile your partner should carefully
rinse out the bomb with some deionised water (see the
section on the nitrogen correction to find out how much, but
20mL is probably a good start) and put in a volumetric flask
ready for titration.
Dry the inside of the bomb then repeat the above procedure
with about 1.0g of glycine. Finely grind the sample and
press it into a pellet as described below. Show that pellet
to the instructor.
The pellet of material is prepared with the IR press. If
necessary, the components of the press can be cleaned with
a small amount of water and then methanol.
Pour the roughly weighed ground sample into the die cavity
(beveled edge up) then put the die into the holder and tamp
the sample down with the plunger (beveled side up). Place
the assembly into the IR press and compress the sample to
about 150kbar (2000psi). Release the press then remove and
invert the die holder. and remove the pellet out by gently
tapping the plunger. Immediately clean all the press parts
with water. Then accurately weigh the pellet and combust it
as before.
Repeat the run.
Finally, clean and dry the bomb before putting it away.
NITROGEN CORRECTION. When the glycine is burnt
some the nitrogen in it (and the air) is converted to nitrogen
dioxide. This reaction is quite endothermic and must be
accounted for to get an accurate value for the heat of
combustion. The nitrogen dioxide dissolves in the water
formed to create nitric acid. You can rinse this acid out of
the bomb and titrate with NaOH to get the actual amount of
NO2 produced Using the maximum value of nitric acid that
could be produced from the pellet to calculate how much
solution you need to make up in order to get an accurate
titration with 0.1M NaOH. (Also, you might want to do some
calculations to see if that amount of NO2 will actually
dissolve in the amount of water produced. If it’s too much
you may need to consider putting some NaOH solution in
the bomb to absorb the NO2 then back-titrating to find how
© P.S.Phillips October 31, 2011
much there was.)
CALCULATIONS. These are straightforward. The
thermal capacity heat of the calorimeter is determined from
the ∆E for benzoic acid (corrected for the burnt wire), the
pellet mass and the temperature rise. The same calculation
is then applied to the sample to determine its ∆E. The main
problem is rather subtle: In order to get the signs right you
must correctly identify the system and the surroundings and
note that
DEsurrounding = -DEsystem
In this case the system is the pellet + O2. The surroundings
are the bomb, water and container. The whole thing is
(approximately) an isolated system.
In detail: First obtain the corrected temperature for each
temperature reading using the correction curve supplied for
the thermometer (if one is supplied, otherwise use the
readings directly). For reach run, plot the corrected
temperature vs. time using an expanded, interrupted (a.k.a.
broken) temperature scale. This cannot be done directly
with Excel – use graph paper. Actually there is a way of
faking it using the 2nd y-axis option of Excel –try it if you
are adventurous.. You can also do these plots using Origin (a
demo is available from the WEB, or a full version is in the
lab.). Given the trouble they are, why do we use a broken
scale graphs?
Figure 3.5. An example of a broken scale graph. Note
the break in the scale.
Determine an approximate temperature change and the
26.4
26.2
Temperature (C)
The total energy ∆Et produced in a run is the sum of ∆Es
due to the combustion of the sample and ∆Eiron due to the
combustion of the ignition wire. That is:
∆Et = ∆Es + ∆Eiron = C.∆T
(3.2)
where C(S) is the heat capacity of the system. ∆E for the
standard (benzoic acid) and ∆Eiron are known:
∆Ebenzoic acid = -6316 cal/g
∆Eiron = -1600 cal/g
From the weight of the benzoic acid sample used and the
weight of the iron wire consumed, determine ∆Ebenzoic acid
and ∆Eiron and thus ∆Et for each run of benzoic acid
combustion. From the equation above, determine the heat
capacity of the system for each run and the average C(S). For
the run of the 'unknown' sample, determine the
experimental ∆E using the heat capacity value (of the
system) and the observed ∆T value. Calculate ∆Eiron from
the weight of the consumed iron wire. From these two
values, calculate ∆Es for the sample and estimate ∆Es per
gram and ∆Es per mole. Thus, what is actually determined is
heat of combustion under a constant volume. The
corresponding (molar) enthalpy change is given by:
∆H = ∆ E + ∆(PV)
(3.3)
If one assumes a perfect gas law, PV = nRT (the assumption
is reasonable in this case), one obtains for ∆H:
∆H= ∆E + ∆(nRT) = ∆E + RT∆ngas
(3.4)
where ∆ngas is the increase in the number of moles of gas in
the system (assume all the water produced is as liquid).
From the chemical equation of the combustion reaction,
determine ∆ngas (per mole of the sample) and then calculate
∆H for the reaction.
26.3
26.1
26.0
ERROR ANALYSIS. A full error analysis will drive you
23.8
23.7
23.6
23.5
the errors on the fit. Using the time for the vertical line and
the two linear equations, you can get the temperature
difference and the error.
-2
0
2
4
6
8
10
12
14
16
18
Time (s)
time at which the temperature was at 60% of the net change.
(the vertical line in figure 3.5). Do an Excel fit to the preand post run temperatures. Only use the linear part of the
post-run (about 11sec onward in figure 3.5 – the fit shown
is not quite correct). Make sure you do a full Excel fit to get
© P.S.Phillips October 31, 2011
squirrelly so proceed as follows:
a) Identify the errors an all quantitative measures and
estimate their size and whether they are systematic or
random.
b) Errors in ∆T can be estimated as indicated earlier. All
others can be made using the tables in the error analysis
section. Identify all other error sources and estimate their
rough size (in this case they will be small or negligible) and
whether they are systematic or random.
c) Identify the largest error and propagate that. Be sure to
pay attention to subtractions.
EXPERIMENT G:9
d) Remember that large errors on small correction are not
usually a cause for concern.
Compare the error you calculate above with the crude
estimate of error from subtracting the values from the
duplicate runs.
APPENDIX I: Weak Acid–Strong Base Titration.
Consider the aqueous titration of a weak acid, HA, with a
strong base MOH to from the salt MA. The reactions and
equilibrium constants are
Ka
HA]H+ + A −
Kb
MOH]M + + OH−
K sp
MA]M + + A −
Kw
H2O]H+ + OH−
(1.1)
(1.2)
(1.3)
(1.4)
Using the condition of electroneutrality we also have
[M+] + [H+] = [A-] + [OH-]
(1.5)
Since MOH is a strong base Kb > 1 so we can neglect
[MOH], i.e. MOH is completely ionized. Similarly, we
assume that MA is completely ionized so that [MA] is
negligible.
Let a be the ‘initial number of moles of non-ionized HA’
divided by ‘total volume’ and b be the concentration of the
base that has been added at any time, i.e. ‘number of moles
of base added’ divided by ‘total volume’. Note the necessity
of defining a and b in number of moles, rather than
concentration, as the total volume is changing all the time.
To get [H+] we use the equilibrium expression for (1.1)
[H+ ][A + ]
Ka =
[HA]
(1.6)
K [HA]
[H+ ] = a −
[A ]
(1.7)
then
Strictly, we should define these equations in terms of
activities, especially since pH meters, like all ion-selective
electrodes, do measure activity, not concentration. We shall
use concentrations for typographic convenience. To convert
to activities all concentrations derived from the equilibrium
expressions should be preceded by an appropriate activity
coefficient. Concentrations in the mass balance equations
are unchanged.
Since the conjugate base, A-, comes from the acid only then
EXPERIMENT G:10
[HA] = a- [A-]
(1.8)
Similarly, since, M+ only comes from the base
[M+] = b
(1.9)
Hence from (1.5), (1.8) and (1.9) and rearranging we can
get [HA] for (1.7)
[HA] = a – b + [OH-] - [H+]
(1.10)
Using (1.10) and (1.8) in (1.7) we get
K (a − b + [OH− ] − [H+ ])
[H+ ] = a
b + [H+ ] − [OH− ]
(1.11)
Assuming the activity of the water in our system is 1, then
we can get [OH] from the equilibrium expression for (1.4)
so that (1.11) becomes
K (a − b + K w /[H+ ] − [H+ ])
(1.12)
[H+ ] = a
b + [H+ ] − K w /[H+ ]
eliminating [H+] from the top and bottom of (1.12) and
rearranging we get
[H+]3 +(b+Ka)[H+]2 –
(Kw+Ka(a-b))[H+]-KaKw = 0 (1.13)
which is a cubic, which can be readily solved to give the pH
at any given point in the titration. To rearrange (1.13) into
the form, (1), in the introduction we need to do some house
keeping. If we let Vao be the volume of the weak acid
solution of initial concentration cao and Vb be the volume of
strong base (titrant) added, (concentration cbo ), then
a = caoVao /(Vao + Vb ) and b = cboVb /(Vao + Vb )
It is convenient to redefine a and b in terms of r and f as
defined in the introduction and hence to get equation (1.1).
APPENDIX II. The whole experiment is done at an ionic
strength of 0.3M. Standard values use pure materials so any
values you do find in the literature will differ slightly from
your experimental values. However, some data is available:
The pKa’s of glycine at 0.3M ionic strength are given by
pK1=-46.7920+2378.22/T+ 16.64log10T
pK2=-16.1083+3165.76/T+ 6.09log10T
You can then use these values with the Van’t Hoff equation (a
form of the Gibbs-Helmholtz equation) to get your
literature value for the heat of dissociation for glycine. I’ll
leave it to you to work out whether the T’s are celsius or
Kelvin.
Use the formula for pK1 to get the heat of dissociation for
© P.S.Phillips October 31, 2011
reaction (2) and subtract it from the observed heat of
solution to get the true heat of solution of glycine.
Also, use the formula for pK2 to get the heat of dissociation
for reaction (1), the dissociation of the conjugate base
(which is the reverse of what you want). This can be
compared with your experimental value.
© P.S.Phillips October 31, 2011
EXPERIMENT G:11
EXPERIMENT G:12
© P.S.Phillips October 31, 2011
Suite H.
INTRODUCTION. The hydrophobic effect accounts for
the behavior of non-ionic species in water. Polar species
dissolve in water because they can hydrogen bond to water
(enthalpically favorable) and then dispersal (entropically
favorable). This is balanced against the breaking of water’s
hydrogen bonds (enthalpically unfavorable), the break up of
the lattice of the polar compound (if solid) and the loss of
entropy caused by the binding of water to solute (solvation).
For small polar molecules ∆G is favorable, but for larger
molecules, where the fraction of polar functional groups is
often small, the molecules are not so soluble. If the fraction
of polar groups is high (e.g. sugars and some proteins) the
molecule will usually be soluble. From these observations,
one may deduce that the hydrocarbon chains are responsible
for the lack of solubility: they do not hydrogen bond and the
entropy of mixing is insufficient to overcome the disruption
of hydrogen bonding. In fact, this is not true. Although
hydrocarbons do not H-bond, the van der Waals forces are
quite large and they should be moderately soluble. This is
where the hydrophobic effect comes in.
Water cannot H-bond to hydrocarbons (note that it just
cannot bond, it is not repelled ), but it can with itself. To
make sure there are no dangling (i.e. unused) H-bonds,
which is energetically unfavorable, the water molecules have
to take on a geometry (on average) to minimize this. It’s a
little difficult to envision, but basically the normal and Hbonds (which are interchangeable in water) organize
themselves so that they
form a hollow polygon
(see the figure). The
hydrocarbon is located
in the cavity. This shell
is labile, but under high
pressures, clathrates can
form. The best known is
methane clathrate, a
white crystalline solid
found on the bottom of the deep ocean. It has the amusing
property of being flammable. The net effect of
hydrophobicity is that water becomes highly structured in
the vicinity of non-polar molecules so ∆S becomes
negative, and since ∆H is small in the absence of polar
groups, ∆G becomes negative and non-polar species do not
dissolve.
HYDROPHOBICITY
have hydrophilic (polar) and hydrophobic (non-polar)
regions. They must fold in such a way that the hydrophilic
sections are inside and the polar sections are on the outside.
It is possible to change the nature of hydrogen bonding in
water thereby reducing the hydrophobic effect allowing the
protein to unfold (denature).
We will do two experiments here. One where we study we
study the solubility of n-butanol and n-pentanol in water
as a function of temperature. And the second the where we
study the solubility of toluene (a generic non-polar species)
in water in the presence of species that change H-bonding
in water (co-solvents).
Part 1. FREE ENERGY OF TRANSFER.
THEORY. For a two phase system, (here we have water and
alcohol) the chemical potential of any give species must be
the same if the two phases are in equilibrium (see the
appendix for details). That is
mAphase 1 = mAphase 2
but (see appendix)
m A » moA + RT ln X A
for any species in solution.
If we consider the transfer (partitioning) of a hydrocarbon,
HC, into water, W, then
X
o
o
mHC
- mW
=-RT ln HC
XW
or, if the hydrocarbon is only slightly soluble (but that’s not
the case here) then
o
DGtransfer
=-RT ln X HC as X W  X HC
(1)
∆Gtransfer is maximum when the solution is saturated so all
we need do is determine the saturation point (and its
concentration) as a function of temperature and we can get
∆So, ∆Ho and ∆Go for the process.
o
DGtransfer
=-RT ln
X HC (sat .)
XW (sat .)
(2)
and
¶DG o ö÷÷
¶DG o /T ö÷÷
o
o
S
and
=
D
÷
÷ = DHtransfer (3)
transfer
¶T ÷÷ø
¶(1/T ) ÷÷ø
P
P
This has a major impact on the structure of proteins which
© P.S.Phillips October 31, 2011
EXPERIMENT H:1
PROCEDURE. RTFM! Rather than titrate in alcohol to
needed to locate the solution to the desired accuracy. The
method is very robust, if there is a solution, this method
will find it with an absolute error of, at most |b-a|/2n after n
steps. However, if there is more than one solution, it will
only find one of them without more information.
The usual way to proceed is to prepare a series of mixtures
solutions in the supplied tubes, say, as follows (label them!) :
0.30 to 11.10g of butanol in 0.40g steps in 10.00g of e-pure
water. 0.40-4.00g of n-pentanol in 0.20g steps again in
10.00g of e-pure water. As usual, the amount doesn’t have to
be exact, just accurately know. (This is roughly equivalent to
doing a titration in 0.2mL steps.) Shake the tubes
thoroughly and put them in the rack in the shaker or other
bath as directed bath. We then repeat the process with npentanol as described below.
Note that are not many restrictions on the nature of a, b and
x. a and b just need to be distinguishable (e.g. by a sign
change). Nor do they need to be continuous, a sorted list will
suffice, in which case it’s called a binary search. This method
one of many similar search algorithms. In this case it’s a
variant of the divide and conquer algorithm. Interested
students can look at Wikipedia, NIST or the Wolfram site, all
of which have fairly accessible material.
In our case a and b are the concentrations of our bracketing
samples, our “equation solution” is the opalescence
concentration and the bracketing test is “one phase” or “two
phase”. Ideally we want “”cloudy” (the cloud point). In
practice it will be cloudy with signs of two phases. We know
what the 0% and 100% samples look like so firstly, you
would normally make up a roughly 10% and 90% solution
and shake the sample. This defines the direction of the
search (the sign change): if the 90% solution separates then
the search direction is low to high, if the 10% solution
separates the direction is reversed. Weighing on a taring
balance is efficient and avoids problems with volume
changes due to non-ideality. We can then convert weight %
to mol% (or molality).
saturation (which takes too long because of the equilibrium
times required) we will prepare a series of samples and
observe which ones are cloudy (saturated and two phases)
and which ones are clear (unsaturated and one phase).
Start at 25C and work your way up to 65C in 5C
increments. Also, make up an ice-water bath for a 0C
point. Ask the prof. about temperatures between 0 and 25 C.
Wait at least 15min at each temperature for equilibrium to
be achieved. Be sure to vigorously shake the sample a few
times. Using the ultrasonic cleaner helps as well. To find the
saturation point, look for a pair of adjacent (in mole
fraction) tubes where one is cloudy and one is clear. If the
cloudy tube is only faintly so (and little other evidence of a
second phase), then take that is the saturation point. If it’s
fairly cloudy then average the mole fraction for the two
tubes. This means your maximum error in X is half the
increment.
Aggghhh! He’s torturing us; death by a million samples.
No… I just outlined it because it makes things a little
clearer. We are going to use a really neat trick to find the
cloud point, which goes as follows: the method above is
called a linear search and unfortunately requires the
preparation of many samples and limits the accuracy to
about 3% for 19 samples, i.e. 5% composition intervals. The
search time is of order of the number of samples,
O(#samples). However, it is possible to get and accuracy of
<1% with nine or less samples in a similar time. This is
achieved by use the semi-numerical method of a bisection
search - search time is O(log #samples).
Bisection is the division of a given curve, figure, or interval
into halves. A simple bisection procedure for iteratively
converging on a solution which is known to lie inside some
interval [a,b] proceeds by evaluating the function in
question at the midpoint of the original interval i.e. at
m=(a+b)/2 and testing to see in which of the subintervals
[a, m] and [m,b] solution lies. The procedure is then
repeated with the appropriate subinterval as often as
EXPERIMENT H:2
This is a really elegant approach to the problem, but there is
one difficulty – what if there is more than one cloud point!
