Chemistry 311
Lecture Notes
Fall 2009
David E. Henderson
Chem 311
Chapter 2 & 3
How do we measure things
RECORDING DATA - USE OF
SIGNIFICANT FIGURES
• INTEGERS (Things you count)
– ALWAYS EXACT VALUES eg.you did the
experiment three times.
• Precision of these numbers is infinite.
• REALS (Things you measure)
– ALWAYS CONTAIN AN UNCERTAINTY.
• Assume error is +/- 1 in the last place unless specified.
• For the number 1.0034 the actual value lies between
1.0033 and 1.0035.
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2
METHODS FOR
EXPRESSING
UNCERTAINTY
• ABSOLUTE UNCERTAINTY.
– Buret reading 40.34 +/- .01 ml
• RELATIVE UNCERTAINTY.
– 0.01 ml/40.34 ml = .00025 relative
• .00025 * 100% = .025% rel.unc.
• .00025 * 1000 ppt= .25 ppt rel.unc. = 0.2 ppt
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SIGNIFICANT FIGURES
• KEEP ONLY THE FIRST UNCERTAIN
DIGIT IN A RESULT.
• Assume that data is presented this way
by other responsible scientists.
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SIGNIFICANT FIGURES
• ROUND OFF SUPERFLUOUS
DIGITS.
– 5 ROUNDS UP IF ODD DOWN IF EVEN.
• Thus the result of rounding the digit 5 is always
a number ending in an even digit. eg..435 =>
.44 .425=> .42
– Round off only once
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SIGNIFICANT FIGURES
• ADDING OR SUBTRACTING
– KEEP ONLY THE NUMBER OF DECIMAL
PLACES IN THE LEAST PRECISE
RESULT.(Remember these numbers will
always have the same units.)
– Note- the number of significant digits in a
number can change dramatically in
subtraction.
•
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SIGNIFICANT FIGURES
• MULTIPLYING OR DIVIDING
•
• Rule of Thumb – Keep the same
number of significant digits in the result
as in the value with the lowest number
of sig. Figs.
• This often doesn’t work out
• 101/99 = 1.02 Chem 311 Fall 2009
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7
SIGNIFICANT FIGURES
• COMMON ERROR 0.7834 gm KHP =
0.0034 moles KHP
• This error appears in far too many lab
notebooks.The student has taken a
number with a relative uncertainty of
1/7800 and reduced it to a number with
an apparent uncertainty of 1/34.
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Common error
• 1.234*(40.35-40.31)=0.04936
• How many significant figures should we
have?
• 1.234*0.04= 0.04936
• 0.05
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SIGNIFICANT FIGURES
• DURING CALCULATIONS
– ONE ADDITIONAL INSIGNIFICANT DIGIT
SHOULD BE CARRIED IN
INTERMEDIATE RESULTS.
• EXCEPTION.The calculation of sums
and sums of squares requires you to
keep all digits
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LOGS
• log consists of two parts,
– characteristic
• eg.pH=1.03 characteristic = 1 mantissa = .03
• The characteristic is a power of ten and is an
integer (counting decimal places).
– mantissa.
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• Measured value - real
• The significant figures which denote the
uncertainty of the value are those in the
mantissa.
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LOGS - General rule
• Number of Sig. Figs is number of digits to
right of decimal
• A two digit mantissa corresponds to a relative
error of approximately 2%,
• A three digit mantissa to 2 ppt, etc.
• EXAMPLE
– pH 1.03 [H+]=9.3x10-2
pH 13.03 [H+] = 9.3x10-14
•
1.02 < pH < 1.04
• 9.1x10-2 < [H+] < 9.5x10-2
9.5x10-14
13.02 < pH < 13.04
9.1x10-14 < [H+] <
• Note that the relative uncertainties are the
same.+/- 2/93 = 2% rel.unc.
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SIGNIFICANT FIGURES
The Correct Way
• Uncertainty of sum or difference
y  abc
s y  sa  sb2  sc2
2
• 40.34 ml +/- .01 ml
• -1.03 ml +/- .01 ml
• 39.31 ml +/-0.014 ml
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0.0002  0.014
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SIGNIFICANT FIGURES
• MULTIPLYING OR DIVIDING
• UNCERTAINTY OF THE RESULT IS
THE SUM OF THE RELATIVE
UNCERTAINTIES.
a *b
y
c
2
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2
s  s  s 
s y   a    b    c 
a   b   c 14
Chem 311 Fall 2009
2
SIGNIFICANT FIGURES
•
•
•
•
•
EXAMPLE
21.1 * 0.029 * 83.2 = 50.91008
Relative Uncertainty
0.1/21.1 0.001/0.029 0.1/83.2
0.0047
0.034
0 .0012
.0047 2 + .034 2 + .0012 2  0. 034
• .03 * 100% = 3% rel. unc.
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CALCULATION OF
MAXIMUM EXPERIMENTAL
ERROR.
• The sum of all errors is best approximated by adding
the squares of all errors and taking the square root of
the resulting sum.
– Follow each step in the procedure
• Add the square of the absolute uncertainties
during addition and subtraction.
• Add the square of the relative uncertainties
during multiplication and division.
– You should obtain an absolute or relative
uncertainty for the final result.
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CALCULATION OF
MAXIMUM EXPERIMENTAL
ERROR -Examples.
• Addition and subtraction
– Volume of titrant = Final buret reading initial reading
• V= 43.24 ±0.01 ml - 0.23±0.01 ml =
43.01 ml
error  0.01  0.01  0.014 ml
2
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CALCULATION OF MAXIMUM
EXPERIMENTAL ERROR Examples.
• Multiplication and division
– Molarity of titrant = grams acid*(mol / gm)/vol. titrant
M  0.5675  .0001 gm 
1 mol
1
1l