Clearly that can occur, we can have a dilute solution of
alcohol in water or a dilute solution of water in alcohol.
However, we are interested in studying the hydrophobic,
interaction. That is, how the alcohol disrupts the water, so we
are only interested in solutions with small mole% of alcohol.
It’s interesting to consider how many cloud points one might
observe with a two component system at constant pressure.
For example prepare a 10% and 50% sample, equilibrate it at
the desired temperature for 15 min then check it. Shake it in
an ultrasonic bath to ensure complete dissolution. If the 50%
sample is a two phase and the 10% solution one phase then
you know the opalescence point lies between 50% and 10%.
You then bisect the concentrations; make up a
[(50+10)/2]% = 30% solution and equilibrate. If that’s clear
then you bisect again to between[ (50+30)/2]% = 40% and
so on to an interval of 1% or less. If the 50% and the 10% are
both two phase then the cloud point is between 0 and 10%
and you bisect accordingly. Record the flanking
concentrations, with a note of the degree of separation in the
© P.S.Phillips October 31, 2011
cloudy one, and take the average. If a sample is only faintly
cloudy (two phases not immediately obvious), you can take
that as the transition point.
Note that the bisection intervals need not be exact as long as
there are no gaps in the search. You should keep each
sample, as they may be reusable at another temperature.
The whole process requires only seven samples or less to
reach a 1% absolute accuracy as opposed to 3% accuracy
mentioned for the linear search method.
As initially described, you still need to vary the temperature.
Make up a beaker with ice and water in it. That’s your 0 C
bath. Start the heated bath at 25C and work your way up to
about 70C in 7C increments. Wait at least 15 min for each
sample to equilibrate (to save time you could make up the
next two bracketing samples needed, then only use the one
you need). Shake the tubes vigorously and regularly. Watch
for pressure build up in the tubes at the higher
temperatures. Crack the tops open to release the pressure
occasionally. For the samples close to the cloud point
sonicate them for five minutes then return them to the bath.
Do pentanol/water and butanol/water systems in parallel.
We will cheat a bit to save time. Your initial solutions should
1 and 15 mol alcohol. Bisect from there
CALCULATIONS.
1) Calculate ∆So, ∆Ho and ∆Go for transfer, and their errors,
using equations (2) and (3).
2) The two alcohols differ by one methylene group. Calculate
the hydrophobicity increment (∆G difference) for
hydrocarbon chains. See if butanol and pentanol are 4 and 5
times this value, respectively.
3) Compare your data with the literature values and
comment.
QUESTIONS.
1) There are many reasons to store solutions of biomolecules
in the cold. Is hydrophobicity one of them?
2) We could use ∆Go= ∆Ho-T∆So to get, why didn’t we ?
(Hint look at the error).
3) At this point, you know what the search direction is. Make
some arguments to show that you could predict it for similar
solvents.
4) Can you think of other measures one could use for the
composition?
Part 2. THE EFFECT OF CO-SOLVENTS
INTRODUCTION. Here we look at the transfer of
toluene (our model for the hydrophobic core of a protein)
into aqueous solutions of “co-solvent” by UV spectroscopy.
© P.S.Phillips October 31, 2011
We will use two protein co-solvents; guanidine chloride –
which denatures (increase solubility of) proteins, and
sodium chloride which crystallizes (decreases solubility of)
proteins.
A co-solvent will denature a protein if it decreases the
hydrophobic effect, thus allowing the hydrophobic core of
the protein to be exposed with a reduced entropy penalty. On
the other hand, if we use sodium chloride the hydrophobic
effect is increased so solubility will be decreased and the
protein will precipitate out.
The exact mechanism by which hydrophobicity is changed
is unclear, but we just wish to demonstrate the effect.
THEORY. As before, except we want the change in
chemical potential (for saturated solutions) of toluene, A,
into pure water, W, vs. toluene into co-solvent, S.
mA,W = mAo ,W + RT ln X A,W
mA,S = mAo ,S + RT ln X A,S .
X
o
DGtransfer
= mA,W - mA,S =-RT ln A,W
X A,S
It’s more convenient to use the concentration scale here.
Since toluene is only slightly soluble and it’s a constant
volume system, we get
c
o
DGtransfer
=-RT ln A,W
c A,S
We can get the concentration, cS, of toluene in the aqueous
phase from the p ® p * transition of toluene at 268nm. cS, is
just the concentration or pure water. So we get
A
o
DGtransfer
=-RT ln W
AS
where AW is the absorbance in pure water and AS that in the
co-solvent.
PROCEDURE. This experiment should be done
concurrently with part 2 or 3. Make up saturated solutions of
toluene (just shake one mL with the solution) in 0-6M
guanidine chloride and in 0-5M NaCl, both in 1M
increments. Equilibrate the solutions at 25C for at least an
hour. Shake the solutions every 15min (or use the shaker
bath). Zapping it with the ultrasonic cleaner a few times
may help, but don’t overdo it or you’ll disperse some of the
toluene into the aqueous phase. Record the UV spectrum of
the aqueous phase from 260-280nm. Use matched quartz
EXPERIMENT H:3
cells with toluene free solutions as the blank.
If the absorbance exceeds one dilute you smaple by
(exactly) a factor of five and go from there.
o
for each concentration and plot it vs.
DGtransfer
concentration.
pharmacy and biochemistry it’s important to know how a
drug or bioactive species distributes itself between the cell
membranes or fat (both non-polar) and water (90% of
most mammals).
Here we will explore the partition coefficient of a simple
species, an acid-base indicator, between water (the most
important polar solvent) and octanol (the canonical nonpolar species – although in food science olive oil is usually
used). We will also examine the effect of pH on the partition
coefficient.
QUESTIONS. Suppose each sodium ion has a solvation
THEORY. The partition coefficient for a solute X, is
You may have trouble making 5M NaCl, in which case
use a saturated solution for the last point (you’ll need to look
up the solubility).
CALCULATIONS. Using the absorbance data, calculate
shell of six waters – we will call this “bound “water. How
much “free” water is there in a 5M NaCl solution (ignore the
chloride ion)? Now consider a 1mM solution of a model
protein of molar mass 100kDa (say poly glycine). Would
there be enough water to hydrogen bond this molecule
completely (assume 2 H-bonding sites per base). Is it
possible that we the effect is not due to hydrophobicity
changes, but a loss of H-bonding?
Part 3. PARTITIONING
INTRODUCTION. In the last two sections we looked at
the mutual solubility of two liquids. Here we will look at how
a solute distributes between two immiscible solvents, and
the effect of pH.
You’ve all heard the expression “oil and water” don’t mix.
To be more specific, oil and water are immiscible and form a
two phase system. The reason for this is the hydrophobic
effect, discussed above.
You’ve also heard the phrase “like dissolves like”. Again,
to be more specific, polar materials dissolve in polar solvents
and non-polar materials dissolve in non-polar solvents.
There are of course many exceptions, acetone dissolves
freely in hexane and water, although these two solvents are
immiscible. This then begs the question, what happens if
you mix acetone, water and hexane? The answer is that the
acetone will dissolve in both; it will partition itself between
the two solvents. The degree of partitioning will relate to the
polarity of the solute and the relative polarity of the two
solvents. This apparently mundane observation is rather
important: we exploit it in the chemistry laboratory (and
industrially) to extract the non-polar species from aqueous
solution (by shaking with a non-polar solvent and
decanting the non-polar solvent off). Similarly, we can
extract polar species using water. In environmental science
it’s important to know how various chemicals (a.k.a.
pollutants) distribute themselves between water (highly
polar), mud (polar) and fish (partly non-polar). In
EXPERIMENT H:4
defined as
K ow =
[X]octanol
[X]water
So Kow tends to be large for non-polar species. Kow is, of
course, an equilibrium constant, albeit for a physical process,
rather than a reaction. The corresponding free energy
DG o =-RT ln K ow
is just the free energy change when one mole of X is
transferred from water to octanol.
One widely overlooked fact is that, for acids and bases
(and amphiphiles), Kow depends on pH. For instance, acetic
acid (CH3COOH) is quite soluble in non polar solvents. It’s
also soluble in water because of H-bonding and also
because the conjugate base (CH3COO-) is very polar. The
degree of dissociation depends on the pH. For a sufficiently
high pH, acetic acid will cease to partition into the nonpolar phase because it’s completely dissociated. This means
that partition coefficients for organic acids and bases vary
with pH. The tabulated values (which are for arbitrary
concentrations of the acid or base) are completely useless for
environmental or biochemical work where the aqueous
phase is nearly always buffered to near neutral.
The system is a parallel (as opposed to sequential)
equilibrium:
Ka
HA(aq) ←→ H + (aq) + A − (aq)
↑ K ow
↓
HA(oct )
which is described by two equations
Ka =
[H + ][A + ]
[HA]
and
© P.S.Phillips October 31, 2011
K ow =
[HA]octanol
[HA]water
as before, where X is now HA. It’s easy to see that
K [HA]
K ow = a + octanol
[H ][A+ ]
This can be rearranged, as shown later, in terms of the mass
of the acid used.
BASIC PROCEDURE. This experiment should be done
concurrently with part 1 or 2. The simplest way to measure
partition coefficients is by mixing the material with water,
shaking the solution with octanol, then titrating the aqueous
layer to find how much is left (or the octanol layer to find
out how much crossed). However, this cannot be easily done
as a function of pH as buffers (which are often organic
acids) interfere with the titration. Here we will use UV-Vis
spectroscopy to measure the concentrations. This is a simple
experiment so some of the experimental details will be left
for you to work out.
There are basically three steps: a) Preparation of stock
solutions. b) Preparation of calibration standards. c) The
partitioning experiment itself.
Make sure all flasks and their caps are clean and dry.
Note that octanol is quite oily, it will pipette slowly. It is also
quite smelly, not too unpleasant, but persistent. You should
wear gloves and work in the fume hood.
Stock Solutions. Weigh out accurately about 20mg of
bromophenol blue (an acid-base indicator) and make up a
200mL aqueous indicator stock. Take 10mL of this stock and
dilute with pH 7 buffer to 100mL (10µg/mL). Take another
10mL and dilute to 100mL with pH 4 buffer (prepare as
indicated on the bottle). Also, make up a similar stock in pH
2 buffer. Also, do pH 5 if directed to do so. These will be your
working solutions.
Calibration Solutions. You need to prepare a range of
indicator solutions in pH 7 buffer, from the stock indicator
solution. About (but accurately known) solutions of 0, 2, 4, 6,
8 µg/mL should do. I’ll leave you to work out the details (but
use a one stage dilution). Do not make them from the
100mL samples above, make them from the stock. Also try
to keep the volumes down; 100mL or less to avoid disposal
problems. Once you have the standards, run their UV-Vis
spectra in the range 320-700nm to get the calibration curve
(discussed later). Check the absorbances are below 2 units.
Save the spectra on a USB drive as directed.
If time permits also make up standards in octanol to the
© P.S.Phillips October 31, 2011
same concentration. Try to minimize the amount of octanol
used.
Partition run. Take the 100mL of your working solution
(pH 7, 4, 5, and 2) and shake it with 5mL of octanol in a
separatory funnel. (Remember to safely vent it. If you haven’t
used one before get the instructor to show you.) Let the
solution settle and drain off the aqueous layer into a beaker
(record it’s pH if directed to do so. This serves as a check as
some of the buffer may partition as well.) Next filter the
solutions with the 45µm syringe filter into a 1cm cuvette
and take their UV spectra. Use the corresponding original
buffer as a blank).
Interpreting the UV spectra. The indicator is the sodium
salt of an organic acid (pKa 3.85) and so exists in two states;
the neutral state, HI, absorbing at 440nm (coloured yellow;
denoted by subscript HI) and its conjugate base, I-,
absorbing at 580nm (coloured purple; denoted by subscript
I). To get a calibration curve simply plot amplitude of the
580nm peak vs. concentration (in µg/mL). You may need to
do some baseline corrections to get the correct amplitudes.
The concentrations of the test samples can then be just read
off this graph.
If you did the octanol standards repeat the above, but
you only need the 440 nm absorbance. You will need to
dilute the samples. Probably at least a factor of 10x.
CALCULATIONS. We are studying a distribution
between octanol (denoted by subscript, o) and water
(denoted by subscript, w). We can define the partition
coefficient many ways, however it’s only useful to define
them in terms of the same species or for total concentrations
(Ctotal). As charged species (i.e. I-) do not partition into
non-polar solvents we can try:
K ow1 =
C HIo
C HI w
K ow2 =
C HIo
Ctotalw
K ow2 is the usual definition of partition coefficient, but is
pH dependant as C HI w and C I w are pH dependant. On the
other hand K ow1 should be pH independent (why?) so is,
perhaps, more relevant. In the literature you will see the
symbol Dow , but there is some confusion as to which of the
two K’s this represents.
The calibration is done at pH 7 where only the charged
species is present so we can get the extinction coefficient for
that species and hence the concentration of I- in the
aqueous phase of all the samples.
AI = eI lC I w
EXPERIMENT H:5
where the cell length, l, is 1cm.
In the aqueous phase the concentration of HI and I- are
related by the Henderson-HasselBach equation (see the
appendix) so
CI
pH = pK a + log w
C HIw
QUESTIONS.
1) Synthetic membranes can be made with bilayers of
phosphatidyl choline (see fig.1). Would you expect the
following species to be able to penetrate the membrane.;
water, any anion, alcohol, oxygen. Briefly explain why.
As the molar mass of HI and I- differ by only one, so we can
write
mI
pH 
pK a log w
mHI w
where m is the mass of the species in the sample. It’s
convenient to define R = mI w mHI w so
pH - pK a = log R
The mass of the indicator can be determined by
conservation of mass:
mHI w + mI w + mHIo = mtotal
so
mHIo = mtotal - mI w (1 )1/ R)
If you did the octanol standards you can get at mHIo from
the spectra.
Hence (since C=m/V)
K ow1 =
APPENDIX. The Henderson-Hasselbach equation relates
the concentration ratio of an acid and it’s conjugate base in a
solution of given pH. Consider an acid HI;
HI(aq)]H+(aq)+I-(aq)
mHI w Vw
My preference is to write H+(aq) rather than the hydronium
ion. H3O+. (or H5O2+ which is probably closer to the truth) )
so for a dilute solution
æ
mI æ 1 ööV
K ow2 = ççç1- w çç1 + ÷÷÷÷÷÷ w
èç mtotal çè R ø÷ø Vo
We have mtotal and mI w from the spectra, so we can use
these equations to get K ow2 and K ow1 at the three pH’s.
Note that there is an interplay between mI w and R that
can result in –ve partition coefficients if these numbers are
just a fraction off. This is easily resolved by noting that the
result is not –ve, but zero within experimental error.
DISCUSSION.
1) Tabulate your results. Are the partition coefficients
consistent with the spectra and the Henderson-Hasselbach
equation?
2) Explain in terms of the UV spectra why you see the
colors that you do.
EXPERIMENT H:6
2) How would expect the following compounds to
partition between octanol and water (i.e. Kow<1, Kow>1 or
other). Briefly explain your answers. Phthalic acid, mercury,
ethanol, sodium chloride.
3) How do detergents affect partitioning (see Exp.M).
4) Name one or more instrumental methods that are
based on partitioning and very briefly describe them.
mHIo Vo
æ Rm
ö÷V
ç
= çç total -(1 ) R)÷÷÷ w
çè mI w
ø÷ Vo
similarly
Figure 1. Schematic of a cross-section of part of a
bilayer in aqueous solution. The sphere is the polar
head. The tails are non-polar chains.
Ka =
but
[H+ ][I-]
[HI]
pKa = -log Ka and pH = -log [H+]
therefore
pH = pK a + log
[I-]
[HI]
This equation can be used to determine the extent of
dissociation of an acid in a buffered solution. Why such a
simply derived equation is named after two people, is a
mystery. You may wish to delve into the literature to try and
discover why.
© P.S.Phillips October 31, 2011
APPENDIX.
V is considered a function of P and concentration is
function of V and n so these two variables are not needed.
Using the slope rule, we get for m components
Pressure Dependence of Free Energy.
We have, by definition, and using the chain rule
G º H -TS
dG =
\ dG = dH -TdS - SdT
so
We define the last term as the chemical potential, µ, the
variation of G with composition i.e.
\ dH = dU + PdV + VdP
ki º
dG = dU + PdV + Vdp -TdS - SdT
dG =
For a reversible change in a closed system of constant
composition (no reactions), with no non-expansion work,
this becomes
U = qrev - PdV
but since qrev = TdS , substituting back into the expression
for dG we get
dG = TdS - PdV + PdV + VdP -Tds - SdT
hence we get
dG = VdP - SdT
(1)
¶G ö÷
÷ =V
¶T ÷øT
so at constant T
Integrating between P1 and P2 assuming P scales inversely
with V (e.g. PV=nRT)
æP ö
G(P2 ) = G(P1) ) RT lnçç 2 ÷÷÷
(2)
çè P1 ø÷
Solids and liquids are incompressible so the volume change
with pressure is tiny, so the change is negligible (1-2 J), but
for gases it’s quite large.
If we measure changes in G with respect to some
reference state, they become ∆G’s. To simplify things further,
we usually make P1 the reference state, so P1 become Po and
∆G(P1) becomes ∆Go , so we get for some pressure P
æPö
(3)
DG(P) = DG o ) RT lnçç o ÷÷÷
çè P ø
Chemical Potential.
Gibbs Free Energy is a function of composition
(n1, n2 ,...nm ) , temperature, T and pressure, P, i.e.
G = f (T , P , n1, n2 ,...nm )
© P.S.Phillips October 31, 2011
¶G ö÷
÷
¶ni ÷÷øT ,P ,all n
k¹i
so (4) becomes
U º q +w
but
(4)
k¹i
H º U + PV
but
m
¶G ö÷
¶G ö÷
¶G ö÷÷
÷÷dT ))
÷÷ dP ...... å
÷÷ dni
n
¶T ø P ,n1 ,n2 ,... ¶P ø T ,n1 ,n2 ,...
¶
÷ø T ,P ,all n
i
i=1
m
¶G ö÷
¶G ö÷
+
+
dT
dP
.......
÷
÷
å mi dni
¶T ÷ø P ,n1 ,n2 ,... ¶P ÷ø T ,n1 ,n2 ,...
i=1
Also, for 1 mol, µ is just G so (2) can be written
æPö
m(P) = mo ) RT lnçç o ÷÷÷
çè P ø
(5)
It’s a little difficult to see why we would introduce chemical
potential; after all, we can only measure changes in it, which,
at constant T and P, is ∆G. There are a couple of reasons, but
the simplest is that it easier to talk about. Saying ∆Gvap is
+ve is the same as saying the chemical potential of a liquid
is lower than the vapor. The latter is somehow clearer and
more intuitive (things roll downhill). Another example is,
that at equilibrium the chemical potential of multiple phases
have the same chemical potential. That statement captures
the situation more easily than some description using free
energy. It also allows us to introduce non-ideality more
easily (chemical potential is also known as the partial molar
free energy). Lastly, (4) is the not whole equation, there are
other terms we won’t discuss here.
Solutions.
The chemical potential of a substance is the same
throughout a sample at equilibrium, regardless of how many
phases are present. This is very important because it allows
us to say something about complicated systems. In
particular, for a liquid/vapor system, if we know the
chemical potential of the vapor, we know the chemical
potential of the liquid. This is important because we can
calculate (or measure) a lot about gases, even non-ideal
ones, but we know very little about liquids and, currently,
can calculate diddly-squat about them, but if we have the
chemical potential of the vapor, we know everything we
need to know (thermodynamically) about the liquid.
EXPERIMENT H:7
Let’s consider a pure (denoted by a superscript *)
solvent, A, in equilibrium with its vapor in a closed system
(no air present), then
mA* (vapor ) = mA* (liquid)
we change X to activity.
Since the liquid is pure, and if we have one mole, it’s in its
standard state (the pressure is not one bar, it’s whatever its
vapor pressure is, but we have shown elsewhere that this
effect is negligible for liquids and solids so we can use the
standard state), so
Raoult’s Law.
mAo (liquid) = mA* (vapor )
However, the chemical potential of the vapor is pressure
dependent, (5). so if P* is the vapor pressure of the pure
liquid we get
æ P * ö÷
*
*
o
o
mA (vapor , P ) = mA (vapor , P ) ) RT lnççç o ÷÷
÷
çè P ÷ø
(6)
The standard state for the vapor being the vapor at one bar
pressure.
Now let’s consider a solution of solvent A and a single nonvolatile solute B (i.e. it has no vapor pressure).
mA* (vapor ) = mA (solution)
since the chemical potential of A must be the same in both
phases. Therefore from (5)
æPö
mA (solution) = mAo (vapor , P o ) ) RT lnçç o ÷÷÷
èç P ø
(7)
where P is now the vapor pressure over the solution.
From (6)
æ P * ö÷
æ P ö÷
mA (solution) = mA* (vapor , P o ) - RT lnççç o ÷÷ ) RT lnççç o ÷÷
èç P ø÷÷
èç P ø÷÷
so
æ P ÷ö
mA (solution) = mAo (liquid) ) RT lnççç * ÷÷
çè P ÷÷ø
but Raoult's Law for an ideal solution is
We can now rearrange this equation to give us the
chemical potential change for converting one mole of
o
solvent to a solution of concentration XA i.e. DGtransfer
Raoult’s Law is empirical and only applies to cases where the
solution is dilute or the solute and solvent are very similar.
This problem can be side-stepped, in the usual way, by
stating “for dilute solutions.....”, however, that defeats the
purpose of studying non-ideal cases. The more useful way
is to define the activity aA(“apparent “ or thermodynamic
concentration) as follows
mA (solution) = mAo (liquid) ) RT ln aA
The activity, aA, is purely empirical, but the equation is
exact. For dilute solutions of non-polar solutes aA → X A .
For dilute solutions of ionic compounds, the activity can be
calculated by Debye-Huckel theory or one of its extensions.
Some Nomenclature.
There are some evil forces at work that refer to the
hydrophobic effect as hydrophobic forces, or worse bonds.
However, there are some sources of confusion. The first
being intermolecular vs. intramolecular. Intermolecular
refers to “between molecules” and intramolecular “within a
molecule” (and is mainly responsible for protein folding).
The next is the distinction between forces, bonds and
effects. A bond involves sharing of electrons and is
directional. Forces are usually electrostatic in nature (ionic
bonds aren’t really bonds, they are an electrostatic force).
They may or may not be directional. Hydrogen bonds, πstacking etc. are electrostatic forces, which we collectively
call intermolecular forces (although they can be
intramolecular forces. π-stacking is almost exclusively
intramolecular.) On the other hand the hydrophobic effect is
just that an effect (on entropy). It is caused by H-bonding,
but is not bonding, or even a force. To avoid confusion were
call all the conditions that organize the structure of
molecules, covalent and ionic bond’s excepted,
intermolecular interactions.
PA = X A PA*
mA (solution) = mAo (solvent ) ) RT ln( X A )
That is, the solute lowers the vapor pressure of the solvent
(since XA is <1). Note that the identity of B is irrelevant;
vapor pressure is a colligative property. For a real solution,
EXPERIMENT H:8
© P.S.Phillips October 31, 2011
Suite K.
INTRODUCTION. This consists of two experiments
(which can be done in any order, but one each period). The
first is familiar to you from Chem. 201. Here we will just
repeat the experiment, but explore non-linear fitting and
also the difficulties of distinguishing 1st from 2nd order
reactions.
The second part is new and not so easy. Here will explore the
kinetics of a reversible reaction, which can be analyzed a
number of ways.
The focus is data analysis, don’t expect it to come easily.
Part 1. FIRST ORDER KINETICS
KINETICS: Fitting of Data
the water levels in both burettes are kept the same. The
pressure inside the system is therefore always the same as
that of the atmosphere. Make sure you record the
atmospheric pressure.
Assemble the apparatus as shown in Figure 1 and test for
leaks by adjusting the movable burette. Set the water bath to
25C. Adjust the water in the fixed burette to read 0.0mL
with the system open (tap of dropping funnel open). Place a
one inch magnetic stirrer flea in the Erlenmeyer flask and
add, using pipette, 20mL of H2O, 40mL 0.1M KI and 2mL of
0.1M NaOH. Allow the flask to sit in the water bath for
several minutes to reach thermal equilibrium.
INTRODUCTION. This experiment should be familiar to
you from 201 (Experiment D) where we investigated the Icatalyzed decomposition of hydrogen peroxide. The rate of
reaction was measured by following the volume of O2
evolved at constant pressure. The theoretical rate was given
by
d[O2]/dt = k[H2O2 ]a[I-]b
where ‘a’ and ‘b’ were determined to be 1. Since I- is a
catalyst its concentration should remain constant
throughout the reaction so for a particular reaction, [I-]b =
constant and thus
rate = k'[H2O2]
where k' = k[I-]
Hence the reaction is first order in [H2O2] and the volume of
O2 will follow an exponential form.
PROCEDURE. The apparatus to be used is shown below.
A 125mL Erlenmeyer flask, the reaction flask, sits in a water
bath with a magnetic stirrer below it. The flask is fitted with
dropping funnel and an outlet connected to a pair of 50mL
burettes. Be sure to secure all joints with clamps or rubber
bands. Use a short arm clamp to stabilize the flask. The left
burette is rigidly clamped, whereas the one on the right can
be raised or lowered: they are connected by plastic hose.
The burettes are initially filled with water such that the
water level is at 0mL in the fixed burette and 50mL in the
movable burette. To do that, raise the movable burette until
its 50mL mark is adjacent to the 0mL mark on the fixed
burette, then fill the burettes with water until the water is
near both the 0mL and 50mL marks. You can then adjust
the movable burette until the water level is exactly 0mL in
the fixed burette. As the reaction proceeds in the reaction
flask, O2 gas is produced. This forces the water level down in
the fixed burette; the movable burette is moved down so that
© P.S.Phillips October 31, 2011
Figure 1. The apparatus.
Pipette 10mL of H2O2 solution into the supplied test tube
and allow it to sit in the 25C water bath for several minutes.
Turn on the stirrer to the highest speed possible without the
flea becoming unstable (usually about four), you may have
to center the flask over the stirrer. Note this stirrer setting
and use it for all subsequent runs. This is important as the
rate of evolution of the gas from solution depends partly on
the stirrer rate. Now turn off the magnetic stirrer and add
EXPERIMENT K:1
the H2O2 to the dropping funnel (tap closed). Now lift the
funnel slightly out of the flask and open the tap. When all
the peroxide is drained, drop the funnel back into place,
close the tap immediately, and turn the stirrer on to the
selected speed, and simultaneously start the timer. Record
the times required to produce 2mL, 4mL, 6mL, 8mL
10mL… etc. up to 24mL of O2. In each case, adjust the
movable burette to give the same level of H2O in each
burette. Repeat this run to get a duplicate.
In the 201 experiment we did a run to determine the value
of Co, here we will not do that we will calculate it from the
data. We can do that because we have an extra piece of
information, we know that the reaction is first order in
H2O2.
DATA MANIPULATION. Suppose the concentration of
H2O2 at time zero is Co , and the volume of the reacting
solution is Vo, V is the measured O2 volume, Then the
concentration C at time t is (see the 201 manual for details)
C = 2P(Vi – V)/RTVo
Where
(1)
Vi=CoVoRT/2P
P = Ptotal − PHo O
2
o
and PH O is the vapor pressure of water at room
2
temperature.
As the reaction is first order with respect to C,
the
-dC/dt = k'.C
(2)
and
or in the integrated form
ln(C) = -k'.t + ln(Co)
(3)
Therefore, a plot of ln(C) vs. t should yield a straight line.
More explicity, for our case, a plot of ln(Vi-V) should be a
straight line
ln{(Vi- V) / Vi} =- k’t
(4)
To verify this we equation we can measure Vi and proceed
as we did in 201, we can guess Vi until our graph is
straight, or we can fit the exponential directly. We will
choose the latter course, but we will still need an
approximate Vi so we will also do some guessing. We will
also investigate the effect of Vi on our results and
determine whether it’s better to measure Vi directly or get
it by fitting. The exponential form of the equation is
V= Vi (1- e-k’t)
CALCULATIONS.
1) Choose one of the two data sets and guess Vi (try 50)
and using (4) do an LSF. Repeat with another (hopefully
better) guess of Vi. Repeat until the calculated data is as
close as you can get it to a straight line. You can generate a
convenient straight line using your guessed Vi and the k’
from the LSF. Use the final choice to get the value for k’. You
could program the computer to do this, just keep
incrementing Vi until the square of the residuals
(difference between guessed line and the generated line) is a
minimum (the convergence criterion).
2) Use (5) and a non-linear fit to get Vi and k’ for both
sets of data. (See appendix – Non-linear fitting with
Origin). Use the values from question 1 as starting
parameters. Also try the non-linear fit with starting
parameters that are way off to see the effect on the fit. You
should note that while (5) is theoretically correct, it’s the
incorrect model for this experiment. You need to add an
extra variable, Vo to account for gas loss (or compression) at
the start of the experiment. Vo should be around –1mL.
Non-linear fitting can be done with Origin or by using the
solver in Excel.
3) Do a t-test on your two values for k and Vi and verify
that they are the ‘same’ within experimental error.
QUESTIONS.
4) Use the data below from 201 Exp. D (some noise has
been added) and fit a straight line for ln([A]) vs. t and a
straight line for 1/[A] vs. t. The data is first order so the
first plot should be linear and the second not, but can you
prove that using the data below?
[A] (M)
69
107
139
173
206
238
271
306
340
375
414
451
t (s)
0.111
0.105
0.109
0.101
0.096
0.095
0.095
0.089
0.090
0.087
0.078
0.080
(5)
Which is a non-linear function.
EXPERIMENT K:2
© P.S.Phillips October 31, 2011
Part 2: A REVERSIBLE FIRST ORDER
REACTION
INTRODUCTION. Here we will study the double
exponential time dependence of the reversible reduction of
Cr(VI) by glutathione (a widespread antioxidant in
biochemical systems) in an aqueous medium, and to obtain
the rate constants of the process.
Most of the rate processes that take place in biochemical
systems cannot be described by the fundamental, textbooktype kinetic models, such as simple first-order or secondorder reactions. Recognizing this fact, many physical
chemistry textbooks devote a separate section to the
kinetics of complex reactions. Reversible, multistep and
consecutive reactions are examples of such kinetic models.
They are often relevant to biological reactions; moreover,
they exhibit fascinating kinetic behaviour. In addition, the
experimental data are amenable to rigorous interpretation if
straightforward computer-assisted data acquisition and
analysis techniques are used.
iated GSH) and Cr(VI) at near-neutral pH is studied. Two
GSH units are coupled together through the thiol groups,
thus being oxidized to glutathionyl disulphide, GSSG. In the
process, Cr(VI), which represents the aqueous chromium
ion in the +6 oxidation state, is reduced to Cr(III).
The reaction is described by the following equation:
+
3+
2CrO24 + 6GSH+10H → 2Cr +3GSSG+8H 2O
This reaction is believed to account (in part) for the toxicity
and carcinogenicity of chromium(VI); hence its kinetics
and mechanism have been the subject of numerous research
investigations. GSH and GSSG function as a redox couple,
both in intracellular and plasma environments. An enzyme
regulates the appropriate proportion of the oxidized (GSH)
to the reduced (GSSH) species, both of which are involved in
other intracellular redox reactions. GSH also functions as a
detoxifying agent that scavenges reactive species, such as
free radicals and peroxides. Thus Cr(VI) has the ability to
interfere with these processes by causing a depletion of
GSH.
The reaction mechanism is believed to involve the reversible
formation of a chromium(VI) thioester intermediate
(formed from chromium(VI) and GSH). There is a
subsequent redox step (followed by one or more kinetically
non-determining, i.e. fast, steps) between this intermediate
and a second molecule of GSH, resulting in the ultimate
products, Cr(III) and GSSG.
2

2CrO2 2CrO4 -GSH (thioester)
4 + GSH 
thioester +GSH → GSSG+2Cr 3+
With excess GSH and H+ concentrations, all three of the
kinetically important (i.e., slow) steps (the forward and
reverse reactions in the first step, and the reaction in the
second step) are pseudo first order in nature. Thus, we can
describe the reaction by the general scheme that we
considered in the theory section below (equation (1)).
THEORY. Consider the reaction mechanism in which the
reactant, R, reversibly forms an intermediate that, in turn, is
irreversibly converted to the product, P. This mechanism is
shown in the following scheme:
k
k
1
2

→P
R 
 I 
Figure 1. The species involved.
In this experiment, the kinetic behaviour of the redox
reaction that takes place between the tripeptide glutathione,
γ-L-glutamyl-L-cysteinyl-glycine (commonly abbrev© P.S.Phillips October 31, 2011
k− 1
(1)
We will assume that each elementary step in the mechanism
is first order in the corresponding reactant species. (Here R,
I, and P are symbols for Cr(VI), the Cr(VI)-GSH thioester
intermediate, and (probably) Cr(III), respectively). The
EXPERIMENT K:3
coupled differential equations that account for the rate of
change in the concentrations of the three species are as
follows:
d[R]
=
−k1[R] + k−1[I]
dt
d[I]
(2)
= k1[R] − (k−1 + k2 )[I]
dt
d[P]
= k2 [I]
dt
We also assume that only the reactant, R, is present at the
beginning of the reaction, i.e., [I(t=0)]=[P(t=0)]=0. We
may now consider three kinetic scenarios for such a system,
depending on the relative magnitudes of the three rate
constants in the preceding mechanism:
Case 1: If (k1 + k-1) >> k2, then the equilibrium (the first
two steps in the mechanism) will be established before the
second step becomes important, and the pre-equilibrium
approximation will apply. Solving the above differential
equations for [R(t)] results in a simple exponential function.