204.23  .02 gm 43.01  0.014 ml 1000 ml
• M=.0646066 Mol/l
error 
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(
0.0001gm 2
.02gm  mol
0.014 ml 2
)  (
)2  (
)
.5675gm
204.23 gm  mol
43.01 ml
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CALCULATION OF MAXIMUM
EXPERIMENTAL ERROR Examples.
error 
(
0.0001gm 2
.02gm  mol
0.014 ml 2
)  (
)2  (
)
.5675gm
204.23 gm  mol
43.01 ml
• error = 0.00038 = 0.0004 relative error
• 0.0004 * 1000 = 0.4 ppt
• 0.0004 * 0.0646066 Mol/l = 0.0000258
Mol/l
• M = 0.06461±0.00002 mol/l
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SIGNIFICANT FIGURES
Other Functions
Partial Derivative Calculus- how does y change
with small changes in the value
of the measured quantity ‘a’
y  ax
sy
s
x a
y
a
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y  log(a)
sa
sy 
2.303a
y  10 a
sy
 2.303sa
y
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Stoichiometry
• Reactants and Products related by
Coefficients
• Many Analytical Procedures relate analyte
to a reaction product or another reactant
• Titrate HCl with NaOH
• H+ + OH-  H2O
– Measure OH with buret
– Moles OH = moles H
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Stoichiometry
• Conservation of Mass
– Mass of each atom is conserved in all Reactions
• Types of Reactions
–
–
–
–
Acid Base = Protons Conserved
Redox = electrons conserved
Complexation = electron pairs conserved
Precipitation = Charge conserved
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Stoichiometry
• Conservation of Mass
– C4H10 + O2  4 CO2 + 5 H2O
– Moles CO2 = 4 x moles C4H10
– Moles H2O = 5 x moles C4H10
– 2 x Moles H2O = 10 x moles C4H10
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Stoichiometry Example
Anabuse
•
•
•
•
C10H20N2S4 + oxidizing agent  4 SO2
SO2 + H2O2  H2SO4
H2SO4 + 2 NaOH  2 H2O
Measure moles of NaOH (buret)
moles NaOHx
1molH 2 SO4
1molSO2
1molAnabuse
x
x
2molNaOH 1molH 2 SO4
4molSO2
 mol Anabuse
• Overall Ratio 1:8
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A Look Inside What We Do
• Usually don’t talk about these things
explicitly.
• Need to convert quantities into NUMBERS
– Counting - M&M colors
– Numbered Scales - Buret
– Digital Displays - Balance
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Resolution
• How finely can the quantity be measured
• 4 place balance - Resolution ±0.0001 gm
• Sartorius balance - Resolution ±0.00001 gm
• 50 ml Buret - resolution ±0.01 ml
– Relative resolution depends on quantity
measured
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Relative resolution uncertainty of measurement
• 1.0000 gm weighed on the balance
• ±0.0001/1.0000 * 1000 = 0.1 ppt
• 150.0000 gm weighed on same balance
• ±0.0001/150.0000 * 1,000,000 = 0.7 ppm
• 0.0100 gm
• ±0.0001/0.0100 * 1000 = 10 ppt
• 30.00 ml titrant
• ±0.01/30.00 * 1000 = 0.3 ppt
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Conversion devices
Quantity being measured
Transducer
Sensor
Thermistor
Temperature probe
Intermediate conversion device
Serial Interface Box
12 Bit A/D
Readout Conversion
Data Logger on PC
Calibrated T readout
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Linear Scales
• Interpolation
– Estimate position between smallest division
• Bias in Interpolation reading
• Look at Buret data from lab
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Volume to Length Converters
•
•
•
•
•
•
Buret
Pipet
Graduate Cylinder
Sensitivity depends on inner diameter
length=V/pi r2
Sensitivity = 1/pi r2
– smaller r= greater sensitivity = more length
change per unit volume - Examples
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Volume to Length Converters
• Pipet Two 10 ml pipets one has 6 mm ID
and the other has 3 mm ID
• Sensitivity = 1/pi r2
– 1/3.1415x32 = 0.0354
– 1/3.1415x 1.52 = 0.1415 4 times more change
in length for a given volume
– smaller r= greater sensitivity = more length
change per unit volume
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Volume to Length Converters
•
•
•
•
•
•
Class A Pipets 1 ppt
Class B Pipets 2 ppt
Electronic Pipetters 2-5 ppt
Graduated Pipets 5-10 ppt
Graduate Cylinders 5-10 ppt
Graduate Beakers and Flasks 20-100 ppt
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Digital Pipetters
• Actual Data for 3 Fisher adjustable pipetters
Pipette
"20-200
Sample Size
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20
200-1000
200
1000-5000
200
1000
1000
5000
1
19.9
200.8 200.3
1004.1
998.4
5021.7
2
20
200.8 199.7
1004.1
997.6
5019.8
3
20
200.7 199.9
1003.1
998.3
5013.6
4
20
200.7 200.5
1003.5
998
5014.1
5
20
200.7 200.4
1003
997.2
5008.3
Average
19.98
200.74 200.2
1003.6
997.9
5015.5
SD
0.045
0.0548 0.344
0.5273
0.5
5.346494
CV
0.224
0.0273 0.172
0.0525
0.0501
0.106599
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Challenge of Digital Data
•
•
•
•
A/D converters electrical signal to number
Computers work in Binary
Thermistor Temperature Measurement
12 bit A/D 111 111 111 111
– Decimal equivalent 212 = 4096
• Serial Interface 0-5 volts ==> 0 to 4096
• Resolution 5 volts/4096 = 0.0012
volts/digit
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Thermistor Temperature probe
• 0.073 deg/digit resolution
• 0.073 * 4096 = 299 degrees possible range
• thermistor only good for about 150 degree
range
• output varies from 0 to 2.5 volts
• Digital Music - Display colors - etc.
– 16 bit vs 24 bit
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A/D - Discrete Data
• Convert continuous function to discrete
function
• Stairstep
• Potentiometric titration
– Sequence of discrete points
– Sampling signal at specific times
• Discrete Calculus
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Null Measurements
• Classic Balance
– Put weights on reference pan = sample weight
• Electronic Equivalent
– Use solenoid to apply restoring force
– amount of current required converted to Digital
Value
• Resolution of A/D
• Sensitivity of null detector
• balances to 0.000001 gm
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Accuracy and Precision
Not Accurate and Not
Precise
Accurate but Not
Precise
Accurate and Precise
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Not Accurate but
Precise
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Accuracy
• ACCURACY - This is how close the
experimental value is to the "true value"
if this is known
• Only measurable if you know “true
value” of measured quantity
• Estimate using statistics - more later
• Measure using Standard Reference
Materials
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Precision
• PRECISION - This tells how close
together the various experimental
results are.
• Assessed using statistical methods
(standard deviation)
• compared with the maximum
experimental error calculated by
analysis of experiment.
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Control Chart Example
Control Chart
Result
1.4
1.2
1
0.8
Data
0.6
0.4
-2 stdev
+ 2 stdev
0.2
0
0
5
10
Experiment Day
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Identification and Separation
• Identification - Not part of 208
– Chem 211-2 Organic
– Chem 312 Instrumental
• Separation - We spend lots of time on this
– Remove Interferences
– Quantitation of Mixtures
– Identification of Mixtures
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Sample Preparation
See Chapter 28
•
•
•
•
Crucial first step in all analysis
Ask Series of Questions
1. Is sample solid or liquid
2. Do you want to analyze all or only a few
components
• 3. Is sample size appropriate
• 4. Is concentration appropriate for detector
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Solids
• Is the particle size appropriate for
dissolution or extraction?
– If not, mill, grind, chop, blend etc.
• Is the sample homogeneous?
– Homogenize
• Take a representative sample - sample
size required is a function of particle
size.
– Lab exercise
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Solids - A Few Components
• Are they the volatile components.
– Headspace analysis, Solid Phase
microextraction, or purge and trap.
• Non-volatile components
– separation is necessary by boiling, soxhlet
extraction, sonication, microwave
digestion, supercritical fluid extraction.
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Solids - All Components
• Sample usually must be dissolved.
• What is the sample soluble in?
– Water
– organics, etc.
• What if the sample is insoluble?
– intact high polymers.
– Inorganic analysis -Ashing techniques - Wet vs
Dry Ashing
– Fusions with Carbonate and Borate
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Strange Techniques
•
•
•
•
•
•
•
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Soxhlet Extraction Solid Phase ExtractionSolid Phase MicroextractionHeadspace SamplingPurge and Trap analysisMicrowave methodsSonication MethodsChem 311 Fall 2009
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Liquids- Few components
• Separation is necessary by extraction or
chromatography.
• Is the concentration of the analytes
appropriate for the measurement
technique?
– If not, dilute or concentrate with extraction,
evaporation, lyophilization (freeze drying).
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Liquids - Few Components
• Is sample unstable
– If yes, derivatize, cool, freeze, store in dark
• Is the liquid or solvent compatible with
the analytical method?
– If not, do solvent exchange with extraction,
distillation, lyophilization.
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Using EXCEL
• Excel powerful tool
– Calculations
– Graphing
– Curve fitting
• Learn to use it well
– Format cells for clear data display
• Learn to document your spreadsheet
– Add equations and text to explain what you have done
• Do your own!!
• Include your name in the File Name
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Chem 311
Chapter 4 Lecture 1
Meaurement and Calculation
Accuracy and Precision
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Experimental Uncertainty
• KHP Titration
– 0.8 ± 0.0001 g KHP
– 40 ± 0.014 ml (two reading of buret)
– 204.23 ± 0.02 g/mol KHP
• MNaOH = 0.8 g x 1 mol/204.23g /0.040 l = 0.09793 mol / liter
• Uncertainty on value
2
2
2
 0.0001   0.02   0.014 
undertainty  
 
 
  0.0004
 0.8   204.23   40 
• 0.09793 ± 0.0004 or 0.0979 ± 0.0004
– About 4 ppt uncertainty
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Experimental Uncertainty
• Calculated uncertainty is worst case
scenario
• Assumes all errors are in the same direction
• Multiple determinations produce average
closer to correct value
• Average = Mean
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Error vs Uncertainty
• Uncertainty is inherent in all measurements
• Related to significant figures available from
measurement devices
• Possible to calculate the Uncertainty of a
measurement
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Precision
• PRECISION - This tells how close together
the various experimental results are.
• Assessed using statistical methods (standard
deviation)
• compared with the maximum experimental
error calculated by analysis of experiment.
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MEANS OF MULTIPLE
EXPERIMENTAL
DETERMINATIONS
• THE STANDARD DEVIATION MAY BE
USED TO ASSIGN UNCERTAINTY
INSTEAD OF EXPERIMENTAL
UNCERTAINTY.
– The mean of many values should be more
accurate than any of the individual values.
– CAUTION - never more than one extra digit
beyond the individual values.This digit is in
fact the extra one carried in the intermediate
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calculations.
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Standard Deviation
• Assume Gaussian Distribution of
Experimental Values
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Standard Deviation
• Standard Terms associated with statistical
treatment of data.
 (x i )
• Mean - arithmetic average. x  n
n
• Median - middle value of the set
• Mode - most common value of the set
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•
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8
Standard Deviation

2
  x  x 
2

• Standard Deviation - sx (sample)
sx 
• or x (population >24)

  x  x 
i
n
n 1

x 
i
n
n
• Variance = square of standard deviation
•
V = sx2 or V =  x2
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Standard Deviation
• Relative standard deviation.
s
% sx
ppt s
x

x
x
s
x
x
 100 %
 1000 ppt
• % relative std. dev. = Coefficient of
Variation (CV)
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Significance of Standard
Deviation
• One standard deviation is the distance from
the mean in which 69.3% of all values are
expected to lie.
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Significance of Standard
Deviation
• 95.5% of all values are expected to lie
within 2 std. dev. from the mean
• 99.8% within 3 std. dev.
• As a general rule, virtually all experimental
data should lie in the range ±4 s.
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Significance of Standard
Deviation
• 99.8% within 3 std. dev.
• As a general rule, virtually all experimental
Fall 2009
data should lie inChem
the311range
±4 s.
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Relative Standard Deviation
• Standard deviation is fine for
– comparing things that are the same. It is like
absolute error and has the same units as the
quantity being measured.
• Relative standard deviation useful
– comparing the deviations of data of differing
magnitude to see which has the smallest
deviation.
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Relative Standard Deviation
• eg. One student reports 25.34% KHP in an
unknown with a standard deviation of 0.05
while another reports 64.34% KHP with a
standard deviation of 0.09.Which is a better
result? Calculate the relative standard
deviation for each. The smallest relative
standard deviation gets the best grade.
• (2.0 ppt and 1.4 ppt)
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5
Confidence Limits
• -for a small number of values where the true
value is not known, the true value may be
estimated from the mean and the standard
deviation.
 = true value
• tn = Student’s t for the particular C.L. and number of replicates
• n = number of replicates
• sx = std. dev.
  x
• x bar = mean value
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tn sx
n
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Confidence Limits
• Assumes there is no determinate error
present.
• Different confidence levels include different
areas of the Gaussian distribution.
– 90% confidence. This means the confidence
limit calculated will include 90% of the total
area under the distribution.10 % is not included,
5% on each side
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Confidence Limits
• The 99% confidence interval includes a larger
area than the 90% and hence the confidence
limits will be greater.
• Note that the larger the value of n, the smaller
the confidence limit. This is due to the fact that
larger n not only increases the denominator but
also decreases Student's t.
t s
  x n x
n
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Confidence Limits
•
•
•
•
•
Example mean = 144 ppm sx = 10.2 ppm
n = 4 t 90% = 2.353 t 95% = 3.182
t 99% = 5.841
 90% = 144 ± 12 ppm
confidence that true value lies in the interval
– 132 ppm <  < 156 ppm
•  95% = 144 ± 16 ppm 128 <  < 160 ppm
•  99% = 144 + 30 ppm 114 <  < 174 ppm
•
•
95% confidence is most commonly used.
•
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  x
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tn s x
n
19
Types of Errors
• Random Errors - Indeterminate errors
– Have no definite cause
• random errors in reading a buret
– Result in decreased precision and wider
confidence limits
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Types of Errors
• Systemmatic Errors - Determinate errors
– Have a definite cause
• Balance not calibrated
• Solution at wrong temperature for volumetric work
– Result in measured values which fall outside
the confidence interval of the measurement
• May be constant relative or absolute error
– Vary Sample size to evaluate
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Types of Errors
• Sampling Errors
– Sample not representative of whole
– M&M experiment
• Method error
– Interferences
• Measurement Errors
– Temperature not 20 deg for Volumetric flask
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Types of Errors
• Personal Errors
– Analyst makes a mistake
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Finding Errors
• Constant errors
– Balance reads 0.002 g high
• Proportional errors
– Balance reads 0.1% high
• Try different sample quantities and observe
the effect of the error
• Use Standard Reference Material to test
method
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ELIMINATION OF
QUESTIONABLE RESULTS
• These are the only methods you are to use
with your experimental data for the course.
• Errors occurred in the experiment.
– Definable errors. eg. you spilled some of the
solution out of the flask during a titration or
obviously overran an endpoint.
• Note the error in the notebook beside the data and
draw a diagonal line through the data.
• Do not erase or obscure the data.
8/3/2009
Chem 311 Fall 2009
25
ELIMINATION OF
QUESTIONABLE RESULTS
• Undefinable error. These are of two types.
– Errors due to learning to do the experiment
correctly or due to problems in start up. These
are common in student experiments.
– You may discard all data prior to any point and
call that data practice.
– Note this in the notebook with the data.
8/3/2009
Chem 311 Fall 2009
26
ELIMINATION OF
QUESTIONABLE RESULTS
• Undefinable error. These are of two types.
– Errors due to deterioration of reagents, operator
patience, or equipment. These occur at the end
of a series of experiments.
• You may discard all data after any given data set
and assume some unknown problem occurred.
• You may NOT discard data in the middle of
a data set unless there is a definable error!!!
8/3/2009
Chem 311 Fall 2009
27
4-
9
ELIMINATION OF
QUESTIONABLE RESULTS
• Q-test.
– measure of the gap between an outlying value
and its nearest neighbor compared to the total
range of the data.
 xnearest
x
Qexp  outlier
– EXAMPLE
xhigh  xlow
– 0.1013, 0.1014, 0.1016 , 0.1024,
0.1024  0.1016
•
Q
 0.727
0.1024  0.1013
• 95% confidence Q4 =0.83 > 0.73
• Cannot discard value
8/3/2009
Chem 311 Fall 2009
28
Significance Testing
• Assume Gaussian Distribution
• Assign Probability to two possible
outcomes
• NULL HYPOTHESIS
– Differences observed are due to random,
indeterminate errors
• ALTERNATIVE HYPOTHESIS
– Differences observed are real
8/3/2009
Chem 311 Fall 2009
29
Significance Testing
• NEVER PROVE ANYTHING IS TRUE
– Prove NOT FALSE
• Use alpha = the area of the distribution not
included – usually 0.05
– 95% of area is included and 5% excluded
• If p<0.05 then the Null Hypothesis can be
rejected. Differences not due to random errors
8/3/2009
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30
4-
10
Significance Testing
• T-test
– Compare mean to true value
– Compare Replicate measurements
– Comparing two methods of analysis
• Useful for comparing new method to existing method
• Do both methods give the same result?
– Compare two data sets
• F-Test
– Compare standard deviations for data sets or methods
8/3/2009
Chem 311 Fall 2009
31
T-test example
• Measured pH of natural and machine made
snow. Are they the same or different?
• Various t-tests
– Variance on each data set is the same
– Variance on each data set is different
– Data in two sets are paired or not
• Excel – Tools  Data Analysis
8/3/2009
Chem 311 Fall 2009
32
Snow data
• Acid Rain – Natural snow should be acidic
• Machine Made snow made from surface
water therefore less acidic
• Use one Tail t-test P= 0.005
– Significant difference
• Mixed Snow – one tail test also appropriate
– P= 0.07 Not significantly different
8/3/2009
Chem 311 Fall 2009
33
4-
11
t-Test: Two-Sample Assuming Unequal Variances
Data for [H+] of Snow Samples
Natural
Machine
Mean
Variance
Observations
Hypothesized Mean Difference
1.47E-05
4.19E-11
7
0
1.51E-06
7.65E-12
11
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
7
5.086709
0.00071
1.894579
0.00142
t Critical two-tail
8/3/2009
2.364624
Chem 311 Fall 2009
34
What does this mean
• P<0.05  95% confidence that values are
different.
– One Tail all 5% area under curve on one side
• Use when reason to expect one value to be smaller
and the other larger
– Two tail – 2.5 % of area at each end of curve
• More rigorous test
• Use when no reason to predict the order of values
8/3/2009
Chem 311 Fall 2009
35
Stream pH
Average pH data
7
6.9
6.8
6.7
pH
6.6
Off Mt
6.5
On Mt
6.4
6.3
6.2
6.1
6
8/1/2004 9/20/200 11/9/200 12/29/20 2/17/200 4/8/2005 5/28/200 7/17/200 9/5/2005 10/25/20 12/14/20
4
4
04
5
5
5
05
05
Date
8/3/2009
Chem 311 Fall 2009
36
4-
12
t-Test: Paired Two Sample for Means
[H+] for two Streams Nov-May
Mean
Variance
Giant
1.35E-06
1.67E-12
Coleman
3.87E-07
8.53E-14
Observations
Pearson Correlation
Hypothesized Mean Difference
df
t Stat
8
0.929994
0
7
2.649175
8
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
8/3/2009
t Critical two-tail
0.016491
1.894579
0.032981
Chem 311 Fall 2009
2.364624
37
4-
13
Chapter 4 Part 2
Calibration, Standardization
8/3/2009
Chem 311
1
Smeas = kCAnalyte + Sreagent
• Calibration necessary for all measurements
• What to use as STANDARDS
– Primary Standards
•
•
•
•
•
8/3/2009
Known stoichiometry
Known purity
Stable for long periods
List in Appendix 2 text
Ex. KHP for Titration
Chem 311
2
Standard Solutions
• Weigh Primary Std. Into Volumetric Flask
• Dilute to mark only after all dissolved
• Do not heat
– Mix at least 10 times
8/3/2009
Chem 311
3
4 part 2-
1
Standard Solutions
• Serial Dilution – for Calibration or dilute
• Pipet portion of stock solution into Vol.
Flask and dilute
• CoVo=CdVd
• Many ways to get to specific concentration
• Errors not the same for each
– problem 4-11
8/3/2009
Chem 311
4
Calibration Methods
• Single Point
• External Standard Method – Calibration
Curve
• Internal Standard Method
• Standard Addition Method
8/3/2009
Chem 311
5
Single Point Calibration
• k= Sstand/Cs
• One Standard
– Assumes response factor k is constant over
entire range
– Assumes linear relationship
– Ignores Blank due to reagents
• Generally not a good idea
8/3/2009
Chem 311
6
4 part 2-
2
External Standard Method
Using a Standard Curve
– Known concentrations vs Signal
– Intercept need not be Zero
– Identify non-linearity if present
8/3/2009
Chem 311
7
External Standard Method
• Using a Standard Curve
–
–
–
–
Vanilla Extraction Lab (S=Absorbance)
Fluoride Lab (S=Potential)
In 111-112 Fe[SCN] Lab (S=Absorbance)
Can also be applied to most other types of
signals.
8/3/2009
Chem 311
8
External Standard Method
• Chromatography
– make calibration curve
– run sample and compare
– Limited by injection accuracy
• 2-4%
• 1-2%
• 0.5%
8/3/2009
manual
auto
valve injections
Chem 311
9
4 part 2-
3
LINEAR REGRESSION
ANALYSIS
(LEAST SQUARES).
• Best linear relationship for a set of data.
– Can be extended to find higher order
polynomial relationships
– Can be extended to data where the assumptions
below are known not to hold
8/3/2009
Chem 311
10
How to Draw the Calibration
Line?
• The best linear relationship is that which
minimizes the sum of the squares of the
deviations on the y axis of all points from
the line
• X values are assumed to be Exact
• DO NOT USE LEAST SQUARES
WHERE BOTH X AND Y DATA
CONTAIN LARGE ERRORS
8/3/2009
Chem 311
11
ASSUMPTIONS
• Values for the x axis are relatively free from error.
– Concentration = independent variable
• Values for the the y axis and may contain some
error.
– Signal = what you measured
• The standard least squares method assumes all
have the same error
– more sophisticated approaches allow weighing factors
for cases where errors differ greatly.
8/3/2009
Chem 311
12
4 part 2-
4
Calculating Linear Regression
on a TI Calculator
•
•
•
•
•
•
•
•
LIST EDIT
Enter values into XSTAT (Independent variable)
Enter values into YSTAT (Dependent variable)
Enter 1 into Fstat column for each Xstat value
EXIT
STAT
CALC
LinR (Enter) Gives slope, intercept and Correlation
Coefficient
• TwoVar (Enter) Gives sums of squares needed for error
calculations
8/3/2009
Chem 311
13
Computing Least Squares
• Excel –
–
–
–
Make XY scatter Graph
Click on data in graph
Right click Select Add Trendline
Options • display equation
• display R squared
8/3/2009
Chem 311
14
Computing Least Squares
• Excel – Getting values for Calculations
– =Slope(yvalues, xvalues)
– =Intercept(yvalues, xvalues)
– =RSQ(yvalues,xvalues)
bo
b1
R2
• All Values are ‘Live’ and update changes
8/3/2009
Chem 311
15
4 part 2-
5
Computing Least Squares
• Excel – Alternate Approach
–
–
–
–
–
Tools ==> AddIns ==> Analysis Pack
Tools==> Data Analysis==> Regression
Select Range for x and Y data
Select where results go
Choose options (some don’t work quite right for
graphics)
– Get lots of stuff - std. Dev of slope and intercept
• Results ‘Dead’ and don’t update changes
8/3/2009
Chem 311
16
Does line go through ZERO
• SEy >= y intercept
– Y-intercept lies within 1 SD of 0
– Repeat Calculation and select Force Zero
Intercept
• SEy < y intercept
– Use full equation from Least Squares
• Be sure to use SEy not overall SE
8/3/2009
Chem 311
17
Figures of merit for LS
• Correlation coefficient
• =RSQ(known_y's,known_x's)
– Known_y's is an array or range of data points.
– Known_x's is an array or range of data points.
– R2 correlation coefficient 0.0 to +1.0
• Variance or standard deviation of the fit
8/3/2009
Chem 311
18
4 part 2-
6
Figures of merit for LS
• A poor fit may be due to one of two causes.
• If the data is fundamentally nonlinear, there
will be definite trends in the residuals,
either bowing up or down.
• If the data is just bad but linear, the
distribution of the deviations will be
random.
8/3/2009
Chem 311
19
Excel Least Squares
A Closer look
0
1.1
2
3.98
5.2
Y values
0.1
1
2.1
4
5
Least Squares
Depe ndent
V a r ia b le
X values
y = 0.9624x + 0.0763
R2 = 0.9974
6
4
Y values
2
0
0
2
4
6
Linear (Y
values)
Independent Variable
8/3/2009
Chem 311
20
Residuals
X values
0
1.1
2
3.98
5.2
Y values Y calc
Residuals
0.1
0.0763
-0.0237
1 1.13494 0.13494
2.1
2.0011
-0.0989
4 3.906652 -0.09335
5 5.08078 0.08078
Residuals
Residuals
0.2
0.1
0
-0.1 0
Residuals
2
4
6
-0.2
8/3/2009
X values
Chem 311
21
4 part 2-
7
Residuals
• Random distribution ==> Data is inherently
linear
• Non-Random ==> Data not linear
– Use a different model
• Errors Greater at one end of Residuals
– Errors in measurement are not constant.
8/3/2009
Chem 311
22
Non-linear data
X values
0
1.1
2
3.98
5.2
Y values Y calculateResiduals
-0.05
0.0669
0.1169
1.15 1.12257 -0.02743
2.14
1.9863
-0.1537
3.89 3.886506 -0.00349
4.99 5.05734 0.06734
Same R squared
as previous data
Non-linear Data
Y values
6
y = 0.9597x + 0.0669
R 2 = 0.9974
Y values
4
2
Linear (Y
values)
0
-2 0
2
4
6
X values
8/3/2009
Chem 311
23
Residuals
• Note pattern in residuals
Residuals
Residuals
0.2
0.1
0
-0.1 0
Residuals
2
4
6
-0.2
X value
8/3/2009
Chem 311
24
4 part 2-
8
Special Precautions
• When computing sums of squares, it is
essential that ALL DIGITS be kept in
calculations.
– Large differences in results occur based on
small round off or truncation errors.
– Different results depending on how carefully
you use calculators and which one you use.
8/3/2009
Chem 311
25
Calculating an Unknown
• The value for an unknown result xc is calculated
from measured value yc
Xs 
y s  bo
b1
• b1=slope bo=intercept
8/3/2009
Chem 311
26
Precision of Unknown
• m = number of observations of unknown
• n = number of calibration points
sx 
sr 
8/3/2009
sr
b1
( yx  y)2
1 1
 