Thus
(3)
[R(t )] = [R(0)]e-kobst
where
=
kobs k1k2 /(k1 + k−1 )
Case 2: If (k-1 + k2) >> k1, then the depletion of the
intermediate takes place faster than its formation, and the
steady-state approximation will apply. Again, the integrated
rate equation for [R] is a single exponential in t. This time,
we find that
(4)
[R(t )] = [R(0)]e-kobst
where
=
kobs k1k2 /(k2 + k−1 )
Case 3: If, however, neither of the preceding conditions
applies, then the solutions to the differential equations for
the time dependencies of [R] and [I] are more complicated.
They are as follows (and can be verified using Maple if you
wish, tee hee!):
=
[R(t )]
[R(0)](λ2 − k1 ) −λ1t
(e
+ Be −λ2t )
λ2 − λ1
[I (t )]
=
and
[R(0)]k1 − λ1t − λ2t
(e
)
−e
λ2 − λ1
[P(t)] = [R(0)]- [R(t)]- [I(t)]
EXPERIMENT K:4
(5)
(6)
where λ1
=
X −Y
X +Y
k −λ
=
λ2 =
B 1 1
λ2 − k1
2
2
and
X =k1 + k−1 + k2
Y = X 2 − 4 k1k2
Notice that λ1is always less than λ2, since both X and Y are
positive. From these equations, we can see that [R] shows a
double-exponential decay (with decay constants λ1and
λ2), and the intermediate I shows an initial build-up (the
negative exponential term), followed by exponential decay.
The values of λ1, λ2, and A can be estimated from the [R(t)]
curve using "exponential stripping" or, alternatively, by
non-linear regression
The rate constants k1, k-1, and k2 can be obtained from λ1,
λ2, and B using the following equations:
Bλ2 + λ1
λ2λ1
k2
=
A +1
k1
k-=
1 λ1 + λ2 - k1 - k2
k1
=
and
(7)
Note that a successful determination of the three rate
constants depends on the extent of difference between
λ1and λ2 and the magnitude of A. Thus, if the values of k1,
k-1, and k2 are such that λ1and λ2 are not very different
from each other, or if A is very large or very small, relative to
unity, one of the kinetic approximations case 1 or 2 will
apply to the system, and the decay of [R(t)] will be
represented by a single exponential function. Thus, the
choice of the appropriate experimental conditions is very
important in such kinetic analyses if all three rate constants
k1, k-1, and k2 are to be determined; otherwise, the single
exponential functions that would describe the kinetic
behaviour of [R] would provide insufficient information.
For convenience, we rewrite [R(t)] in (5) as
=
[R(t )] D(e −λ1t + Be −λ2t )
(8)
[R(0)](λ2 − k1 )
λ2 − λ1
Because λ2 > λ1, it follows that the contribution from the
faster component (i.e., the e − λ2t term) becomes
increasingly less significant, with time, in the decay of R.
Thus, after a sufficient time has elapsed (denoted by t ', see
fig. 2), the decay approximates to a single exponential
function with a decay constant ; λ1. i.e. for t>t’
where
D=
[R’(t)] = D e − λ1t
thus
ln([R’(t)]) = ln D- λ1t
(9)
© P.S.Phillips October 31, 2011
where [R’(t)] is the concentration of R at long times. It is
now evident that we can estimate D and λ1 from a straightline fit to the linear portion of the ln[R] vs. t curve using (9).
Using these values, we can now extrapolate the slow
component function, [R’(t)], back to early reaction times
and subtract it from the observed [R(t)] curve to obtain the
fast component portion of the decay. Thus for t<t’:
(10)
[R(t’)]- [R’(t)]= DB e − λ2t
A linear fit of ln([R(t)]- [R’(t)]) vs. t yields estimates of DB
(and hence B) and λ2. Once we have estimates of λ1, λ2,
and B, we can evaluate the three rate constants k1, k-1, and
k2 using equations (7). This approach, which has been
called "exponential stripping," is illustrated in Figure 2.
Aλ = ε λ Cl
where ελ is called the molar absorptivity coefficient, and l is
the path length of the absorption cell (in centimeters).
The time dependence of the Cr(VI) concentration can be
followed by monitoring its absorbance at 370nm. The
evolution and decay of the thioester intermediate can be
followed, if desired, at 430nm. However, in that case, for a
quantitative analysis, the time dependence of the 430nm
absorbance must be corrected, because Cr(VI) has a small,
but finite, absorption at that wavelength. Note that it is not
necessary to convert the absorbance values at 370nm to
Cr(VI) concentrations because the rate parameters obtained
from the decay curve, i.e., λ2 and λ1, are pseudo first order
and thus do not explicitly depend on concentration. Also, the
other rate parameter, A, is dimensionless).
The three pseudo-first-order rate constants k1, k-1, and
k2, besides being dependent on the concentration of GSH
and reaction temperature, are also highly sensitive to the pH,
the nature of the buffer and the buffer concentration. Hence,
the reaction conditions have to be chosen carefully in order
for the system to exhibit well resolved, double exponential
kinetics.
Figure 2. An illustration of the "exponential
stripping" method. The ‘long-time’ portion (t>t') of
the observed curve is fitted to a straight line. This line
is extrapolated back to t=0, and then the log of the
difference between the observed curve and the
extrapolated line is plotted vs. t.
An alternative approach is to do a non-linear fit of (8), i.e.
we fit four the four unknowns; λ1, λ2, B, k1, directly. We
still use linear stripping though, to get starting estimates for
λ1, λ2, B, k1. We will use the method outlined in calculations
though.
PROCEDURE. A nice feature of this reaction is that
Cr(VI) (the reactant, R) and the thioester intermediate, I,
have reasonably different absorption spectra, rendering the
spectrometric study of the reaction very easy and
convenient. This very common experimental strategy is
based on the linear relationship between the absorbance, A,
of a species and its molar concentration, C. At a given
wavelength, λ, we may write
© P.S.Phillips October 31, 2011
You will be given (or have to make up) the following
aqueous stock solutions:
1.6x10-3M K2Cr2O7 (the oxidant)
0.40M K2HPO4 (buffer)
5.0x10-3M HC1 (to adjust pH)
8.0x10-3M GSH (the reductant)
1M HCl and 1M NaOH (to trim pH)
Note: Since GSH solutions undergo slow oxidative
degradation in air it is necessary to prepare the stock
solution on the day of the experiment and store it in a
refrigerator if necessary. This may be done for you already.
Small volumes (<10mL) of the first three solutions are
needed; 20mL of the GSH solution is required.
1. Trim the pH. The pH of the reaction medium must be
brought to a value of 6.0. Pipet 20mL of the GSH solution
into a test tube or other convenient vessel, such as a small
beaker or flask into which a pH electrode can be inserted.
Into that vessel pipet 4mL of the K2HPO4 buffer and 6mL of
the HC1 solution. Mix thoroughly, and measure the pH. Add
drop wise, sufficient 1M HCI or NaOH to bring the pH to
6.0.
2. Pipet 3mL of the pH-trimmed reaction solution into a
stopper-fitted 1-cm spectrophotometer sample cell (it is
EXPERIMENT K:5
assumed that the cell volume is ~3.5 mL). Add the same eqns. 9 and 10). Note: transform only about the first 75% of
solution to the reference cell and place it in the reference this "early-time" portion of the data to avoid negative
compartment. Set the spectrophotometer wavelength at numbers. Now, transform these subtracted values to their
370nm. The sample cell should be kept at constant natural logarithm and plot vs. time. Use linear regression to
temperature (20-25°C) during the experiment.
furnish values of λ2 and BC (see equation (9)). Next,
3. Place the sample cell in the cell compartment and zero the calculate the amplitude ratio, B.
instrument at 370nm (where the Cr(VI) absorbs). Remove 5. Carry out a non-linear regression analysis of the original
the sample cell and begin data acquisition (ask the data using equation (11) below, a modified version of (8)
instructor if you are unfamiliar with the operation of the UV that incorporates the start time t0 which is the (unknown)
spectrometer). Inject 20µL of the Cr(VI) solution into the time delay between starting the spectrometer and mixing
sample cell, stopper it, invert it several times, and place it in the sample; typically 0.5-1.0s. (The data for the first 20the cell compartment. You should do this quickly to ensure 30s may be missing, but that is a different problem). A good
that the data is collected as close to the start as possible. estimate of R(0) can be obtained directly from the data. Use
Continue data acquisition for at least two half-lives (~30- values of λ1, λ2 and A obtained from linear stripping as
initial guesses. Good starting values are very important
40min), obtaining a total of 500-1000 data points.
4. Ask the instructor to check your run to see if you need to since this is essentially a six dimensional problem. See the
repeat the procedure if necessary. In particular check the notes section at the end.
absorbance is between 0.2 and 1, the 20µL may need
[R(0)](λ 2 − k1 )  −λ1 (t −t 0 ) k1 − λ1 −λ 2 (t −t 0 ) 
e
[R(t )]
=
+
e
 (11)
changing.
(λ 2 − λ1 ) 
λ 2 − k1

5. Finally, repeat the experiment, but monitor the reaction at
430nm (where the GSH-Cr thioester, I) absorbs. Use the Note that R appears on both sides so its units cancel. That
GSH reaction solution in both cells to zero the absorbance at means you can use the absorbance data instead of the actual
430nm. You should observe buildup, followed by decay. You concentrations.
may be able to set the spectrometer up to do parts 3 and 4 6. Once you have obtained the regression values of λ1, λ2
and B as required (and their standard deviations), calculate
simultaneously.
the rate constants k1, k-1, and k2 (see (7)). Using
CALCULATIONS AND DATA ANALYSIS
propagation of errors, determine the uncertainties in the
1. Import the data file into a scientific spreadsheet as rate constants.
instructed. Estimate where time zero is (when you added
7. At 430 nm, the absorbance of the thioester is
the stuff to the cell and started scanning). Eliminate the data
contaminated by residual absorbance by the Cr(VI) species.
points between when you started the scan and when you
Thus (6) cannot be used directly. The 430nm reaction curve
reinserted the cell and closed the door) from the data
must first be "corrected." To do this, scale the 370nm (R)
(basically where the start of the decay looks clean – again
curve by the ratio of the t = 0 value of the 430nm curve to
ask the instructor if unclear).
that of the 370nm curve (or at least the first clean values for
2. Transform the dependent variables (absorbance) to their them as close to t=0 as possible), then subtract the scaled
natural logarithms, and plot them against the independent curve from the observed 430nm curve. Thus
variable (time). Identify a time, t’, that defines the beginning
 A (t = 0) 
of the linear portion of the decay curve (see Figure 2).
A430
=
(t , corr ) A430 (t , obs) − A370 (t , obs)  430

 A370 (t = 0) 
3. Copy the rows for t > t' from the time and absorbance
columns to new columns, transform absorbance to the where "370" and "430" denote the absorbance vs. time
natural logarithm, make a plot of ln(absorbance) vs. time (t curves at 370 and 430 nm.
> t'). Perform linear regression to obtain values of C and λ1 Once the 430nm data are corrected, you can analyze them
(see (9)). You may wish to combine steps 2 and 3 by doing according to (6). Once again, nonlinear regression analysis is
an interactive LSF to the portion of interest. A broken line fit necessary, and you must supply seed values of the three
parameters λ1, λ2 the pre-factor and the start time. You
may help also.
can
use λ1and λ2 values obtained from the previous 370nm
4. Transform the original absorbance data for t < t' into
another column by subtracting D.exp(-λ1t) from it (see analysis, and you can estimate the pre-factor to (6), D', as
EXPERIMENT K:6
© P.S.Phillips October 31, 2011
follows. It can be shown that the regression parameter, D,
obtained from the analysis of the 370nm data (8), along with
the expression for k1 (7), can be combined to approximate
D'. Thus
 Bλ + λ 
D ' = YD  2 1 
 λ 2 − λ1 
where Y is the ratio of the absorptivity coefficients of I at
430nm to R at 370nm. For the purpose of obtaining an
initial estimate of D', you can assume Y~1. With this value
of D', along with previously obtained values of λ1, λ2 and A,
you can fit the observed 430nm reaction curve and see how
well the optimized parameters agree with those you
obtained from the 370nm curve.
QUESTIONS.
1) Derive equation (4) from equation(2).
2) By substitution, show that equation 5 is a solution of
equation (2)
3) Origin’s ExpDecay2 function also fits the data as well as
the logarithmic and reciprocal functions. What does this tell
us about the use of fits to determine the mechanism of the
reaction.
4) Find an equation that gives a reasonable fit to the data
below. Theoretically, it should fit to the sum of two
exponentials.
Conc (M) Shift(ppm)
0.000
0.000
0.0002
0.007
0.001
0.061
0.002
0.123
0.004
0.260
0.010
0.517
0.015
0.654
0.020
0.737
0.040
0.980
0.070
1.186
Table 1. Concentration of tetraphenylboron ion in
EPC membranes, and the chemical shift difference.
5) Generate data in Excel using the equation
=
y A1 e − xt1 + A2 e − xt 2
for x=0-1 in increments of 0.1. Then use Origin to fit the
data to a double exponential. Either write your own function
or use a built in one (ExpDecay2 if I recall correctly). Either
way, use one as the starting value for all four parameters.
Press the ‘10 iteration’ button until you get a good fit. Note
the number of iterations taken to converge. Reset the
starting values to one and repeat using the ‘10 simplex
© P.S.Phillips October 31, 2011
iterations’ button instead. Note how many iterations it takes
to converge. Comment.
6) Repeat question 4) but add some noise to the data. (Do
that by appending 4*(rand()-0.5) to your function. Since
rand changes every time you change your spreadsheet you
might want to cut and paste-as-value to fix the noise).
Compare the convergence rate to the case of no noise. Also,
compare the fit you obtain (simplex to normal and to q4).
NOTES.
Equation 11 is rather formidable to fit, so do a practice run
using Origin’s built in ExpDecay2 with y0 and x0 fixed and
set to zero. Then, using your starting values, estimated
elsewhere, use equation 11 with t0 set to zero and fixed at
first then let it free later.
For starting parameters I found, by simulation, exponential
stripping, guessing and examination of the data that
R(0)~0.2 (actually it’s the absorbance at your first data
point), A~1.4, t0~4, λ1~0.00034, λ2~0.003, k1~0.00005
worked ok if times are in seconds. The fit was very good, but
the parameter errors were large, which implies that the
parameters are not unique. A good fit does not mean good
parameters. See the aphorism on elephants at the start of the
manual for further insight. One partial resolution is to
recognize that the fit is not very sensitive to some of the
parameters and fix those after the preliminary fit. For
instance, you have good initial guess for R(0) and t0 so if the
fit does not shift them too far from the original values you
can fix them after the first iteration. In fact you may have to
do that, fit, then use the fitted parameters as starting values.
You can verify that the fits are not too sensitive to them with
the simulation mode. In fact, you should (if time permits)
check the sensitivity of the fit to all the parameters. Often
with double exponentials, almost any combination of the
two time constants will fit, as long as they are within an
order of magnitude of each other.
This all illustrates a general problem with kinetics. It is
impossible to calculate anything from theory and nearly
impossible to measure anything to better than an order of
magnitude. For simple reactions, kinetics has told us much
about chemistry, but for complex reactions, the returns are
less. Fortunately, enzyme reactions are often simple enough
to be tractable and this keeps the area alive, never-the-less,
it is one area of physical chemistry I find unrewarding.
You need a USB drive for this lab.
EXPERIMENT K:7
USING ORIGIN
Origin can use Excel directly for its data source, by opening
Excel files directly in Origin. However, it’s best, at first, to use
Origin’s native mode. You just cut and paste Excel data into
Origin’s data tables. (Just mark and copy in Excel, then point
to the first cell in Origins table to paste). Like Excel, you can
customize many of the graph items with right or left mouse
clicks. These instructions are for Origin 6. The newer
versions may differ slightly.
Non-linear Fits. Non-linear fits may be done with a
number of built in functions or you may define your own.
1) Start Origin as usual, or in Excel mode (see Fitting
Peaks)
2) Paste your data in and plot it. You cannot do anything
until you have plotted it.
3) Select non-linear curve fit from the analysis menu. You
must plot your data first.
4) If the dialog pops up in basic mode press the more
button.
5) Select New from the function menu to create a custom
function or select function if there is a pre-defined function
suitable for use.
6) If there is a built in function proceed to item 9.
7) Tick the ‘User-defined’ box and change the ‘Form’
option to ‘equations’.
8) Set number of parameters to 3 or 4 or whatever the
number of unknowns you have and then enter the
parameter abbreviations (separated by commas). Use two or
more letter abbreviations for the abbreviations. It helps if
they are meaningful e.g. L1 for λ1
9) Enter your equation into the equation box. This bit is a
bugger. For say y=mx+c you type y=m*x +c. Make sure you
get all the brackets in. One trick is to type the equation into
Maple in text mode (using *’s etc.). It will reformat it to our
“normal” mode and you can check to see if it’s right. You can
then cut and paste the text line into Origin. Don’t hesitate to
ask for help on this or it will drive you squirrely.
10) Click on Action/Dataset to select your data set. Watch for
0,0 data points if you’ve added one. Do not include this point
unless you actually measured one. Make sure you set the
data set (look at the top entries) and don’t get your X and Y
mixed up.
11) Open Options/Control. Near the top left you see a set of
options marked with the variables. Use these to set the
number of sig. figs. to four. If you don’t the answers may not
display properly.
12) Click on Fit and set the starting guesses for the
parameters. Make sure the vary box is ticked.
EXPERIMENT K:8
13) Select the 10 iterations button and hopefully all will
work. If the results are good selecting 10 iterations again will
not change the results. If they change there is a problem. You
may need to change your starting values. If it doesn’t work
check your equation syntax very carefully. Also be sure you
recheck your data is set properly.
14) You may want to play with the Action-Result options to
get some output. You can also get some initial guesses for
the parameters by using the Action/Simulation option.
Fitting Peaks. The overlap of peaks does not matter; we
just deconvolve it then incorporate it into our calculations
(you need to think about how). To do this we use Origin as
follows:
a) Import your UV data (or other spectra) into an Excel
sheet.
b) Start Origin
c) Select Open Excel for File menu
d) Select Excel file and open
e) Select Open as Origin Sheet (if you open as an Excel sheet
you can only access Origins plotting options). Alternatively,
you can just copy and paste from Excel, but in this case it
gets very tedious.
f) Select Line from Plot menu
g) Select X and Y columns you want to plot. NB. In general,
you must plot data before you can analyze it with Origin.
h) Select Analysis-Fit multiple peaks-Gaussian (or
Lorentzian as required)
i) In the dialog, enter 3 as the number of peaks. You can
probably use the estimated line-width given to you by
origin. Check it to see if you need to adjust it.
j)Now, working from left to right (the manual is unclear
about this, but you must do it) put the cursor on the top of
the peaks and double click. If the click ‘takes’ a vertical line
will appear. The first peak is a shoulder, just guess where it
is. Repeat for the second and third peaks. As soon as you
enter the third peak Origin takes over (so mean it when you
double click) and will return a bunch of windows: the
parameter estimates, the graph with fitted peaks and the
fitted data.
k) Check the fit; if satisfied note the parameters and exit. If
not, close the plot window (do not save) go back to f) and
repeat with some other starting guesses for width and
positions. If you keep getting the same answer, then, that is
the best answer. However, you may need to do baseline
correction (Origin will do it, ask me how) or you might try
(in general) Lorentzian lines, or you may have to give up, i.e.
the lines are not Gaussian or Lorentzian.
Plotting Double Error Bars. Origin has an obscure
way for adding error bars. To add the double error bars set
up two columns in your spreadsheet containing the x and y
© P.S.Phillips October 31, 2011
errors. Plot the x-y data as a scatter plot as usual. Next
select the graph option from the top menu then select Add
Plot to Layer, then Scatter. This will pop-up a panel that
allows you to add new data (don’t), labels for the points and
x and y errors. If you only need to add y errors you can do
that directly from the original plot menu or from the Add
Errors option of the Graph menu.
Broken Line Plots. These are straightforward to do in
Origin. Just follow your nose around the menus.
© P.S.Phillips October 31, 2011
EXPERIMENT K:9
EXPERIMENT K:10
© P.S.Phillips October 31, 2011
Exp. M.
INTRODUCTION TO SELF ASSEMBLY
INTRODUCTION. What is the greatest mystery of the
universe? A physicist would probably answer ‘the origin of
the universe’; a biologist, ‘life’; a psychologist,
‘consciousness’; a chemist, well, what would the chemist
answer? Chemists being somewhat prosaic (in matters
philosophical), usually poach ideas from other fields of
endeavor. But, what if they were asked to keep the answer
in the domain of chemistry? What would you answer?
(No, that is not a rhetorical question – answer it briefly,
and not with the answer I’m about to give). I would
answer self-assembly. How does secondary and tertiary
structure in biomolecules arise? (e.g. why is DNA a helix;
how did cell membranes form; how do proteins fold etc.)
This sounds biological (because it is the first step to
biology), but it is not, it is essentially a physiochemical
process. Self-assembly violates the spirit (although not
the letter) of the second law, which in itself is a mystery. It
also requires one to consider random systems, chaotic
behavior and emergent systems, areas of study on the
leading edge of physics. An understanding of selfassembly is probably essential to nano-technology,
arguably the leading edge of engineering. The list goes
on, but we will not pursue anything as grandiose as those
studies here. We will make a start though, by studying the
simplest of self-assembling systems – micelles.
non-polar tail. Such molecules are called amphiphilic or
ambipathic (from the Greek, ‘likes it both ways’) or
surfactants (a contraction of surface active agents. Socalled because of the affect on surface tension). Some of
these agents are used commercially where they are called
soaps (metal salts of natural fatty acids), detergents (if
synthetic, usually sulphonate or phosphate derivatives of
fatty acids), foaming agents or floatation agents (after
there usage). Other materials of importance in this
category are phospholipids, triglycerides and liquid
crystals. Not all amphiphiles form micelles, some form
other structures such as membranes and some just affect
surface tension.
A typical micelle (fig.1) consists of a disordered
hydrocarbon core and a charged shell made up of the
polar head groups. Another layer (not illustrated),
consisting of the counter-ions and their hydration shells,
is outside this. (These two ionic layers are called the
Stern layer). Finally, there is a third layer consisting of
more counter-ions and orientated water molecules. This
last layer is called the Gouy-Chapman layer. The micelle
often has a fixed size (or range of sizes) for a given
amphiphile. That size is described by its aggregation
number (or mean aggregation number if there is a range
of sizes); the number of molecules in the micelle. The
concentration at which micelles start to appear (selfassembly starts) is called the critical micelle
concentration or c.m.c. This is usually a well defined
concentration, but is sometimes a range of
concentrations. The most well studied amphiphiles have
fixed aggregation numbers and sharp c.m.c.’s. Typically a
micelle will be spherical, ~5nm in diameter and contain
~100 molecules.
THEORY. The Yin and the Yang. There is an aphorism
Figure 1. Diagram of micelle, showing
monomers and micellular assemblies (the top
left figure is a ‘cut away’ and the bottom right
the spherical aggregate). This standard
representation is somewhat misleading:- the
heads are not as tightly packed as shown and
the tails are mobile and can curl up .
What is a micelle? Micelles are aggregates of long
molecules. The molecules have a polar head group and a
© P.S.Phillips October 31, 2011
in chemistry that says ‘like dissolves like’. The like refers
to the solvent polarity so that polar solvents (e.g. water)
will dissolve polar materials (e.g. alcohols and ionic
solids) and non-polar solvents (e.g. hexane) will dissolve
non-polar materials (e.g. other hydrocarbons). While
the reason for the pairings is clear, it is not immediately
clear why a non-polar material will not dissolve in polar
materials. The answer is, as always, free energy; polar
materials stick together (-ve enthalpy; favorable) albeit
to form structured solutions (-ve entropy; unfavorable).
The enthalpy term from the polar bonding dominates,
giving a –ve ∆G for dissolution. The non-polar materials
Introduction to Micelles:1
do not stick (the enthalpic term is very small) and
therefore cannot form structured solutions so the
entropic term dominates and dissolution is favorable.
When you mix polar and non-polar materials, there is no
sticking, but the non-polar material will disrupt bonding
in the polar solution (+ve enthalpy; unfavorable). At the
same time, structure is forced in the solvent. The number
of degrees of freedom the solvent has is reduced as the
solvent has to form a ‘cage’ around the hydrocarbon (-ve
entropy; unfavorable). This is called the hydrophobic
effect and ∆G is thus unfavorable. Note that the process
is due to the lack of bonding. It is not due to the socalled hydrophobic bonding that is alluded to in some
texts.
The question now arises as to what happens if the solute
is amphiphilic. It turns out that at low concentrations they
behave like normal compounds, with the enthalpy terms
dominating dissolution. At higher concentrations, the
hydrophobic effect for the tails kicks in as well and they
aggregate into micelles (essentially they undergo a phase
separation). Higher temperatures favor micelle formation,
as aggregation is entropy driven (∆S is +ve). (Which is
why you wash in hot water). Not all amphiphilic materials
form micelles, some are equally happy as monomers or as
arbitrarily sized aggregates, in which case they are said to
undergo isodesmic association. However, micelles are
usually spherical, but there are other possible structures
such as vesicles, bilayers and tubes.
The above is a simplified model, there are in fact four
factors to consider: i) The hydrophobic effect, ii)
interaction between the tails including steric effects, iii)
interaction of the head groups with each other, iv)
interaction of the head group and the solvent. None of
these effects are easily quantifiable, if at all, other than to
show that at least three of them have a similar magnitude.
That means that the simplest model will contain at least
three adjustable parameters. Such models are difficult to
interpret physically so we will not pursue them further
here.
STUDYING MICELLES: Labeling and Probes.
There are a number of methods available for studying
micelles, including light scattering, conductivity,
thermodynamic studies and various forms of
spectroscopy. One particularly useful method, general to
liquids, membranes, liquid crystals and related materials,
is to use labels or probes. A label or probe is a molecule
with some specific property that is position , medium or
Introduction to Micelles:2
motion sensitive. The oldest of these methods is radiolabeling, where the molecule is radioactive and can be
tracked with a Geiger counter or similar device. More
modern probes use some spectroscopic property such as
paramagnetism or fluorescence.
Labels and probes are essentially identical, the only
difference being that a label is chemically bound to some
part of the system (e.g. 14C is incorporated into an amino
acid). Probes are just distributed in the system by
dissolution or absorption. Here we will restrict the
discussion to fluorometric probes in micellular systems.
Aggregation studies with fluorometric probes.
Consider an aqueous solution of a surfactant that has a
bulk concentration, [S]o which is above the CMC, the
critical micelle concentration. If we make the simple
assumption that the surfactant molecules are present
either as monomeric units or as micelles that contain N
monomers, there will be a concentration of such micelles,
[M], which can be expressed as
[S]o − CMC
(1)
N
where CMC is the concentration of free monomers in
solution. In reality, a micellar solution is not a static
system containing only two solutes, monomer and
micelle. Micelles constantly undergo assembly and
dissociation, and at a given instant in time micelles are
characterized by a distribution of aggregates containing
different numbers of monomer units. Thus in equation
(1), N represents the mean aggregation number, and [M]
accordingly represents an average micelle concentration.
Because the numerator in equation (1) can be directly
determined (the CMC can be obtained experimentally),
we could find the value of N if we knew the average
micelle concentration in the system.
[M] =
Such information can be obtained from micellar systems
using light scattering, which is sensitive to the density of
very large, colloidal particles, such as micelles. However, a
more indirect approach that relies on a fluorimetric
technique can be used. This essentially relies on adding a
fluorescent probe to the micelles and a quencher, to
quench the fluorescence. The method involves several
simple but important assumptions:
1. A luminescent probe molecule is added to the micelle
system. This probe is exclusively associated with (i.e.,
dissolved in or bound to, a micelle rather than being
dispersed in the aqueous medium. The luminescence
© P.S.Phillips October 31, 2011
intensity of the system is, then, proportional to the
fraction of labeled micelles (not all micelles have a probe
in them).
2. There are many more micelles present than probe
molecules. Thus, only a fraction of the micelles present
contains the probe molecules; a micelle is either empty or
associated with a probe molecule.
3. The quencher is associated with micelles only; it is not
solvated in the aqueous medium.
4. These solubilized quenchers occupy micelles randomly,
irrespective of whether they are vacant or occupied by a
luminescent probe molecule.
5. If a probe shares a micelle with one or more quenchers,
the probe will not luminescence.
An interesting variation to this approach is to use a
quencher that is water-soluble only and a probe that
distributes itself between the two media. You can then
spectroscopically explore the label in aqueous solution
only and compare it with the probe in micelles only (the
aqueous probes can be deactivated with the quencher in
the aqueous phase).
The micelle is continually exchanging monomers with the
solvent (at a rate of roughly several thousand times per
second) whereby it undergoes a complete reorganization
tens of times per second. Therefore a probe being used to
determine its mean aggregation number (a static
concept) must “take a snapshot” of the micelle on a time
scale of much less than 1-10 ms. Luminescent probes
easily satisfy this criterion because their intrinsic
lifetimes for light emission are usually less than 1ms.
The luminescence intensity of the system is proportional
to the number of micelles that are occupied by a probe
molecule but no quencher. Thus for a particular (bulk)
quencher concentration, the ratio of the luminescence
intensity, I, to that when no quencher is present, Io (the
bulk probe concentration being constant) is equal to the
fraction of probe-containing micelles that do not contain
a quencher molecule.
If q quenchers are placed randomly in m micelles, the
distribution of these quenchers in the micelles is
governed by Poisson statistics (if q and m are large). Such
a distribution means that the probability of finding n
quenchers in a randomly selected micelle is given by
Pm = q
© P.S.Phillips October 31, 2011
ne
−q
n!
(2)
where <q> is the overall probability that a micelle
contains at least one quencher, i.e., <q> = q/m.
Macroscopically, <q> = [Q]/[M], where [Q] is the bulk
quencher concentration and [M] is the (mean) micelle
concentration. Of particular interest to us is the
probability that a micelle contains no quencher, because if
such a micelle contained a probe, it would produce
luminescence. Thus we have from equation (2), where
n=0, (Remember 0! = 1)
−q
=
Po e = e −[Q]/[M]
Finally, we relate the measured quantity I/Io to the
fraction of quencher-unoccupied micelles:
[Q]
−
I
(4)
= e [M]
Io
Recapping, Io is the luminescence intensity of the probecontaining surfactant system in the absence of quencher.
It is proportional to the number of micelles containing a
probe. I is the luminescence intensity in the presence of Q
moles per liter of quencher, and it is proportional to the
number of micelles containing a probe, but without a
quencher. Substituting the expression for [M] from
equation (1) into equation (4) and rearranging, we have
 I 
-[Q]N
ln   =
 I o  [So ] - CMC
(5)
We can use equation (5) to determine both N and the
CMC, depending on the dependent variable used, [Q] or
[I]. In either case, the concentration of the luminescent
probe is held constant throughout the experiment. If the
surfactant concentration is fixed (i.e., constant [S]o), and
[Q] is varied, we can use a regression analysis of ln(I/Io)
vs. [Q] to obtain N (see equation (5)). Alternatively, if [Q]
is constant and [S]o is varied, we may find both N and the
CMC from an appropriate regression analysis based on
equation (5).
In the former experiment (constant [S]o), the emission
intensity decreases with increasing [Q], as expected. But
when [S]o increases (at fixed [Q]), the luminescence
intensity should increase because the number of micelles
increases, thereby decreasing the probability that a given
micelle will be occupied by both a probe molecule and a
quencher. In this case, it is assumed that the smallest [S]o
value used is larger than the CMC, i.e., we begin with a
micellar system.
Introduction to Micelles:3
STUDYING MICELLES: Other Methods. The
problem with probes and labels are they perturb the
system and it’s sometimes unclear whether one is
studying the micelles or some special case. A considerable
amount of work has been done using ESR by attaching a
NO moiety to the monomers (spin labels) or introducing
similar amphiphiles also with an NO attached (spin
probes). This approach can also be done by replacing
some protons with deuterium in the monomers and using
deuterium NMR to look at the relaxation times or the
spectrum. Such isotopic substitution has relatively little
effect of the system, but is difficult to do. Ideally we
should use a method that does not perturb the system at
all. One such method is light scattering. Another is 31P
NMR (which works for phospholipids and phosphate
detergents). Proton NMR is difficult because water is 55M
and solvent suppression methods tend to interfere with
relaxation times in unpredictable ways. One way round
that is to use D2O or to look at the incorporation of
benzene (which is well clear of the water signal). It can
also be done with indirectly using 13C NMR, but takes a
while.
Another, an oft neglected technique is conductometry. We
will use conductivity measurements. A micelle has a
mobility well below that of the monomeric species so the
overall conductivity drops rapidly at the onset of micelle
formation. Since the c.m.c. tends to be sharp so is the
conductivity change. We exploit this to measure the c.m.c.
Introduction to Micelles:4
© P.S.Phillips October 31, 2011
Suite M.
INTRODUCTION. For a discussion of micelles see the
introductory section. Here we will the measure the
critical micelle concentration, c.m.c., by conductivity, of a
common detergent, (SDS, sodium dodecylsulphate,
NaOSO 3 C 12 H 25 ) and look at the effect of salt on the c.m.c.