m n b12  ( xi  x) 2
(y
i
 yˆ i ) 2
n2
( yi  yˆ i )  residual for point
Chem 311
27
4 part 2-
9
Precision of Unknown
• Equation hard to use. Errors occur if any
sum value is not taken with all digits
sx 
sr 
sr
b1
( y  y)2
1 1
  2 x
m n b1  ( xi  x) 2
(y
i
 yˆ i ) 2
n2
8/3/2009
( yi  yˆ i )  residual for point
Chem 311
28
Precision of Regression
• sx function has a minimum value when the mean
value for the unknown is close to the mean value
of the calibration curve.
– (yxbar - y bar) = 0
• The standard deviation of the unknown can then
be used to calculate a confidence limit for the
value of the unknown in the usual manner using
Student’s t and the equation given previously.
8/3/2009
Chem 311
29
Precision of Unknown
• Confidence Limit for unknown
xtrue  x  ts x
8/3/2009
Chem 311
30
4 part 2-
10
Error in b1 and bo
• Std. Dev. of slope and intercept define an
envelop
• This envelop is narrow at the mean of the
calibration curve and expands on both sides.
8/3/2009
Chem 311
31
95% CL best case
6
5
Y calues
4
Exp. Values
3
-b+m
2
+b-m
1
0
-1 0
2
4
6
X values
8/3/2009
Chem 311
32
Non-Linear LS
• Data obtained in a real experiment may not
be linear even though it should be in theory.
• Use a second order fit: (See Text fopr
EXCEL Instructions)
•
y= a + bx + cx2
• Calculation of Unknown gives 2 values
• Quadratic Solution Required
8/3/2009
Chem 311
33
4 part 2-
11
Non-Linear Data
• If an obvious trend is seen, then data may
be non-linear. • Use other statistical tools (higher order fit)
• Drop data from non-linear part and repeat
regression analysis.
– Common if you exceed the Linear Range of the
Method
• Don’t drop points from the middle
8/3/2009
Chem 311
34
4 part 2-
12
Chapter 5
QA & Calibration
8/3/2009
Chem 311
1
QA/QC
• Critical part of any analysis
– Does the method work?
• Instruments OK?
• Reagents OK?
– Is the analyst doing a good job
• How much confidence in result?
8/3/2009
Chem 311
2
Important terms
• Sensitivity – Slope of Calibration
• Selectivity – Do other things give a
response?
• False Positive
– PSA Test for Prostate Cancer
• False Negative
– Mammograms (X-Ray)
8/3/2009
Chem 311
3
5-
1
Range of Method
•
•
•
•
Limit of Detection
Limit of Quantitation
Limit of Linearity
Limit of response
• Range statistics vary depending on many
factors R2=0.995 in text is rarely met
8/3/2009
Chem 311
4
Limit of Detection
8/3/2009
Chem 311
5
Limit of Detection (LOD)
• Slod= S + z sigma
• Z=3 gives 99.86% confidence that
substance is present
• S=mC +b from Least Squares
• Clod = (Slod – b)/m
• < 1% chance of false positive
8/3/2009
Chem 311
6
5-
2
Quantitation Limit
• Sloq= S + 10 sigma
• Gives quantitation with 10% rel. error
• Cloq = (Sloq – b)/m
• 1 sig fig quantitative result possible
8/3/2009
Chem 311
7
Limit of Linearity
• Data deviates by 10% from Least SQ line
• Usually Negative deviation so results from
calibration are high
• No mathematical way to determine this
– Interpolate residuals to find 10%
• Requires enough points to get good value
– Compare linear and quadratic fit
8/3/2009
Chem 311
8
Precision
• Repeated analysis of same homogeneous
material – Instrument precision
• Repeated sample preparation of same
sample – Method precision
• Precision between instruments and analysts
– Method Ruggedness
• Precision between labs –
– Interlaboratory Precision
8/3/2009
Chem 311
9
5-
3
Accuracy
•
•
•
•
8/3/2009
Run SRM’s similar matrix
Use two independent methods
Spike sample with know amount - Recovery
Compare Standard Addition with
Calibration result
Chem 311
10
Recovery Study
• Validate sample preparation/extraction etc
• Run Sample
• Run Sample with known addition
8/3/2009
Chem 311
11
Standard Addition
• Useful if matrix of sample has background
signal which cannot be accounted for in a
blank or calibration curve
• Quick analysis if only one or two samples
are to be run
8/3/2009
Chem 311
12
5-
4
Standard Addition
• Three approaches to Std. Add.
– Dilute unknown and standard additions to
constant volume.
• 50 ml sample + 10 ml std  100 ml
– Add micro amounts of standard and ignore
dilution.
• 100 ml sample + 0.1 ml std.
– Add standard and correct signal for dilution.
8/3/2009
Chem 311
13
Graphical treatment of std.
addition
• Graph Signal vs Spike Concentration
• X-Intercept= -CAVo/Vf
8/3/2009
Chem 311
14
Std. Addition as Check on
External Calibration
• Compare value of k (slope) for external
standard and standard addition calibrations
• IF EQUAL  Method is good and there are
not matrix effects
• IF NOT EQUAL  Matrix error present in
external standard calibration
8/3/2009
Chem 311
15
5-
5
Analysis Methods
• Internal Standard Method
– eliminates injection error in Chromatography
• - only integration error is left
– Eliminates need for careful sample workup in
many methods (Chocolate Lab)
– add standard to each sample use it to correct for
variation in injection and in sample workup etc.
• Single point - determine peak ratio with one standard
mixture
• Calibration curve - plot area ratio vs mass ratio
8/3/2009
Chem 311
16
Internal Standard Method
• Data from GC
experiment
20:0
16:0
7.0000
10.0000
6.0000
Area Ratio
Area Ratio
8.0000
y = 0.9287x + 0.0426
R2 = 0.9999
5.0000
y = 0.8809x + 0.0549
4.0000
3.0000
2.0000
2
R = 0.9999
6.0000
4.0000
2.0000
1.0000
0.0000
0.0000
0
2
4
6
8
0
8/3/2009
5
10
15
Mass Ratio
Mass Ratio
Chem 311
17
Selecting an Internal Standard
• Chemically Similar to Analyte
– HPLC Lab – Theophylline for Caffeine
• Isomers or close homologs
– GC Lab C17 fatty acid
• Once Internal Std and Sample are made
homogeneous – all further steps need not be
quantitative (within limits of linearity and
detection)
8/3/2009
Chem 311
18
5-
6
Selecting an Internal Standard
• Mass Spectrometry – Isotopic labels
– D, 13C, 15N, etc
– All chemical properties same as Analyte
– Mass Spec gives separate signals
• Cocaine methods for Chem 312
8/3/2009
Chem 311
19
Blanks
• Complicated issue
– Reagent Blank – Add all reagents at their final
concentrations to the solvent
– Method Blank – Carry a matrix matched blank
sample through the entire method
– Field Blank – Create a blank when samples are
collected to include all environmental
conditions
8/3/2009
Chem 311
20
Control Chart
• Monitor QA over time
– Hg Analyzer
• Run 100 ul of 1 ppm each day as first sample
• Put result on graph
• Monitor changes
8/3/2009
Chem 311
21
5-
7
Chem 311
Chapter 6
Chemical Equilibrium
8/3/2009
Chem 311
1
Chemical Equilibrium
• Bottom of energy well
• Change in concentration of any species
requires input of energy
• Any external change away from equilibrium
is adjusted back to new equilibrium
• Marble in a bowl analogy
8/3/2009
Chem 311
2
Equilibrium constant
• Free Energy change is related to chemical
potential
G  G o  RT ln Q
c
d
  c   d 
 o   o 
• Note difference from Eq 6.2
 c  d
– Ratio of activities to Std. St. Q 
a
b
 a    b 
– Dimensionless
 o   o 
 a  b
8/3/2009
Chem 311
3
6-
1
Equilibrium constant
• At Equilibrium
c
G o   RT ln K eq
d
  c   d 
 o   o 
K eq   c  a  d  b
 a   b 
 o   o 
 a  b
where a' s are equilibrium values
8/3/2009
Chem 311
4
Equilibrium constant
• Normally write using Concentrations
• (6-2)
K eq 
Ceqa Deqd
Aeqa Beqb
– All values are dimensionless (ratio to std state)
– Ignore Activity effects in most cases
• (Chapter 8)
8/3/2009
Chem 311
5
Properties of Keq
• Reverse Reaction  Invert K
• Cu + 4 NH3  Cu(NH3)4
Kf 
[Cu ( NH 3 ) 4 ]
[Cu 2 ][ NH 3 ]4
• Cu(NH3)4  Cu + 4 NH3
Ki 
8/3/2009
1 [Cu 2 ][ NH 3 ]4