We will also determine the c.cmc. using a spectroscopic
probe. Finally will also use fluorimetry to get the
aggregation number.
It should be clear from the introductory section that the
entropy of the solvent plays an important role in micelle
formation. We will therefore also explore the effect of
NaCl concentration on the c.m.c. In fact, this is quite
important: life probably evolved via liposomes, which are
very similar to micelles, if micelles cannot form, then
neither can liposomes. If micelles cannot form in salt
water, then life could not have originated in the sea (or at
least the sea didn’t exist as we know it now).
You may have seen these experiments in 304. Here you
will get beaten up on the write up a bit more. Especially
the sig figs and answers to the questions.
PROCEDURE. The experiment consists of three parts.
They can be done more or less independently as you wish.
You have quite a few solutions to do so you may want to
think of ways to speed this up. For instance you can prep
the samples in the NaCl solutions while your partner does
the normal aqueous ones.
MICELLE PROPERTIES
immersed. Set up the conductance meter and get a ‘blank’
reading.
3) Now, using an Eppendorf pipette of the appropriate
size, titrate in 1.5mL aliquots of the 0.08M stock SDS
solution to a total of 40mL. After each aliquot, stir the
mixture by gently moving the electrode up and down.
You should be able to get a stable conductance reading
after <10 secs. Do not use a magnetic stirrer as it may
interfere with the cell readings. Record both the delivered
volume and conductance. You should do a rough plot of
your data as you go along.
4) Calibrate the Eppendorf by pipetting an aliquot of
water into a beaker and weighing it. The density will give
the true volume.
Part 2. C.M.C. determination by spectroscopic
probe. For the this part of the experiment we use a
probe to follow the micellation process. A probe is simply
a compound that changes some fundamental and easily
measure characteristic when its local environment
changes. They are widely used in biochemistry, but suffer
from one problem; they must not perturb the system.
That is the environment must change them, but they must
not change the environment. In this case, we assume that
micellation is the only thing that affects the probe, and
the probe does not change the c.m.c.
Part 1. C.M.C. determination by conductivity. Here we will use a UV probe, benzoyl acetone (a.k.a. 1This is a simple titration. We just add standardized
detergent solution to water (or saline) and measure the
conductivity as a function of concentration. Our
detergent will be SDS, sodium dodecyl sulphonate (a.k.a.
sodium lauryl sulphate), NaOSO3C12H25. This is the most
common non-phosphorus clothes detergent. (Most
washing powders consist of SDS, brighteners, perfume,
pH balancers and sometimes bleach). The titration is
rather lengthy and conductivity and micelle formation
are temperature sensitive so it is desirable to do the
titration, and keep all solutions, in a 25C water bath.
Make all solutions in e-Pure water.
1) Make up a 500mL standard solution of SDS, ~0.08M.
Make a concentrate first, and then dissolve that by
stirring. Do not shake! It’s a detergent!
2) Pipette 100mL of water into a 250mL measuring
cylinder. Clamp the cylinder and put the electrode in the
cylinder. Make sure the electrodes are completely
© P.S.Phillips October 31, 2011
phenyl-1, 3-butadione, or BZA). This exists in a ketonic
form that absorbs at 250nm and an enolic form (37.5% in
water) that absorbs at 312nm. The later forms by
intramolecular H-bonding (draw both structures) and is
favoured in non-polar environments where there are no
competing species for H-bonding. By following the UV
spectrum as a function of SDS concentration and
examining the proportion of the tautomeric forms we can
determine the c.m.c.
Prepare a concentrated solution (5mg/mL) of BZA in
dioxane. From this stock solution (~0.03 mol L-1)
prepare an aqueous BZA solution by pipetting 0.40 mL
into 25mL volumetric flasks and diluting to the mark
with water. To get the spectra transfer 0.40 mL of the
aqueous BZA solution with a pipet into a 1.0cm quartz
cell together with the appropriate amount of surfactant,
and the water volume necessary to give a 3mL total
volume in the cell ([BZA]~7 x 10-5 mol L-1). The
reference cell should contain the same concentrations of
Exp. M. Micelle Properties:1
surfactant as the sample. The spectrum of BZA in the
presence of varying surfactant concentrations. Prepare 9
or 10 solutions containing 70µM BZA probe and between
0 and 16mM SDS, in uniform increments. Measure the
UV spectrum between 220-360nm in matched quartz
cells and and SDS reference samples.
Repeat the experiment using 0.1 NaCl solutions, instead
of water, to make the SDS solutions to see if NaCl changes
the c.m.c.
You can use the blanks from the section above. (We can
do this a little more easily with the conductivity meter,
but the NaCl tends to mask conductivity changes in the
SDS).
Part 3. Aggregation number. We will measure the
aggregation number, as outlined in the introductory
section, by fixing the quencher concentration and varying
the surfactant concentration. Again, make all solutions in
e-Pure water.
To be explicit, we will hold the Ru(bipy) 3 2+ concentration
constant at ~7 x l0-5M (note the ~, but the concentration
should not exceed 7.2x10-5M), keep the quencher
concentration at 1 x l0-4M and vary the surfactant
concentration between ~0.01 and 0.05M.
First, prepare a 5mL aqueous stock solution, in e-pure
water, of ~7x10-3M in Ru(bipy) 3 C1 2 .
Next, prepare two 50.0mL standard solutions of SDS in
e-pure water, one about 0.01M (solution A) and the other
about 0.05M (solution B). Set aside 10.0mL of solution A
for the standard.
Also, make up 5.0mL of a 0.050 M solution of the
quencher, 9-methylanthracene, in absolute ethanol,
sonicating if necessary, to achieve dissolution. Inject
100µL of the quencher stock into solution B and also
inject 80µL of the quencher stock into the remaining
40mL of solution A.
Next, prepare seven solutions of A and B (now with the
quencher in them) in 10mL volumetric flasks as shown in
table 1. Be sure to read the caption for complete details.
Don’t forget to repeat the experiment in 0.3M NaCl.
It is important to keep these deliveries as uniform as
possible so that the resulting probe concentrations are
equal. Make sure you shake the samples thoroughly, but
don’t generate too much foam. Sonicate each solution for
a few minutes as well. Each of the six samples and the
standard should be clear, pale yellow-orange in
appearance. Label each solution and put into a 25C water
Exp. M. Micelle Properties:2
bath to equilibrate before measurement. For each solution
measure the luminescence intensity at 665nm with
λexcite=440nm. (An instructor will help you with the use
of the fluorometer. Once you’ve set it up it’s important that
you do not change the gain or span or other instrument
parameters).
A (mL)
1.00
2.00
4.00
6.00
8.00
9.00
5.00
10.00#
B*
9
8
6
4
2
1
5
0
Ru(bipy) 3 2~
100µL
“
“
“
“
0
100µL
Solution
1
2
3
4
5
6
Blank
Standard
Table 1. *Pipette the aliquot of A into a 10mL
volumetric flask, then make up to the mark with
solution B. Do not pipette in a separate aliquot of
B. #This is the 10mL of the original A solution, it
contains no quencher. The Ru(bipy) 3 2+ is the
7x10-3M stock solution; add this to your 10.0mL
sample to make a final 10.1mL solution.
CALCULATIONS. The c.m.c. will be calculated from
the conductiometric and probe data and both the c.m.c.
and aggregation number will be calculated from the
fluorometric data.
Conductiometric. The first thing you need to do is to
convert all the added aliquots into a final concentration of
SDS in solution. The second thing is to subtract the
conductance of the starting solution from all your
conductance readings to get the adjusted conductance
readings.
1) Plot adjusted conductance vs. [SDS] for each of the
solutions. The concentration at the line break is the c.m.c.
The break point can be determined with Broken Line
option of CurveFit (which may not work as the lines may
be slightly curved) or you can fit a pair of straight lines
‘manually’, using Excel or some other program.
2) If we assume that there are no micelles below the
c.m.c. and only micelles above the c.m.c. we can get the
conductance for the two species.
Plot the equivalent conductance vs. [SDS] (equivalent
conductance = adjusted conductance/[SDS]). Use Excel
or the Broken Line option of CurveFit to find the intercept
© P.S.Phillips October 31, 2011
(equivalent conductance at zero concentration, Λo) for
the two line segments. Remember to adjust for the
conductance of the sodium ions (one per SDS molecule,
λNa= 50.1 Ω-1 cm2 mol-1). Do the two Λo’s you obtain
make sense in light of the relative size and charge of the
micelle and monomeric SDS ?
Probe. By making use of a broken line plots of the
absorbances of the two species vs. SDS concentration will
reveal the c.m.c.
Fluorometric. Analyze the data using the recast form
of equation (5) from the introduction:
−1
  I 
CMC [So ]
−
 ln  =

[Q]N [Q]N
  Io  
(6)
have for trying to wash in seawater?
8) A common problem with probes is that they interfere
with each other; there should be one probe only in each
micelle. Consider a sample of 10mg of a probe (molar
mass 84) solubilised in 100mL of 0.08M surfactant. The
surfactant has a mean aggregation number of 70 and a
c.m.c. of 6.0x10-3M. On average, how many probe
molecules are there per micelle (what is the mean
occupation number, assuming all the probe is in the
micelles)? What fraction of micelles contain no probe?
What fraction contains more than one probe molecule?
How much probe would be needed to ensure that only
10% of micelles contained more than one probe
molecule? (Hint; use the Poisson distribution).
where [So] is the bulk concentration of the surfactant, [Q]
is the bulk concentration of the quencher, N is the
aggregation number and CMC is the critical micelle
concentration, I is the fluorometer reading corrected for
the blank reading and Io is the reading for the standard
solution. Plot the LHS vs. [So] to obtain N and CMC from
the regression values of the slope and intercept.
QUESTIONS.
1) Compare the c.m.c.’s from the two methods with each
other and, along with the aggregation number, compare
with the literature values.
2) Why does conductivity change the way it does when
the c.m.c. is reached? Do the two Λo’s in calculation 2)
make sense in light of the relative size and charge of the
micelle and monomeric SDS?
3) Suggest other techniques that may be suitable for
measuring c.m.c.
4) If the hydrocarbon core of a micelle is 3nm in
diameter and the core contains one molecule of the
fluorescent probe, calculate the molar concentration of
the probe in the core and comment.
5) Since the data is discontinuous, differentiating the
data may help find the break. How many times would you
need to differentiate to get the break as a peak? If
instructed to do so, use the Cubic Spline option in
CurveFit.
6) We can calculate the aggregation number of a micelle
if we have [surfactant], [micelles] and the c.m.c. Derive
the algebraic relation for this. (Explain your steps)
7) Explain why the NaCl changes the c.m.c. and
aggregation number. What implications do the results
© P.S.Phillips October 31, 2011
Exp. M. Micelle Properties:3
NOTES
Exp. M. Micelle Properties:4
© P.S.Phillips October 31, 2011
Suite P.
This is a suite of three miscellaneous experiments, but they
are united by a central theme of modeling (see appendix).
All experiments demonstrate a foundational principle with
fairly obvious applications, but are also useful for
demonstrating modeling, as opposed to theory. The
osmosis/permeability demonstrates two very important
processes in biology – it is a model for passive transport
through membranes and simple cells and diffusion. This
experiment is short and not terribly exciting. The wine
experiment is straightforward and is about buffering in
complex solutions and how to model them. The
experimental is easy: modeling not so much. The final one is
about glow in the dark stuff. This is a ROB experiment
where you develop the methodology. It’s straight forward, we
are pretty sure it works, and you will be given help with the
fluorimeter. It demonstrates phosphorescence, which is not
that well understood. Your data will, in principle, form a
model for the process. We then may be able to develop a
theory.
Experiment 1 Osmosis and Permeability.
Be sure to read the question section before you start; they
effect the procedure.
INTRODUCTION. Roughly speaking, a permeable solid
is one that permits the passage of materials through it. A
semi-permeable material is one that allows the passage of
some materials, but not others. Such discrimination is made
of the basis of molecular polarity or size. This is widely
exploited in chromatographic methods to analyze materials
based on size or polarity and in dialysis, which separates low
molecular weight components from solution. The latter is
used to remove waste product from blood (without
removing proteins), alcohol from wine (why?) or smoke
taint from wine. A good understanding of permeability is
necessary to understand transport across bio-membranes
and fluid movement in rocks. An important feature in
understanding permeability is osmosis, which is what drives
the materials across a membrane, and also diffusion, which
describes motion in fluids. This experiment demonstrates
osmosis and diffusion, but the focus is on permeability.
METHOD. Diffusion, permeability, osmosis are often
simply illustrated in first year biology labs. by dropping a
piece of sealed dialysis tubing, full of sucrose solution, into a
beaker of water and watching it get fat – this models what
happens when you drop a cell into water (it destroys them).
© P.S.Phillips October 31, 2011
Potpourri
We are going to exploit this to get a quantitative value for the
permeability of the dialysis tubing to water. We could use
salmon fry in salt water but it would get vetoed. No wait;
salmon are adapted to survive that. Besides they are
inhomogeneous. This is a short experiment. Note I’m leaving
a lot of details out deliberately.
A schematic of diffusion across a semi-permeable
membrane (SPM) is shown below
SPM
Water
[A]
Figure 1. Schematic of the experiment. The right
hand side represents the dialysis bag. There will be a
net transfer of water to the solution of A, in the bag.
Species A does not cross the membrane.
Here we use a semi-permeable bag (made by clipping
the ends of dialysis tubing). Water will enter the dialysis
tubing due to the concentration gradient of 10% solute,
changing the weight of the tube. The mass change will
follow some kind of exponential curve.
Do the experiment with 10%, 20%, 30% and 40%
sucrose. (Uh oh! What does 40% mean? 40g/100g solution
or 40g/100g water. Doesn’t matter, except that’s why you
should never use % or ppm as a concentration unit –it’s
ambiguous, just make sure it matches what you find in the
CRC tables for density of sucrose solutions).
THEORY. Consider the expression for general first order
kinetics (of a species S)
dnS
(1)
= − kr nS
dt
Note the use of number of moles not concentration. In
inhomogeneous systems (i.e. real ones, particularly ones
separated by a membrane, e.g. cells) this expression must be
used. This is a very important point and commonly missed.
If your reaction is not in a single container, then start all
calculations with (1). (In homogenous systems [S]=nc/V so
the V cancels on both sides giving the usual expression).
Now we need to introduce a new definition; flux, J. Flux
is the amount of material passing through unit area per unit
Potpourri:1
time so
1 dnS
(4)
JS =
A dt
where A is the area (not to be confused with a species A). By
Fick's first Law of diffusion we have
dc
(5)
J S = DS S
dz
Where DS is the diffusion coefficient and z the distance.
Thus
dnS
d[S]
(6)
= − ADS
dt
dz
Now, membranes are pretty thin, say l, so we can
approximate to D[S]/Dz using simple differences
dnSi
D[S] ADS
([So ] − [Si ])
=
− ADS
=
dt
Dz
l
(7)
Where the subscripts ‘i’ and ‘o’ denote in and out
respectively. Now we can see that our rate constant is sort of
related to the diffusion constant. This makes sense, but we
are not there yet. The concentration gradient is the gradient
within the membrane, not across it! That is the
concentrations need to be modified by the partition
coefficient, K of species S between the solution and the
membrane.
dnSi
AD K
(8)
=
− S S ([So ] − [Si ])
dt
l
This illustrates another important point; diffusion
coefficients actually don’t vary much in solution for small
species so the transport of species across membranes is
mainly dictated by the partition coefficient, that’s why these
rather mundane looking constants are so important in real
systems.
The constant DK/l is called the permeance, P, and
represents; well you tell me. (Hint, look at the units. Note
that the permeability is DK, but we don’t have l so we settle
for permeance, but some texts confuse the two). It also turns
out to be relatively easy to measure (compared to D and K).
So we get
dnSi
(9)
=
− AP ([So ] − [Si ])
dt
Replacing nSi with Vi[Si] we finally get
d[Si ]Vi
(10)
=
− AP ([So ] − [Si ])
dt
which is in terms of readily measurable parameters.
Potpourri:2
Equation (10) looks like what we would have expected from
simple kinetic arguments based on (1), except for the buga-boo of Vi. (Which is why I laboured through this
derivation).
In general, concentrations are easy to work with, but not
as easy as mass. So using []=n/V and dropping the subscript
S (In this case note that it’s water that crosses the
membrane, not the sucrose – the sucrose just provides the
concentration gradient) and using i and o to represent inside
(the bag) and outside respectively we get
n n 
dni
=
− AP  o − i 
dt
 Vo Vi 
but n=m/MW (mass over molecular weight) so
(11)
m m 
dmi
=
− AP  o − i 
(12)
dt
 Vo Vi 
where (just as a reminder) mi is the mass inside, mo the
mass outside and Vi and Vo are the respective volumes.
Next, we recognize that the m/V terms are just densities
and our observed mass is
mi ,total =mi ,water + mi ,sucrose + mtube +clips
So
dmi dmtotal
=
dt
dt
Now, if we restrict ourselves to short times and make
sure that Vo >>Vi , then both densities will be constant
providing that sucrose does not cross the membrane so
dmtotal
=
− AP ( ρo − ρi ) =
constant, Q
dt
Integrating (13) we get
− AP ( ρo − ρi ) t + R
mtotal (t ) =
(13)
(14)
i.e. a plot of total mass vs. time a straight line (it’s a zero
order process) that dead ends when the bag is empty. The
slope is − AP ( ρo − ρi ) so you can get P. The R, of course, is
just the mass of the empty bag + clips.
This derivation illustrates, very nicely, the dilemma of
applied thermodynamics. The physical chemistry concepts
needed for real systems (diffusion, permeability etc.) are
quite simple. However, the maths is much worse than in
traditional thermodynamics and is full of pitfalls; this is not
even a complicated system.
QUESTIONS
1) One parameter you need is the MW cutoff for the dialysis
tubing. What does this mean and what value does it have in
© P.S.Phillips October 31, 2011
this case.
3) Find a permeability value for a biological system and
compare it with that of the dialysis tubing.
4) Does our constant density approximation at short time
seem reasonable in light of the experimental results?
5) There is a serious flaw in the design of this experiment
for use with sucrose. What is it? How would you demonstrate
(if possible) that this flaw exists?
6) Following up on the question above. I tried this
experiment with a strong solution of polyvinyl alcohol, MW
about 30000, and also starch of a similar MW. They are
extremely viscous solutions. Would you expect the
experiment to work properly?
7) Plot the initial rate of permeation vs. % concentration of
the sucrose solutions. Would you expect this value to change
or be constant. Explain. Support your answer with numbers.
8) Define diffusion, effusion, permeation (or permeability),
percolation, porosity, osmosis, partitioning, convection and
(ion) conduction. Be sure the definitions distinguish each
process clearly. Incorporate comments on their
relationships, if any. And don’t use Wikapedia!
9) How would you test the approximation that sucrose does
not diffuse. Hint use sugar in the tube, and work out how to
analyse for sucrose. Do the experiment if time permits.
10) Plot the permeability vs. sucrose concentration and
comment. Given an explanation of the data if needed.
11) Analyze and present the data. Answer the questions. In
addition write up this experiment for a second year lab, just
the procedure. I’ve left a lot of details out.
Experiment 2. Buffer Capacity of a Wine
INTRODUCTION. (Draft) Grapes are very unusual in
that the principle acid in them is tartaric acid. In fact, they
are the only fruit that contains significant amounts of
tartaric acid.
They also have
the
highest
concentration
of sugar of any
fruit. The high
sugar levels
gives them a
propensity to
ferment
producing
alcohol or what we call wine, although some people refer to
© P.S.Phillips October 31, 2011
it as “nectar of the gods”. (Note the small “g” and the “s”.
Monotheistic religions tend to disapprove of alcohol.) The
inter play between the sweetness of the sugar, the tartness of
the acids, and the fieriness of the alcohol (ok that’s probably
just tolerated – it’s the inebriating effect) can make a
pleasant drink that plays a significant role in our social
history.
The flavor is also influenced by the grape skin (red vs.
white wines), which give them individual flavors and
determine which wines are best suited to drink with various
food. This is not just snobbery, red wine will overpower
chicken, but try a gewürztraminer with a light curry. Also,
wines from a given grape can vary from year to year and
from vine to vine. (The Dirty Laundry in Peachland has
three or four kinds of gewürztraminer). However, given that
in double blind tests so called wine experts can’t distinguish
between red wine and white wine dyed red, ones choice
comes down to three things, how much is it, how much of a
hangover do you get, and whether you like the taste.
A final comment is that wine is potable, unlike most of
the water in the Mediterranean regions. This probably
contributes to it’s popularity.
Given the influence of the balance of the acid, sugar, and
alcohol (in white wine in particular) we are going to model
the acidity of wine. Our model will be tartaric acid, malic
acid, sugar and alcohol.
The malic acid occurs in northern grown grapes making
them too acid. To raise the pH the malic acid is removed by
adding calcium carbonate (calcium malate is insoluble) or
by converting it to weaker lactic acid (there are other
methods). The latter, called malolactic fermentation,
produces biogenic amines, which are responsible for the
mild allergies some people have to red wine and some
chardonnays. If I could find out which wineries did this I
would avoid their wines. Note that there is an interplay
between alcohol and sugar. Low sugar and a long
fermentation would leave little sugar and all the acid. High
sugar and long fermentation gives you high alcohol (14%)
and some sugar, but in my experience it taste pretty foul. (It’s
interesting to take a dry wine – high acidity – and add sugar,
alcohol, and change the pH –with chalk or food grade NaOH,
and see how it effects the taste. Sugar of course sweetens it,
alcohol can make it “chemically”, and most interesting,
raising the pH makes it flat and bland. Unfortunately, we
have a bureaucratic ethics committee that prevents us from
doing this experiment.)
Probably the most important determinant in the basic
flavor of a white wine is the pH so we will model our wines
Potpourri:3
using mixtures of tartaric acid and malic acid and their
potassium salts. Potassium is the most prevalent metal ion
in grape juice. Sugar doesn’t seem to affect pH, but we need
to quickly verify that, but alcohol does, although the
mechanism is not understood. We will look at that briefly.
So here’s what we will do. Will measure the pH of an
unbuffered solution of tartaric acid and see how it changes
the pH. We will get a titration curve for tartaric acid and
make sure we can find its two pKa’s. Then we’ll mix in some
malic acid and see what that does to the titration curve.
Then, we add in some potassium hydrogen tartrate (Make it
from tartaric acid and KOH then add in more tartaric acid
and malic acid.) We will use quantities commensurate with
a typical must (the crushed grape mix used for making a
wine). Finally we will titrate a red wine. We will use red wine
because it adds some interest when using a pH meter to do
titrations. We will do the titrations over a wide range
because we want to get some insights into pH changes in
moderately complex systems. To be specific we want to look
at buffering.
Buffering is important in biological systems so that
minor changes (say increased CO2 in the blood when
exercising) doesn’t cause wild pH fluctuations. It’s similarly
important in environmental systems. A poorly buffered lake
cannot tolerate much acid rain without its pH plummeting
and killing all the fish. In wine, buffering effects the palette.
A poorly buffered wine will shift pH in the mouth, affecting
its flavor. There are other important effects as well, but they
are beyond the scope of this discussion. How little a system
changes pH when acid is added is called the buffer capacity.
One of the problems about buffers is that if you look
them up in a biochemistry text the authors will waive their
arms and refer you to a physical chemistry text. If you look
in a physical chemistry text, you will rarely find an index
entry for buffers. Sometimes you will find an entry under
acid-base equilibria. Even then, you might find they refer
you to a biochemistry text. Anyway, if you want some
background you will have to hunt around.
PROCEDURE. Let’s do some experiment design. Our
auto-titrators are tied up so we want to minimize our
titrations. We don’t want to measure a whole titration curve
(pH 3-13) every time so let’s look at what we need. You may
need to fill in some experimental blanks.
These are simple pH titrations. First, you will need to
calibrate the pH meter, using the provided standard buffers
- pH 2.00, pH 7.00 and pH 9.00 or 10.00 (You may need
help with this unless you have a pre-calibrated meter; ask
the instructor).
Potpourri:4
You may have to let the pH meter stabilize between
readings. You should be able to get stable values to +0.01 pH
units). Make sure you collect data beyond the end-points to
get a good “baseline” (see fig.1). Don’t forget your 0mL pH
reading.
We want to see if there are significant impacts on the
activity of the acids by alcohol and sugar to see if we need
them in our model system. If there are then we need to get
our corrected pKa’s but for now we can do as follows. Make
up 500mL 7.0g/L solution of tartaric acid. Split it in five (use
a 100mL pipette – that’ll be good enough) samples. Take
two samples and pipette (graduated pipette) or titrate in
three 6mL aliquots of water to one sample, measuring the
pH at each stage (four pH measures) – this is your control.
Now repeat with alcohol. Plot the data against each other.
Any deviation from a straight line of slope one means the
alcohol affects the pKa. To test the effect of sugar just add
10g to 100mL of the acid solution in a measuring cylinder
(you’ll have one sample for a spare), then measure the pH,
and record the volume. then add another 10g and get the pH
and volume again. 20g of sucrose That’ll give you two pH’s
measures. Show me your data. The question then becomes
how much and how do you calculate the pKa from the pH.
We’ll worry about what to do with the data when we see it.
Next we need to get the composition of our wine sample
so we need to do HPLC to get the tartaric and malic acid
concentration. We also need to get the mono-cation
concentration. No wait: you are doing this course to avoid
analytical chemistry. If you really want to try this, you can, I
have some papers; we should have the columns. Instead,
we’ll assume it’s a typical wine and just do the titration
curve up to about pH11 (it should be about pH3.4 to start.
and get it’s shape and measure the buffering capacity.
Now Next we just make up our model wine to compare
the real wine with. Take 7.00g/L tartaric acid, 5.00g/L malic
acid and 1400ppm of potassium ions (as KOH) and do the
titration curve up to about pH11 using 0.25M KOH in 0.5mL
increments. Get it’s shape and measure the buffering
capacity. The curve is broad so you don’t have to use small
increments.
Finally, we will titrate a red wine with the 0.250M KOH
to pH11. (Buffer capacity is more important in white wines,
but that’s for drinking. Red is only suitable for dyeing cloth
and chemistry experiments.). Smell the wine before and
after titration.
CALCULATIONS. Now how are we going to interpret
this data? For the influence of sucrose and alcohol samples
simply set up an ICE box to get the pH at the various
© P.S.Phillips October 31, 2011
concentrations (remember an ICE box works with moles not derivative off your differential graph. The buffer capacity
concentrations). Compare your results with the calculated (for the purposes of this experiment anyway) is the
results. Plot graphs as needed. Tables are good to.
reciprocal of that value. Get the buffer capacity of the wine
The alcohol should have a small effect. Redo the at the pKa of acetic acid (when wine goes off it generates
calculations assuming that the alcohol doesn’t affect the acid acetic acid), pH 3.4 (a typical wine pH) and pH 6.8 (pH of
concentration. Alternatively assume the alcohol dilutes the the mouth).
water, so five mole% water will shift the hydrogen ion
concentration by 5% (you’ll need to show me how I did that
calculation). If that doesn’t work, speculate how alcohol may
influence the activity of the acid. Hydrogen bonding is an
obvious choice, but sucrose does that as well, but you should
find that it does not change the pH.
Non-polar solutes tend not to change the activity of
other species in solution, so we should not see an effect.
However, the concentrations used here will affect the activity
of water re: osmotic pressure so there may be an indirect
effect. We could measure the pKa using a conductiometric
titration, but I suspect for high sucrose concentrations we
would see an effect (not the effect mentioned above). Why
do you think I suspect that?
Buffering capacity is important. It tells us if the wine is
likely to shift in taste as it ages (as the acids change). Also,
Figure 2. Titration of a diprotic acid. The two pKa’s
the mouth is alkaline, a poorly buffered wine will shift in
are determined from the pH at the ½ equivalence
taste with each mouthful if it’s poorly buffered. The buffer
points (e.g. ½V2 and pK2 on the diagram). Note ½V1
capacity is simply a measure of how well a solution resists
(not marked) is ½ way between 0 and V1. ½V2 is ½
pH changes when acid or base is added. Typically for a wine
way between the two equivalence points – this is the
it’s the amount of KOH that needs to be added to raise the
buffer zone.
pH by one point (and is bizarrely expressed in equivalents of
tartaric acid). We will take a physical chemistry approach. MODELING. We can compare the shapes of the titration
It’s simply the differential of titration curve. Close to zero curves to see if our model is reasonable. They will not match
means a high buffer capacity in that region. The bigger that because the compositions are different, but the overall shape
region, the better the buffering. The width of the region as should be the same. To test this properly we need to be able
defined by some convenient parameter is the buffer capacity. to match our compositions. However, we are just after
insights, we can skip the chemistry altogether and simulate
See the glycine experiment on how to differentiate data.
If you want a simple reminder of the effects of buffering the titration curves. This is the physical chemistry bit. ICE
take 50mL of water stick a pH electrode in, measure, and will not work so we have to start from the ground up.
then and add 1mLof 0.25M KOH, it should shift the pH Diprotic acids dissociate as follows:
about 3 units. Repeat the experiment with pH 7 buffer. There
K1
K2


H2 A 
H + + HA- 
H + + A 2should be little effect.
1) Determine the end-point and hence the two pKa‘s of where
a +a a + a 2the acid directly from a plot of pH vs. VHCl. (Use the
H HA
=
K1 =
K2 H A
Henderson-Hasselbach equation – look it up). Also refer to
aH2 A
a HA
the figure 2 below.
a
is
the
activity
which
we
will
approximate
to
2) The buffer capacity can be calculated from the inverse
of the differential of the titration curve. Typical results are concentrations and ignore the fact that pH electrodes
shown in figure 1. To get the buffer capacity at a certain pH actually give the activity. We will have another two equations
use your titration data to find the volume corresponding to for the other acid.
K1
K2
the desired pH. Then use that volume to read the value of the


H2 M 
H+ + HM- 
H + + M 2© P.S.Phillips October 31, 2011
Potpourri:5
K1
a +a a + a 2H HM
=
K2 H M
aH2 M
a HM
Next we invoke mass balance
[H2 A]total = [H2 A]+ [HA-] + [A 2-] and
[H2M]total = [H2M]+ [HM-] + [M 2-]
Now we get to the bit that may be new to you, charge balance
[K + ]+ [H + ] = [OH - ]+ [HA-] + 2[A 2-] and
[K + ]+ [H + ] = [OH - ]+ [HM-] + 2[M 2-]
Note the potassium ion because we need potassium
salts to model our wine. We can ignore the hydroxide below
pH 7 (why?). You can get the hydroxide concentration from
[H + ][OH − ]=K w = 10 −14
I’ve never done a simulation past pH 6 so I’m not sure if
Maple stays stable in this region; i.e. with this equation
added in.
Since we make up our own solutions we have the total
amount of acid and potassium (we include the potassium
counter ions in with the total acid). We now have seven
equations and seven variables. If you rearrange this you end
up with cubics in [H+]. This is where Maple (or whatever, I
haven’t had any success with MatLab or MathCad though).
comes in it can solve this kind of thing easily, but there are
two problems. The first is that Maple is quite general so it
will give you all three solutions for the [H+]. You have to
make sure you get the real +ve root only. You then have to get
Maple to generate all the concentrations for given starting
values, in a nice table or an array. To do that you have to put
everything in a loop. Finally, you have to get Maple to plot it,
although it might be easier to cut and paste your table into
Excel. Ask me for my Maple hints page.
SAFETY NOTES. HCl, KOH and NaOH solutions are
corrosive. Use with caution. Wine is toxic if ingested in large
amounts. The symptoms are too well known to bother
describing here. Stealing the wine stock bottle is even more
hazardous. Symptoms include loss of dignity, credibility,
marks, and external organs.
Experiment 3. Luminescence.
Don’t do this unless instructed to do so.
Basically we will take three samples. Illuminate them at a
high frequency (blue light), cut that off, that’s the tricky bit,
and then observe the sample at a lower frequency in a
fluorimeter. Sample one is a strip of “Glow in the Dark”
paint. (In an alternate reality you would have to prepare the
Potpourri:6
paint – copper doped zinc sulfide; we just want to do proof
of principle.) Mount it a 45o and get the light intensity as a
function of time. You may need to “prime” the paint with a
light bulb rather than the fluorimeter. You’ll have to check
that out. The decay may consist of two parts so you will have
to do some kind of stripping as described in suite K. Repeat
the experiment with the supplied europium salt. (In another
alternate reality you would have to prepare the salt.) Then
repeat the experiment with a terbium EDTA complex which
you will make from terbium chloride and EDTA. I suggest an
small excess of EDTA because Tb3+ alone phosphoresces,
albeit much more weakly. Furthermore is TbCl3.xH2O, you’ll
need a work around for the “x”. Write it up and tell me
what’s going on in the experiment and about
phosphorescence in general. Remember, I don’t know what’s
going on so a clear and informative report earns lots of
brownie points.
Why did we do a phosphorescence experiment instead of
fluorescence experiment? Fluorescence has more scientific
applications.
SAFETY NOTES. None of the materials have noted
toxicity, but it would be a poor idea to eat them or slather
yourself with them.
APPENDIX. Modeling, Theories, Laws,…
A theory a set of statements or principles, often
expressed as equations or laws, and occasionally postulates,
devised to explain a group of facts or phenomena. To be
accepted as a theory, as opposed to cacodoxy, it must have
been be repeatedly tested and can be used to make
predictions about natural phenomena.
A model is schematic description of a system or
phenomenon that accounts for its known or inferred
properties, and may be used for further study of its
characteristics. A model may be a simplified version of the
system. This makes studying it more tractable and enables
you to deduce the critical elements. A model can be a
physical system or software.