Kf
[Cu ( NH 3 ) 4 ]
Chem 311
6
6-
2
Precipitation Reactions
•
•
•
•
AgCl(s)  Ag+ + ClKsp= [Ag+] [ Cl-]
Note solid does not appear – in different phase
Only works for a few species
– Silver halides
– BaSO4
• All others have complex chemistry which make
the simple treatment useless.
8/3/2009
Chem 311
7
Precipitation Reactions
• PbI2(s)  Pb+2 + 2I• Ksp=[Pb+2 ][ 2I-]
• Also need to consider
– PbI+ , PbI3- , and PbI42– Simple equilibrium gives wrong answers
8/3/2009
Chem 311
8
BRONSTED-LOWRY ACID
BASE CONCEPT
• We use this concept because it applies to any
solvent.
• ACID - donates proton to solvent
• BASE- accepts proton from solvent.
• HCl + H2O <===> H3O+ + Cl• acid + base
8/3/2009
conj.acid conj.base
Chem 311
9
6-
3
Look at half reactions
•
•
•
•
•
8/3/2009
Acid1 ==> H+ + Base1
Base2 + H+ ==> Acid2
Sum these to get
Acid 1 + Base2 ==> Base1 + Acid2
conjugate Acid-Base pairs (subscripts)
Chem 311
10
Acid-Base Strength
Relative
• Strong acids have greatest energy release
when losing proton
• Strongest bases have greatest energy release
when accepting a proton
• Products must be weaker than reactants
– HCl + H2O ==> Cl- + H3O+
– Stronger acid+ stronger base==> weaker base + weaker acid
8/3/2009
Chem 311
11
Acid-Base Strength
Relative
• In water - H3O+ is strongest acid
• Anything above it reacts with
• water to produce H3O+
– HCl, HwSO4, HBr, HI, HClO4
• Anything below water is weak acid
– Farther below water the weaker it gets
– None react completely
– Equilibrium
8/3/2009
Chem 311
12
6-
4
Strong Acids
• Above H3O+
HCl + H2O <===> Cl- + H3O+
•
• Cl- very weak proton acceptor
• HCl very strong proton donor.
• Thus there is a complete proton transfer.
– Ka >>> 100
8/3/2009
Chem 311
13
Weak acids
• Acetic acid for example:
– CH3COOH + H2O <===> CH3COO- + H3O+
• Ka = 1.75x10-5
• acetate ion stronger proton acceptor
than water so proton tends to remain on
the acetate (making it acetic acid).
8/3/2009
Chem 311
14
Strong bases
•
O2- + H2O <===> 2 OH>>>100 strong base
Kb
• Anything which yields OH- ions in
solutions
– NaOH, KOH, Ba2OH - must be soluble
– Cu(OH)2 insoluble not strong base
8/3/2009
Chem 311
15
6-
5
Weak bases
• NH3 + H2O <===> NH4+ + OH• Kb= 1.7x10-5 weak base
• Amines, conjugate bases of weak acids
– phosphates, carbonates, acetate, etc.
8/3/2009
Chem 311
16
Acid and Conjugate Base
• Strengths are related to the solvent.
• CH3COOH + H2O <===> CH3COO- + H3O+
Ka 
[H  ][OAc ]
[HOAc]
• CH3COO- + H2O <===> CH3COOH + OH-
Kb 
8/3/2009
[OH  ][HOAc]
[OAc ]
Chem 311
17
Add reactions – multiply K’s
• CH3COOH + H2O + <===> CH3COO- + H3O+
Ka
• CH3COO- + H2O <===> CH3COOH + OH- Kb
•
•
•
•
8/3/2009
+ add two reactions
2 H2O <===> H3O+ + OHSolvent Autoprotolysis
Equilibrium constant Kw = Ka x Kb
Chem 311
18
6-
6
Acid- Base Pair Relationship
• Ka x Kb = Kw
– This relationship is true for any conjugate acid
base pair in water.
• KaKb
= Ks
For any solvent
– If you know the Ka you can always get the Kb.
– Also note that for a solvent of different Ks the
relationship between the Ka and Kb will be
different.
8/3/2009
Chem 311
19
Temperature Effects
• Ka and Ks vary with temperature
Temperature (C )
0
25
50
100
37
8/3/2009
Kw’
0.114 x 10-14
1.01x10-14
5.47x10-14
49x10-14
3.2 x10-14
Chem 311
20
What is a neutral solution?
•
•
•
•
•
8/3/2009
25 deg C Kw= 1.0x10-14 = [H3O+] [OH-]
[H3O+]= 1.0x10-7 pH = 7.00
At 50 deg C neutral water pH=6.63
Ice water neutral pH = 7.42
Very important for biochemist who work at
37 C ( normal human body temp) pH=6.74
Chem 311
21
6-
7
Solubility Equilibria
• AgCl <==> Ag+ + Cl• Ksp = [Ag+] [ Cl-]
• Solubility = how many moles dissolve in 1 liter of
water
• S=[Ag+] = [Cl-] = Ksp1/2
• Al(OH)3 < Al3+ + 3 OH• S= [Al3+ ] = 1/3 [OH-] so [OH-] = 3S
• Ksp = [Al3+ ] [OH-] 3 = S x (3S)3 = 9S4
8/3/2009
Chem 311
22
Solubility Equilibria
• Its not so simple
• Most slightly soluble salts have complicated
chemistry
– Anions act as weak bases- must consider
fraction in simple form
– anions act as complexing agents- must consider
fraction of metal in uncomplexed form
8/3/2009
Chem 311
23
Bottom Line
• AgCl, AgBr, AgI and BaSO4 are the only
cases which work even tolerably well
• Silver halides form higher complex ions
• AgCl2-, AgCl3-2, AgCl4-3, AgCl(aq)
8/3/2009
Chem 311
24
6-
8
Coordination Complexes
• Lewis Acid Base Theory
• Acids = electron pair acceptor
– H+, Metal ions Fe3+, Cu2+, etc.
• Base = Ligand = electron pair donor
– OH-, Cl-, :NH3, CN-, H2O, etc.
• Acid + Base ==> Complex ion
8/3/2009
Chem 311
25
Coordination Complexes
• Complex ions Co complex lab
• All ions in water are hydrated
– Cations =Lewis acids ==> accept electron pair
from :O on H2O
• Fe3+ + 6 H2O <==> [Fe(H2O)6]3+
– hexaaquo iron (III) ion
• Formation of other complex ions by
Displacement
8/3/2009
Chem 311
26
SEQUENTIAL COMPLEXATION BY
SIMPLE LIGANDS
• Ni(H2O)42+ + 4 Cl- <===> NiCl42- +
4H2O) REACTION OCCUR IN A SERIES OF
STEPS
[NiCl ]
K 
• Ni (H2O)42+ + Cl- <===> Ni (H2O)3 Cl+ 1

• Ni (H2O)3 Cl+ + Cl- <===> Ni (H2O)2 Cl2+K 2 
• Ni (H2O)2 Cl2+ + Cl- <===> Ni (H2O) Cl3- K 3 
• Ni (H2O) Cl3- + Cl- <===> NiCl4-2
8/3/2009
Chem 311
K4 
2
[Ni ][Cl  ]
[NiCl 2 ]
[NiCl  ][Cl  ]
[NiCl 3  ]
[NiCl 2 ][Cl  ]
[NiCl 4  2 ]
[NiCl 3  ][Cl  ]
27
6-
9
Overall Formation constants
• ß1= K1
ß2= K1K2
2 
[NiCl 2 ]
2
ß3= K1K2K3
ß4=K1K2K3K4
 2
[Ni ][Cl ]
•
• WRITE A MASS BALANCE FOR NICKEL
• CNi = [Ni 2+ ] + [NiCl+ ] + [NiCl2 ] + [NiCl3- ] + [NiCl42- ]
8/3/2009
Chem 311
28
General Approach – Complicated
Equilibrium Systems
• Calculate the fraction of each form in an
equilibrium under specified conditions
•  will be used to identify fraction
– Ni2+ = fraction of total Ni in the Ni2+ form
– HA = fraction of weak acid (HA) in
undissociated form.
– A- = fraction of weak acid (HA) in dissociated
form.
8/3/2009
Chem 311
29
Species present
• Three techniques
– Calculate fraction in each form - alpha
– Log Concentration plots (computer)
– Line diagrams (qualitative)
8/3/2009
Chem 311
30
6-
10
Species present at a pH
•
•
•
•
Calculate alpha’s
HA <==> H+ + ACHA = [HA] + [A] Mass balance
Define  fraction of total in specific form
 HA 
8/3/2009
[ HA]
C HA
A 
[ A ]
C HA
Chem 311
31
Species present at a pH
• Substitute values from Ka
• CHA=[HA] + [A]
[ HA]
 HA 
C HA
[ HA] 
8/3/2009
A 
[ A ]
C HA
K ' [ HA]
[ H  ][ A ]
[ A ]  a 
'
[H ]
Ka
Chem 311
32
Species present at a pH
• For monoprotic acid - Exact equation
 HA 
A 
8/3/2009
[H  ]
[ H  ]  K a'
K a'
[ H ]  K a'