A simulation is done entirely with a computer. The input
information is the theoretical equations and maybe some
constraints. There is no reference to real data, although it
may be compared with data at the end. This is useful for
spectral analysis where the theory and constraints are well
known and the solutions tend to be unique. Some believe
that computers can substitute for an experiment. They can
be a useful as a starting point, but eventually you have to get
your hands dirty.
© P.S.Phillips October 31, 2011
There are fuzzy areas. Generating a straight line is a
simulation. A least squares fit to a straight line is a model –
the model being that the data is linear. An equation that is
part of a theory could of course be of the form y=mx+c.
Anyway, a model is a route to a theory, but there is no real
requirement for prediction, or laws, or for it even to be a
physical entity. They tend to be used for multipart or
complicated systems where the interrelationships are not
always known. They are useful for eliminating or
determining those relationships. The use of computer
models without experimental verification is just plain
stupid. Simulations are ok for well-defined systems, but
given that the early models for the weather led to the
discovery of chaos theory. You can see how much you can
become unstuck. Anyway, they are an important and a
powerful tool if handled with care.
The models here are just simplifications of real systems.
The osmosis model tends to breakdown because of
something called active transport (there are pumps in the
membranes). The wine model can be extended successfully
to much more realistic versions of wines, but in the end a
vineyard is just a farm with a marketing manager: they are
not interested in computer models. The phosphoresce
experiment is a little simpler. We analyze the data using a
model based on kinetics and all that implies. There is, a
priori, no reason to believe that photochemical data will
conform to kinetic equations.
© P.S.Phillips October 31, 2011
Potpourri:7
3
Potpourri:8
© P.S.Phillips October 31, 2011
Exp T. MYOGLOBIN TRANSITIONS
INTRODUCTION. There are four levels in the
hierarchy of protein structure that are recognized. They
are: primary – the linear sequence of amino acids;
secondary – the regular, recurring orientation of the amino
acids in a peptide chain due to H-bonds; tertiary- the
complete 3-D shape of a peptide due to weak dipoledipole interactions, p-stacking and van der Waal’s forces;
and quaternary – the spatial relationships between
different polypeptides or subunits.
Figure 1. 3-D ribbon diagram showing the
structure of myoglobin, with extensive a- helices
and haem binding site, undergoing a transition to a
b-pleated sheet.
Myoglobin is a metalloprotein that acts as a temporary
storage of oxygen needed for aerobic metabolism in
muscle. Like hemoglobin the oxygen binds at a heme site
containing iron. Unlike hemoglobin it is a monomer (it has
no quaternary structure); hemoglobin is a tetramer and can
carry four dioxygen molecules. Here will investigate
changes in the secondary and tertiary structure of
myoglobin. Common types of secondary structures include
a-helices, b-pleated sheets, random coils and b-turns,
usually in various amounts. Myoglobin is unusual in that it
consists almost entirely of a-helices. Myoglobin is
characterized as a globular protein; its tertiary (3-D)
structure consists of eight a-helices which fold in such a
manner that most of the hydrophilic groups are on the
outside of the protein, facing the aqueous environment
(what else would a hydrophilic group do?).
The hydrophobic groups are, as expected, mainly inside
the protein. The hydrophobic effect plays a large role in
maintaining the stability of the folded protein. Anything
that disrupts the hydrophobic effect will change the protein
structure. Here we will primarily look at the effect of
© P.S.Phillips October 31, 2011
temperature. Remember, ∆G=∆H-T∆S and since the
hydrophobic effect is an entropic one, it’s clear that
temperature will affect it. We will also look the effects of
SDS, guanidinium·HCl and pH.
METHOD. By using model compounds, amino acids,
and proteins to classify the IR spectra of proteins,
biochemists have found the most useful vibrations to be
the C=O stretch (amide I, 1655cm-1), N-H bend and CN stretch (amide II, ~1550cm-1) of the polypeptide
backbone. The variation in absorbance spectra of proteins
with different secondary structure (and to some extent
tertiary structure) is due to the characteristic hydrogenbonding patterns of the C=O and N-H bonds. For a
protein that is predominantly a −helical, IR spectra show
amide I peaks centered around 1650 cm-1. Proteins mostly
composed of b-sheet conformation show maximum
intensity around 1640 cm-1. Random chain proteins have
an amide I peak around 1643 cm , and denatured and or
aggregated proteins show absorbencies around 1610–1628
cm-1.
One problem of IR spectroscopy is the strong absorbance
of water in the amide I region. However, if very short path
lengths are employed, spectra can be obtained in water.
We can also shift the water absorbance by making use
of the isotope effect. If we measure the spectra in
deuterium oxide there is a ~400 cm-1 shift of solvent
vibrations to lower energy. Furthermore, the use of D2O
allows greater distinction between a-helices and random
coils as the latter has a larger shift upon deuteration.
Amide I peaks shift about 5-10cm-1, but the amide II
peaks shift about 100cm-1. The tertiary structure will also
influence the position of these vibrations: a-helices are
around 1650cm-1 when buried inside the protein and shift
down to 1635cm-1 when the helix is solvated; aggregated
proteins often display intermolecular anti-parallel bsheet structure with distinct sharp bands showing up at
1615 and 1685cm-1.
We will use IR spectroscopy to monitor these peaks and
how they change as a function of temperature, pH, and the
effect of H-bond disruptors. We will also compare
myoglobin with two other proteins: chymotrypsin and
lysozyme.
PROCEDURE. We will use FTIR coupled with either an
ATR attachment or a short path-length IR cell with
calcium fluoride windows and a 25mm spacer. The
EXPERIMENT G:1
comparison of the different denaturants and protein
solutions will be carried out using the ATR, while the
temperature denaturation of myoglobin will be performed
in the short-path cell. We will use 10-20mL sample of
about 60mg/mL of the appropriate protein in deuterium
oxide. The protein stock solutions must be stored on ice.
Solutions of myoglobin in 160mM SDS, 3M
guanidine·HCl or pH 2 buffer made with H2O or D2O, may
also be supplied along with solutions of other proteins.
These samples need only be 0.1mL. Make sure you have no
air bubbles in the cell.
If possible use two water baths: one you take your sample
from and one heating up to the next temperature while you
are taking the spectrum. (If it’s an Isotemp bath be sure to
set the safety cutoff knob to maximum.)
For the ATR samples, the experiment is very simple. Place
10-20mL of a blank on the ATR crystal and measure the
background using 25-50 scans and a 4cm-1 resolution
(or as instructed).
Overlay all the temperature spectra on a single plot
from 1300-1800 cm-1. This will allow you to identify the
positions of largest change.
Repeat with 10-20mL of your sample. Collect all your
data as absorbance spectra (rather than the more familiar
transmission spectra). This will enable you to compare
peak intensities directly and calculate difference spectra.
Clean the crystal with a small amount of methanol after
every run and be sure to allow the crystal to dry thoroughly
before running your next sample. Measure IR spectra of
myoglobin in 3M guanidinium·HCl, 160mM SDS and at
pH2. Remember to take blanks of the appropriate solvent.
Measure the IR spectra of each of the other two protein
solutions provided. It would be interesting to see if the pH
effect are reversible by adding NaOD until the pH is 7. We’ll
skip that for now.
When all the ATR runs are complete, remove the ATR
attachment (ask for help) and install the cell holder in the
sample compartment. For the variable temperature run, fill
the cell with D2O buffer first and measure a background at
room temperature. Use this room temperature blank for all
subsequent temperature runs.
Fill the cell with myoglobin sample and take a room
temperature spectrum to compare with the other spectra.
For the temperature series, Place the cell inside a zip-lock
bag and submerge the bag in the water bath. Try to keep
the cell from getting wet as the water vapour from
evaporation in the FTIR will cause problems. The cell
should stay in the bath for at least 15 min to let the
sample equilibrate (see the appendix). The temperature
range should be 45C to 85C (see the safety note) –
choose equally spaced temperatures (about every 8-9
degrees) but make sure that you will have enough time
(about 20 minutes per temperature point) to get to 85C.
© P.S.Phillips October 31, 2011
Remember to save all your spectra in csv format. Bring a
USB drive so you can take it home.
CALCULATIONS. This consists of two parts:
determining the transition temperatures for myoglobin and
identifying the main contributors to the secondary
structure of each protein.
You should also try difference spectroscopy. Subtract your
room temperature myoglobin spectrum from the other
myoglobin spectra and plot an overlay of the subtracted
spectra from 1300-1800 cm-1. This should highlight the
appearance of the intermolecular antiparallel b-sheets.
The a-helices will probably appear as –ve peaks, but the
quantitative relationship is retained.
To find the transition temperature, plot the absorbance at
selected frequencies vs. incubation temperature. The
amide I peak is an obvious frequency to try, but you
should try a few others and compare the results. Does the
transition temperature depend on the peak chosen?
For other spectra you should try to identify the main
changes in the tertiary structure. Calculating the second
derivative of the spectra may help, but then the
quantitative relationships become unclear. Find literature
values if possible. Tabulate your results.
QUESTIONS/DISCUSSION. The questions and
discussion are somewhat interlocked so read this whole
section before proceeding.
How do we know that the transitions we see are due to the
unfolding of helices? Well it’s historically the other way
round; we know there are helices because they unfold –
there is a phase transition! Nowadays we can get good
structures of hydrated proteins from X-ray
crystallography, but even then you need to know that there
are helical structures to solve the diffraction patterns. What
you will do to complete this experiment is to explore the
enzyme structures using modeling programs and use them
to study the folding/unfolding based on the structures. The
programs interfaces, and there, capabilities are all different
so that is discussed in another document provided on-line.
EXPERIMENT G:2
Play with the various programs (note the plural: playing
with different methods of data analysis is part of the
course). Print up a couple of pictures of your compounds
that make the structural differences clear.
That was fun wasn't it? The PDB ProtienWorkshop (and
other programs) have some nice visualization features.
Conformation Type and Hydrophobicity are the two that I
find of most interest. Hydrophobicity: To a first
approximation the proteins will fold (if sufficiently
hydrated) to a structure where the hydrophobic regions are
on the inside and the hydrophilic (least hydrophobic) are
on the outside. Do the structures you see conform with
those expectations? Cross check with other programs. The
ones showing surface hydrophobicity may help.
REFERENCES
1. F. Meersman, L. Smeller, K. Heremans Biophys. J. 82,
2635-2644 (2002).
2. See help sheet for the PDB programs on the course web
site.
APPENDICES.
INFLECTION POINTS. To determine the inflection
point of a sigmoidal curve dy/dx vs. x. (here y is
absorbance and x temperature). Setup Excel to do a simple
derivative using dy / dx  ( yi1  yi )/(xi1  xi ) Typical
results are shown in figure 2. The inflection point is the
maximum of the derivative.
Conformation: The conformation types are listed in PDBWS are Turn, Helix, Coil, Strand. The elements I'm familiar
with are a-helix, Random Coil, Chain and b-pleated
sheet, ribbon. So help me out here; what's what? What’s
with the a and b? Be sure to explain things in terms of
structures and intermolecular interactions (H-bonding,
sulphur bridges, Pi stacking, hydrophobicity etc.)
Also, some of the programs (Ramplot and Swissplot) have
options for Ramachandran plots which seems a neat way of
sorting out the different structural types. So what are
Ramachandran plots (Wikipedia is as good as any place to
start)? Apply them to the species you studied.
At room temperature the more ordered helical structure
exists in preference or the less ordered b-sheet, or more to
the point a random coil. This would appear to violate the
Second Law, but it doesn’t; explain. (i.e. explain the
transitions between helices and whatever in terms of
enthalpy and entropy, as well as intermolecular
interactions.
Rationalize the spectral changes you saw in terms of
structural changes (and accompanying changes in
intermolecular interactions) with pH, guanidine, SDS and
temperature.
See if you can find an X-ray structure of myglobin above
it’s transition temperature (i.e. above 90C). Print it out.
SAFETY NOTES. The maximum safe temperature for
domestic water is 50C. Water at 80C will definitely
scald you, so be careful with the water bath above 50C.
Make sure you do not use a plastic water bath. pH 2 buffer
is no fun in the eyes. The rest of the stuff is pretty benign,
but don’t eat it, it’s too expensive.
© P.S.Phillips October 31, 2011
Figure 2. Figure 2. Typical sigmoidal curve and its
differential. (It’s for a electrochemical titration in
this case).
EQUILIBRATION TIMES. The experiment may
seem strange; we spend 15 min equilibrating a tiny
sample, and then stick it into a room temperature FTIR
sample compartment. You are able to do this because
t h e t r a n s i t i o n s a r e s l o w . In some cases the
transition is actually irreversible e.g. boiled eggs. Many
proteins are destroyed by heat, pH changes or H-bond
disruptors. This is called denaturation and is a result of
aggregation, polymerization or folding. Some show “real”
phase transitions (i.e. reversible changes). However, you
should note that such changes are intra-molecular not
inter- molecular, that is, they are changes in molecular
structure, not macroscopic structure. So even though the
proteins are in solution, these phase changes are
essentially solid-solid (or in the case of membranes, gelgel) transitions, which are very slow. Long equilibrium
times are required, >15min, even for tiny samples. You
are not just trying to bring the sample up to temperature –
you have to wait for the transition (in either direction).
EXPERIMENT G:3
© P.S.Phillips October 31, 2011
EXPERIMENT G:4
USING THE PROTEIN DATABASE (Draft. Report any problems to me.)
Sign onto www.rcsb.org with you web browser. The home page is shown below. As you can see it is very
cluttered there are only two points of interest – see comments to right.
Comment [PSP1]: This
button leads you to a list of
important proteins and their
stories.
Comment [PSP2]: This the
search bar. Type the name of
the molecule here. Watch you
spelling. You can also use the 4
letter code.
This is what you get lots and lots of stuff (336 structures). You need to narrow it down.
Comment [PSP3]: Click on
items in the list. For us
organism and method are good
lists to use to narrow stuff
down.
I selected humans and a 1-2 resolution X-ray structure. You still get tons of stuff and need to scroll through
items at the bottom of the page until you get the one you want. Here we have two or three examples with the
same information. Plea ignorance (i.e. say you are a chemist) and select one. In this case exceptional ignorance
as somewhere it decided to insert hemoglobin into the myoglobin list. Better go find that 101 button at the top.
Anyway lets click on 2HHb, or more specifically the the title next to it.
Comment [PSP4]: Yay! Our
first Windows 7 pop up. This
one is insidious as it can pop up
under the window not on top,
so don’t touch the keyboard or
mouse once you hit that title
bar. Just click run. Do not check
the box or it won’t work. This is
for IE9 under Windows 7. Other
OS’s/browsers may behave
differently.
A picture at last. I’ve scrolled down so we can see the bottom menus. These give some interesting views,
especially under the surface options. We’ll get back to that later.
There are other viewing options so let’s scroll back up to see them.
Comment [PSP5]: Here’s our
other options. Simple and other
viewers are simple. Protein
Workshop gives the best
pictures. Jmol is the default
one.
The Workshop option has a couple of wrinkles.
Comment [PSP6]: After
dealing with the popup below
click here to launch the
workshop.
Now wait for Java to load. It’s called Java because you have to go to coffee while it loads. I think it should be
called C2 (crippled computing) although this applet seems to be well programmed. Anyway after you’ve done
this a few times you will want to try off-line programs such as Jmol, Pymol, Ramplot, and SwissView are some.
I can put them on disk or they maybe emailable, or you can find them online. To be able to use them we have to
download the data files To do that find the download menu.
Comment [PSP7]: Click on
save. It’s a little java snippet
that can be delete later. There
maybe other popups when you
first run the workshop because
it installs itself on your
computer
Comment [PSP8]: The
download option is a dropdown
menu. Save the files using the
PDB file (Text option) then hit
save when the popup appears
at the bottom.
Before we go on and discuss the viewing programs (Jmol, Pymol, Ramplot, and SwissView) in detail here’s a
few pointers.
The online Jmol is mainly a viewer but it has some dropdown menus at the bottom that make it a very
interesting viewer. I love the way it refers to the standard text book view for proteins as cartoons.
The offline Jmol is just the simple viewer in the options list. If that’s what you want go for it.
Kiosk (the “other” viewer) makes a good screen display for open house.
The Protein Workshop is a supped up viewer. I think it give the best pictures. There are a few bells and whistles
I have checked out yet. When you first run it it installs itself on your computer.
I my humble opinion Pymol is garbage.
RamaPlot (Ramchandran Plot Explorer) is possibly the most interesting. It’s old and the visualization is not
fancy but it seems to give stuff other programs don’t, or at least the kind of stuff relevant to this course
SwissView (Swiss-PDB Viewer) Lots of options but no fancy pictures.
Qutemol is interesting if you want to see the importance of lighting and shading when rendering 3D molecules.
For other options see
http://en.bio-soft.net/3d.html
http://www.pdb.org/pdb/static.do?p=software/software_links/molecular_graphics.html