Chem 311
33
6-
11
Species present at a pH
• For polyprotic acid - Exact equation
 HA 
[ H  ]n
'
[ H  ]n  K a' 1[ H  ]n 1  K a' 1 K a' 2 [ H  ]n  2  ...K a' 1 K a' 2 ..K an
 Am 
'
[ H  ]n  m K a' 1 K a' 2 ..K an
'
[ H  ]n  K a' 1[ H  ]n 1  K a' 1 K a' 2 [ H  ]n  2  ...K a' 1 K a' 2 ..K an
 A2 
[ H  ]n  2 K a' 1 K a' 2
'
[ H ]  K [ H ]  K a' 1 K a' 2 [ H  ]n  2  ...K a' 1 K a' 2 ..K an
 n
'
a1
 n 1
8/3/2009
Chem 311
34
Species present at a pH
 HA 
 n
 n 1
[H ]  K [H ]
'
a1
[ H  ]n
'
 K a' 1 K a' 2 [ H  ]n  2  ...K a' 1 K a' 2 ..K an
 Am 
'
[ H  ]n  m K a' 1 K a' 2 ..K an
 n2
'
'
'
[ H ]  K [ H ]  K a1 K a 2 [ H ]  ...K a' 1 K a' 2 ..K an
 A2 
[ H  ]n  2 K a' 1 K a' 2
'
[ H ]  K [ H ]  K a' 1 K a' 2 [ H  ]n  2  ...K a' 1 K a' 2 ..K an
 n
 n
'
a1
'
a1
 n 1
 n 1
• Each term in denominator represents one
form of the acid
8/3/2009
Chem 311
35
Species present at a pH
• Plot  vs pH - Useful to see what is present
as function of pH
• Sketch approximate alpha plots
• pH=pK at 50% crossover
pK '1 pK '2
1.0
A2-
H2A
0.8
alpha
0.6
0.4
0.2
0.0
8/3/2009
Chem 311
0
2
4
6
8
p[H3O+]
10 12 14
36
6-
12
Advantages of alpha
• Rigorous – No assumptions
• Define pH and do calculation
• Concentration of total acid does not matter
• Useful for simplifying equilibrium
calculations for non-acid/base chemistry
• Useful in predicting titration curves
8/3/2009
Chem 311
37
Using Fraction Titrated
• Avoids problem of figuring out
stoichiometry
• Avoids need to recognize species present
• Pick pH and calculate fraction titrated
• Only way to do spreadsheets
8/3/2009
Chem 311
38
8/3/2009
Chem 311
39
6-
13
8/3/2009
Chem 311
40
6-
14
Chem 311
Chapter 8
Activity
Systematic Equilibrium
ACTIVITY
• Describes the real, effective concentration of
the species in the solution (Their chemical
potential)
• Not always same as concentration
• Activity is not always easy to determine.
• Some techniques actually measure activity
directly (eg.pH electrode) but unless they can
be calibrated with standards of known activity
this doesn't do any good.
8/3/2009
Chem 311
2
Activity of HCl solutions
Activity vs Concentration for HCl
Activity
1
0.8
0
5
10
Concentration (F)
15
Activity H+
Activity H+
Activity vs Concentratino for HCl
800
700
600
500
400
300
200
100
0
0.6
Series1
0.4
0.2
0
0
8/3/2009
Chem 311
0.2
0.4
0.6
Concentration (F)
0.8
1
3
8-
1
ACTIVITY see Chapter 8
• Activity coefficient
– Finagle constant
8/3/2009
 x   xC x
Chem 311
4
ACTIVITY
• Problem of definition. What are the
conditions where f=1.00000 ? The value
of Keq will depend on how this is
chosen.
8/3/2009
Chem 311
5
Henryan System
• Used for Solutions
• f = 1 at limit C ==> 0
8/3/2009
– Chemistry at infinite dilution.
– Graph values at low Conc. then extrapolate
to 1.0 M
– At infinite dilution, the solvent is
unperturbed by any solute particles and the
each solute particle feels no forces other
than from the solvent.
Chem 311
6
8-
2
Concentration Effects
• Concentration increases
– Ions get close enough to be attracted and
repelled by other ions
– All ions are solvated (Solvation number)
• Very High concentration
– Run out of solvent for hydration
• Activity coefficients range widely
8/3/2009
Chem 311
7
Activity Coefficients
• Function of Ionic Strength
S
1
 [ A z  ]z A 2  [ B z  ]z B 2  ...
2
• Ionic strength depends on charges of ions
– More highly charged ions make S>> [Conc]
• Na2SO4 [Na]=2x [SO4] but S=1/2([Na] + [SO4]x4)
• S=1/2(2x [SO4] + 4x [SO4] ) = 3x [SO4]
8/3/2009
Chem 311
8
Calculating Activity Coef.
• DHLL - excellent but only under trivial
conditions S=0.0001 M or less
• DHE (EDHE)- OK to S= 0.01
– still not terrible useful
– Doesn’t work for blood, urine, or sea water
• Davies Equation - empirical - curve fit
8/3/2009
Chem 311
9
8-
3
Cut to the Chase
• Ignore Activity Coefficients in most work
– Can’t get them accurately
– Places limit on absolute accuracy of all
equilibrium calculations
• Biochemists making buffers to match
physiological conditions
8/3/2009
– Use 1:1 salts for best accuracy
– Use highly charged ions to get high ionic
strength at low conc.
– Large errors due to Chem
lack311of dissociation
10
Cut to the Chase
• Makes Great excuse for why things don’t
work quite right
• Potentiometric titration data fit
– Use activity coefficients as excuse for some
deviations from theory
8/3/2009
Chem 311
11
Cut to the Chase
• Activity effects on Non-polar species
• Activity coefficients >1
• Salting in and Salting out
– Add a lot of salt to force something out of
solution • Protein separations
• Acetone extractions
8/3/2009
Chem 311
12
8-
4
Systematic Approach to
Equilibrium Problems
• If exact answers are needed
• Systematic Set of steps to take to solve a
problem – Any problem
• Use Acid Base as example
8/3/2009
Chem 311
13
Acid Base Equilibria
Step 1. Write all chemical reactions and
their equilibrium constant expressions.
8/3/2009
Chem 311
14
Example - Benzoic Acid
• 2 H2O <===> H3O+ + OH•
Kw = 1.00 X 10-14
C6H5COOH + H2O <==> C6H5COO- + H3O+
Ka 
[H  ][BA ]
5
 6.3x10
[HBA]
• Too Many Unknowns to solve
• Need additional Equations
8/3/2009
Chem 311
15
8-
5
Example - Benzoic Acid
• Step 2 – Write additional equations defining the system – One
Charge Balance
• CHARGE BALANCE – Solution is electrically neutral
• Sum [+ ions] = Sum [- ions]
• [H +] = [BA- ] + [OH- ]
– rearrange
• [BA- ] = [H +] - [OH- ]
• Phosphoric acid /potassium phosphate equilibrium
8/3/2009
Chem 311
16
Example - Benzoic Acid
MASS BALANCE - Conservation of
matter
Multiple equations for complex systems
• CHBa = [HBA] + [BA- ]
8/3/2009
Chem 311
17
Example - Benzoic Acid
• Step 3 – Use Algebra to simplify things and remove
unknowns
• Substitute from Charge Balance into Mass Balance
• [BA- ] = [H +] - [OH- ]
•
•
•
CHBA = [HBA] + [H +] - [OH- ] REARRANGE
[HBA] = CHBA - [ H+ ] + [OH- ]
SUBSTITUTE INTO Ka EXPRESSION
Ka 
8/3/2009
[ H  ][ BA ]
CHBa Chem
[ H311 ]  [OH  ]
18
8-
6
Exact solution
• Substitute from
Ka 
– Charge Balance
• [OH-] = Kw/[H+]
8/3/2009


[ H  ] [ H  ]  [OH  ]
C HBa  [ H  ]  [OH  ]

K 
[ H  ] [ H  ]  w 
[
]
H

Ka 
K
C HBa  [ H  ]  w
[H ]
Chem 311
19
Exact solution
• Clean it up
Ka 
[ H
 2
]  Kw

K
C HBa  [ H ]  w
[H ]

• You don’t really want to do
this. (cubic)
[ H  ]3  K a [ H  ]2  K a [ H  ]C HA  K w [ H  ]  K w K a  0
• Solutions of very weak acids
HCN
– Ka= 6x10-10
8/3/2009
Chem 311
20
Example - Benzoic Acid
• Approximate solution
– Ignore OH
• OH <<H since this is an acid
Ka 
• If CHBA>> [H+]
8/3/2009
[ H  ][ Ba  ]
C HBa  [ H  ]
[H]  CHAKa
Chem 311
21
8-
7
Example - Benzoic Acid
• Solution
Ka 
[ H  ][ Ba  ]
C HBa  [ H  ]
[ H  ]2  K a [ H  ]  C HA K a  0
• Solve on calculator
• Works as long as water contribution [OH] is
negligible
8/3/2009
Chem 311
22
Monoprotic base
• Two ways to solve - Approximate
[OH  ]  K bCb
• More Exact
[OH  ]2  [OH  ]K b  Cb K b  0
8/3/2009
Chem 311
23
Solving on a TI Calculator
• TI-86
– POLY
•
•
•
•
•
Order =2 Enter
A2=1
A1=Ka
A0=-CaxKa
SOLVE
– You get two answers- choose the reasonable
one (positive and not greater than Ca)
8/3/2009
Chem 311
24
8-
8
Solving on a TI Calculator
• TI- 83
–
–
–
–
–
Set up Equation in Solver
Put in values for things you know
Put cursor on unknown and press SOLVE
Select bounds to eliminate negative answers
If You get two answers- choose the reasonable
one (positive and not greater than Ca)
8/3/2009
Chem 311
25
Solving on a TI Calculator
• TI- 82
– Math
• go down list of functions to Solve (last function on
list)
– (H^2+K*H-C*K,H,guess .00000001)
• numbers for K and C use small value for guess
– Make sure result is positive
– Make sure result is less than C
8/3/2009
Chem 311
26
Solubility Equilibria
• Very complicated
– Acid base component
– Coordination complex component
• Multiple species
• Lots of Algebra fun
• Identifying all Chemical Reactions often
hardest part
8/3/2009
Chem 311
27
8-
9
Chem 311
Chapter 9
Monoprotic Acid-Base
8/3/2009
Chem 311
1
Calculation pH of anything
• Six cases to address
– Strong Acid/Base > 10-6 M
– Strong Acid/Base <10-6 M
– Weak Acid
• Acid or conjugate acid of weak base
– Weak Base
• Base of conjugate base of weak acid
– Buffer
• Acid plus its conjugate base
– Amphiprotic substance - polyprotic systems Chapter 10
8/3/2009
Chem 311
2
Strong Acid/Base
• Completely dissociated
– [H+] = CHA
– [OH-] = CB
• If Conc > 1x10-6 M then dissociation of
H2O can be ignored
8/3/2009
Chem 311
3
9-
1
Strong Acid/Base
• If Conc. < 1x10-6 M then dissociation of
H2O must be included
• Acids never > pH 7
• Bases never < pH 7
• Quadratic solution from Systematic
treatment
• [H+]2 + CHA[H+] – Kw = 0
8/3/2009
Chem 311
4
Monoprotic acid or base
• Acid
[ H  ]2  K a [ H  ]  C a K a  0
• Base
[OH  ]2  [OH  ]K b  Cb K b  0
8/3/2009
Chem 311
5
Buffers
• Resist Change in pH
– Added acid
– Added base
– dilution
• Very important in all chemistry
• Acid + conjugate base
8/3/2009
Chem 311
6
9-
2
Exact Solution buffers
• Example - Base Buffer
•
.200M
+
.100M
•
NH3
+ NH4NO3
• NH3 + H20 <====> NH4+ + OH• NO3- disassociated - no Rx
8/3/2009
Chem 311
7
Buffer Example
• Change balance [NH4+] + [H+] = [OH-] + [NO3-]
• Mass balance 0.200 + 0.100 = [NH3] + [NH4+]
• By substitution from Charge Balance
• [NH4+] = [OH-] + [NO3-]- [H+]
• 0.200 + 0.100 = [NH3] + [NO3-] + [OH-] - [H+]
• [NO3-] = 0.100 Therefore subtract from both
sides
• 0.200 = [NH3] + [OH-] - [H+]
• [NH3] = 0.200 - [OH-] + [H+]
8/3/2009
Chem 311
8
Buffer Example
• Mass Balance rearranged
• [NH3]= 0.200 + 0.100 - [NH4+]
– substitute in expression for NH3
• 0.100 = [NH4+] - [OH-] + [H+]
• Rearranging we see that :
•
[NH4+] = 0.100 + {[OH-] - [H+]}
• and
•
[NH3] = 0.200 - {[OH-] - [H+]}
8/3/2009
Chem 311
9
9-
3
Buffer Example
K 'b 
[OH  ][ NH 4 ]
[ NH 3 ]
• Substitute
K 'b 



[OH  ] C NH 4  [OH  ]  [ H  ]


C NH 3  [OH  ]  [ H  ]
• Exact Solution
• Just like acid but with Conc of Conjugate included
8/3/2009
Chem 311
10
Acidic buffer
[ H ]C  [ H ]  [OH ]
K 


A
'
a



C HA  [ H ]  [OH ]
• Completely rigorous – all monoprotic cases
– Nasty cubic equation
• Simplify
– If Acidic H+>>OH- Drop OH term
– If Basic OH>>H Drop H term
K a' 
8/3/2009
Chem 311


[ H  ] C A  [ H  ]
C HA  [ H  ]
11
Acidic buffer
• Simplify
– If Concentrations of Acid and Salt are high
• C >> [H+]
• C >> {[H+]-[OH-]}
– Drop those terms
K a' 
8/3/2009
[ H  ]C A
C HA
Chem 311
12
9-
4
Acidic buffer
K a' 
[ H  ]C A
C HA
• Take -log of equation
• Henderson-Hasselback
8/3/2009
Chem 311
 [ H  ]C A 

 log K a'   log

 CHA 
C  
pK a   log[ H  ]  log A 
 CHA 
C
 
pK a  pH  log A 
 CHA 
C  
pH  pK a  log A 
 CHA  13
Solution to Ammonia example
•
•
•
•
Base/Acid
 0.200 
pH  9.244  log
  9.545
 0.100 
NH3 is base (A-)
NH4+ is Acid (HA)
Things to check
– If more base than Acid then pH should be
higher than pK. Good way to make sure you
get signs right.
8/3/2009
Chem 311
14
Buffers- Resist pH Change
• Weak Acid-Conjugate Base pair
• Henderson-Hasselbach Eq
C  
pH  pK a  log A 
 C HA 
• Since CHA and CA apply to same
solution==> volumes cancel
• Use ratio of moles salt/moles acid
8/3/2009
Chem 311
15
9-
5
Buffer Capacity
• Maximum at pH = pK
• Useable in range pH=
pK 2
8/3/2009
Chem 311
16
9-
6
Chem 311
Chapter 10
Poly-protic systems
8/3/2009
Chem 311
1
Polyprotic systems
• Each proton is harder to remove
– mostly due to the increased energy
required to separate the charges.
• H3PO4 Ka1 = 7.5x10-3 Ka2 = 6.2x10-8
Ka3 = 4.8x10-13
• Polyprotic bases.
– PO4-3
– polyamines such as ethylene diamine.
• NH2-CH2-CH2-NH2 Kb1 = 9.1x10-5 Kb2
= 1.5x10-7
8/3/2009
Chem 311
2
Polyprotic systems
• If K1 >K2 solve as monoprotic acid
– (or base)
– Use K1 and quadratic
• [H+] from first Eq. Suppress other reactions
– Additional dissociation = K2
8/3/2009
Chem 311
3
10-
1
Polyprotic systems
• H3P04 + H20 <===>
K a1 
H2P04-
+
H30+
[H ][H 2 PO ]
[H 3 PO4 ]

4
• H2PO4-2 + H20 <===> HP042- + H30+
2 
K a2 
• HP04-2 + H20
[H ][H PO 4 ]
[H 2 PO 4 ]
<===> P04-3+ H30+
3 
K a3 
8/3/2009
[H ][ PO 4 ]
[H PO
2 
4
]
Chem 311
4
How much does K2 contribute
2 
K a2 
[H ][H PO4 ]
[H 2 PO4 ]

[ H  ]  [ H 2 PO4 ]
2
K2 
[ H  ][ H PO4 ]
[H  ]
2
K 2  [ H PO4 ]
8/3/2009
Chem 311
5
Amphiprotic substances
• Both acids and base reactions
• Intermeditate forms
– HC03– H2P04, HP042-
• Amino acids (e.g.alanine)
• weak acid - weak base salts
– ammonium acetate
– ammonium formate
8/3/2009
Chem 311
6
10-
2
NaH malate example
• HMal- + H20 <===> H2Mal + 0H– Kb2 = Kw/Ka1 =2.5x10-11
• HMal- + H20 <===> Mal-2 + H30+
– Ka2 =8.9x10-6
• Which reaction has larger K?
• Solution will be acidic
8/3/2009
Chem 311
7
NaH malate example
• 5 Unknowns [H2Mal] , [HMal-] ,[Mal2-], [H+] ,
and [0H-]  Need 5 equations
• Mass Balance
• CNaHMAl = [H2Mal] + [HMal-] + [Mal2-]
• Charge Balance
• [Na+] + [H+] = [HMal-] + [0H-] + 2[Mal2-]
8/3/2009
Chem 311
8
NaH malate example
• 5 Unknowns [H2Mal] , [HMal-] ,[Mal2-],
[H+] , and [0H-]  Need 5 equations
• Ka2 = [H+] [Mal2-] / [HMal-]
• Kb2 = [0H-] [H2Mal] / [HMal-]
• Kw = [H+] [0H-]
8/3/2009
Chem 311
9
10-
3
NaH malate example
• [Na+] + [H+] = [HMal-] + [0H-] + 2[Mal2-]
• [Na+] = CNaHMAl
• CNaHMal + [H+] = [HMal-] + [OH-] +2[Mal2-]
– Subtract Mass balance below
• CNaHMAl = [H2Mal] + [HMal-] + [Mal2-]
8/3/2009
Chem 311
10
NaH malate example
• [H+] = [Mal2-] - [H2Mal] + [0H-]
Ka2 
[ H  ][ Mal 2 ]
[ HMal  ]
[ Mal  2 ] 
[OH  ] 
Kw
[H  ]
K a 2 [ HMal  ]
[ H Mal ][OH  ] K w
[H  ]

Kb2  2
[ HMal  ]
K a1
[ H 2 Mal ] 
8/3/2009
K w [ HMal  ] [ HMal  ][ H  ]

K
K a1
K a1 w
[H ]
Chem 311
11
NaH malate example
K [ HMal  ] [ HMal  ][ H  ] K w
Ka2
[H ]
[H  ]
a 2 2-

[ H+] ]= [Mal
• [H
] - [H2Mal] + [0H ]
[ H  ]2  K a 2 [ HMal  ] 
[ H  ]2 
8/3/2009
[ HMal  ][ H  ]2
 Kw
Ka2
[ HMal  ][ H  ]2
 K a 2 [ HMal  ]  K w
Ka2
 [ HMal  ] 
  K a 2 [ HMal  ]  K w
[ H  ]2 1 
K a 2 


[ H  ]2 K a 2  [ HMal  ] 
K311
Chem
a 2 K a 2 [ HMal ]  K a 2 K w


12
10-
4
NaH malate example
• Rigorous equation
[H  ] 
K a1 (K a2 [HMal ]  K w )
[H  ] 
K a1  [HMal ]
• Problem
– Don’t know equilibrium concentration till we
solve equation
8/3/2009
Chem 311
13
NaH malate example
K a1 (K a2 [HMal ]  K w )
[H  ] 
K a1  [HMal ]
• Simplifying Assumptions
• 1. If [HMAl] >> KA1
• then Ka1 + [HMal-] = [HMal-]
[H ] 

K a1 (K a2 [HMal ]  K w )
[HMal ]
8/3/2009
Chem 311
14
NaH malate example
[H  ] 
K a1 (K a2 [HMal ]  K w )
[HMal ]
• Simplifying Assumptions
• If KA2 [HMAl] >> Kw
[H  ] 
K a1 K a2 [HMal ]
[HMal ]
• then drop last term - conc. cancels
[H  ] 
8/3/2009
K a1 K a2
Chem 311
15
10-
5
NaH malate example
[H  ] 
K a1 K a2
• Equation independent of concentration
• Works at high concentration only
• Use for Amino Acids
8/3/2009
Chem 311
16
NaH malate example
[H  ] 
K a1 K a2
• For NaHMal
– [H+] = (4.0x10-4 x 8.9 x 10-6 )1/2 = 5.97 x
10-5
8/3/2009
Chem 311
17
NaH malate example
• What if assumptions don’t work
• 0.0005 M NaHMal
– [HMAl]  KA1
• Calculate approximate value using
simple form
8/3/2009
Chem 311
18
10-
6
NaH malate example
• [H+] = = 5.97 x 10-5
• 1 at this pH
– [H+]2 = 2.56x10-9
– K1 [H+] = 2.39x10-8
– K1K2
=
3.56x10-9
8/3/2009
1 
2.39 x10 8
 0.770
3.10 x10 8
Chem 311
19
NaH malate example
1 
2.39 x10 8
 0.770
3.10 x10 8
• Calculate [Hmal-] =
0.0005x0.770=0.000385
8.9 x10
• Plug into
equation
 4 rigorous
6
[H  ] 
4 x10

x0.00038  1.00 x10 14
 4.18 x10 5
4 x10  0.00038
4
8/3/2009
Chem 311
20
NaH malate example
• Calculate new alpha at this pH
– alpha=0.76
• Repeat
[H  ] 


4 x10  4 8.9 x10 6 x0.000381  1.00 x10 14
 4.25 x10 5
4 x10  4  0.000381
• Result OK
8/3/2009
Chem 311
21
10-
7
Summary
• Weak Acid
[ H  ]2  K a [ H  ]  C HA K a  0
 2

• Weak Base [OH ]  [OH ]K b  Cb K b  0
C  
pH  pK a  log A 
 C HA 
• Buffer
• Amphiprotic
8/3/2009
[H  ] 
K a1 K a2
Chem 311
22
Summary
• Have to be able to tell what is present
– Stoichiometry
– Recognize acids and bases
8/3/2009
Chem 311
23
Fractional forms
• See previous lecture notes
• Alpha calculations
8/3/2009
Chem 311
24
10-
8
Chem 311
Chapter 11
Titration
8/3/2009
Chem 311
1
Simple Titrations
• No Equilibrium Chemistry to worry about
• Strong Acid-Strong Base
• Anything with really huge Keq
• Stoichiometry determines curve
8/3/2009
Chem 311
2
Simple Titrations
• Moles titrant = CtVt
• Moles Analyte = CoVo
C
• Moles un-titrated = CoVo – CtVt
Ca 
8/3/2009
CoVo  CtVt
Vo  Vt
Chem 311
3
11-
1
Molarity vs volume
• 0.1 M HCl with 0.1 M NaOH
0.12
0.1
0.08
0.06
Series1
0.04
0.02
0
0
8/3/2009
5
Chem 311
10
15
20
4
pH vs Volume
• Note rapid change at 15 ml
8
7
6
5
4
Series2
3
2
1
8/3/2009
Chem 311
0
0
5
5
10
15
20
After the Endpoint
• Stoichiometric addition of excess titrant
• Relative excess changes rapidly at EP
• Change becomes more gradual as you get
farther along.
Ct 
8/3/2009
Chem 311
CtVt  CoVo
Vo  Vt
6
11-
2
Simple Titration Curve
14
12
10
8
Series2
6
4
2
0
0
8/3/2009
5
10
15
20
25
30
Chem 311
7
Titration Calculations
• Moles Analyte = moles Titrant (x
stoichiometry factor from reaction)
• CaVa = CtVt (Stoichiometry factor)
8/3/2009
Chem 311
8
Volumetric Analysis
• Equivalence Point - Theory
– moles titrant= moles analyte
• End Point - Practice
– Indicator Changes Color
– Signal reaches specified value
– Analysis of output indicates Equivalence point
8/3/2009
Chem 311
9
11-
3
Detecting Endpoints
• Visual Indicators
• Potentiometric Titrations
– Accurate graph of data. Use compass to
find midpoint of graph.
– Curvefit to theory
– Derivatives of plot
• Titrate to specific pH
8/3/2009
– Alkalinity methods for water analysis do
Chem 311
this
10
Visual Indicators
• http://inst.santafe.cc.fl.us/~chem/intbl.html
8/3/2009
Chem 311
11
End Points
•
•
•
•
End point is where the titration is stopped
Equivalence point is where acid=base
Not always equal
Indicator error ==> Do blank titration
– add salt present at Equivalence point +
indicator and titrate
8/3/2009
Chem 311
12
11-
4
End Points
• At end of Titration – Stoichiometry
produces very large changes in the relative
amount of analyte for small additions of
titrant.
8/3/2009
Chem 311
13
Decision Tree for Weak
Acid/Base Titration Problems
Is more that one reagent added
Yes
What is limiting reagent?
Calculate concentration of all reactants and products
No
Weak Acid Only
What chemicals are Present?
Quadratic solution using Ka1
Amphiprotic Substance
Weak Acid + Conjugate Base
Weak Base Only
pH=1/2(pK1 + pK2)
Buffer - HH Equation
Quadratic solution using Kb1
8/3/2009
Chem 311
14
Practice Problem
• Calculate the pH of 25.0 ml of a 0.100 M
solution of phthalic acid after the addition
of 0, 10.0, 25.0, 35.0, 50.0 and 75.0 ml of
0.100 M NaOH
• K1’=1.12x10-3 pK1 = 2.95
• K2’=3.90x10-6 pK2 = 5.41
8/3/2009
Chem 311
15
11-
5
Practice Problem
• 0 ml weak diprotic acid only treat as
monoprotic
• K1’=1.12x10-3
[ H  ]2  1.12 x10 3 [ H  ]  0.10 x1.12 x10 3  0
[ H  ]  0.0106
8/3/2009
pH  1.97
Chem 311
16
Practice Problem
•
•
•
•
•
•
8/3/2009
10.0 ml base
moles acid = 25.0x0.1 = 2.5 mmoles
moles base = 10.0x0.1 = 1.0 mmoles
acid reacted to NaHP= 1.0 mmoles
H2P acid remaining = 1.5 mmoles
Buffer solution - use HH ignore dilution
 1.0 
pH  2.95  log   2.77
 1.5  17
Chem 311
Practice Problem
•
•
•
•
•
•
8/3/2009
25.0 ml base
moles acid = 25.0x0.1 = 2.5 mmoles
moles base = 25.0x0.1 = 2.5 mmoles
acid reacted to NaHP= 2.5 mmoles
H2P acid remaining = 0 mmoles
Amphiprotic ignore dilution
[ H  ]  1.12 x10 3 x3.90 x10 6  6.6 x10 5
Chem 311
18
pH  4.18
11-
6
Practice Problem
•
•
•
•
•
•
•
•
8/3/2009
35.0 ml base
moles acid = 25.0x0.1 = 2.5 mmoles
moles base = 35.0x0.1 = 3.5 mmoles
acid reacted to NaHP= 2.5 mmoles
base remaining = 1.0 mmole
NaHP reacted with base = 1.0 mmoles
NaHP remaining = 1.5 mmol
P2- formed = 1.0 mmole buffer HH ignore
dilution
Chem 311
19
Practice Problem
• 35.0 ml base
• NaHP remaining = 1.5 mmol
• P2- formed = 1.0 mmole buffer HH
 1.0 
pH  5.41  log   5.23
 1.5 
8/3/2009
Chem 311
20
Practice Problem
• 50.0 ml base
• moles acid (both protons) = 25.0x0.1x2 =
5.0 mmoles
• moles base = 50.0x0.1 = 5.0 mmoles
• All acid converted to phthlate P2• Weak base - treat as monoprotic -with
dilution [OH  ]2  [OH  ] K w  C K w  0
Ka2
Ka2
1x10
25 1x10 14
 0.1x x
0
6
3
.
90
x
10
75
3.90 x10 6 21
Chem 311

6
[OH ]  9.24 x10
pOH  5.03 pH  8.97
[OH  ]2  [OH  ]
8/3/2009
b
14
11-
7
Practice Problem
• 75.0 ml base
• moles protons = 25.0mlx0.1mM/mlx2 protons M=
5.0 mmoles
• moles base = 75.0x0.1 = 7.5 mmoles
• phthlate conc = 2.5 mmoles/100 ml = 0.025
• Excess base= 2.5 mmoles/100 ml = 0.025 M
• Strong base + weak base ==> strong base
• [OH-]=0.025 M pOH=1.60 pH=12.40
8/3/2009
Chem 311
22
Using Fraction Titrated
• Avoids problem of figuring out
stoichiometry
• Avoids need to recognize species present
• Pick pH and calculate fraction titrated
• Only way to do spreadsheets
8/3/2009
Chem 311
23
8/3/2009
Chem 311
24
11-
8
8/3/2009
Chem 311
25
11-
9
Chem 311
Chapter 12
Complexometric Titration
8/3/2009
Chem 311
1
SEQUENTIAL COMPLEXATION
BY SIMPLE LIGANDS
• Ni(H2O)42+ + 4 Cl- <===> NiCl42- + 4H2O)
REACTION OCCUR IN A SERIES OF STEPS
• Ni (H2O)42+ + Cl- <===> Ni (H2O)3 Cl+
K1 
• Ni (H2O)3 Cl+ + Cl- <===> Ni (H2O)2 Cl2+
• Ni (H2O)2 Cl2+ + Cl- <===> Ni (H2O) Cl3• Ni (H2O) Cl3- + Cl- <===> NiCl4-2
8/3/2009
K4 
[NiCl  ]
2
[Ni ][Cl  ]
K2 
K3 
[NiCl 2 ]
[NiCl  ][Cl  ]
[NiCl 3  ]
[NiCl 2 ][Cl  ]
[NiCl 4  2 ]
[NiCl 3  ][Cl  ]
Chem 311
2
Overall Formation constants
• ß1= K1
ß2= K1K2 ß3= K1K2K3
ß4=K1K2K3K4
[NiCl ]
2 
2
2
 2
[Ni ][Cl ]
•
• WRITE A MASS BALANCE FOR NICKEL
• CNi = [Ni 2+ ] + [NiCl+ ] + [NiCl2 ] + [NiCl3- ] + [NiCl42- ]
• Rearrange K's to get mass balance in terms
of [Ni ] and [Cl ]
8/3/2009
Chem 311
3
12-
1
Rearrange Betas
[NiCl+ ] = K1 [Ni2+][Cl- ]
[NiCl2 ] = K1 K2 [Ni2+][Cl- ]2 = ß2 [Ni2+][Cl- ]2
[NiCl3- ] = ß3 [Ni2+][Cl- ]3
[NiCl42-] = ß4 [Ni2+][Cl- ]4
Substitute into Mass Balance
CNi = [Ni2+] + b1 [Ni2+][Cl-] + b2 [Ni2+][Cl-]2+ b3
[Ni2+][Cl-]3+ b4 [Ni2+][Cl-]4
•
•
•
•
•
•
8/3/2009
Chem 311
4
Define alpha metal
2
[Ni ]
C Ni
 Ni 
2
 Ni 
[Ni ]
2
2
2
2
2
2
3
[Ni ] +  1 [Ni ][Cl  ] +  2 [Ni ][Cl  ] +  3 [Ni ][Cl  ] +  4 [Ni ][Cl  ]
Ni
M
4
1
1 +1[Cl] +2[Cl]2+ 3[Cl]3+ 4[Cl]4
1
 2
3
1 + 1 [L ] +2 [L ] + 3 [L] +... n [L]

8/3/2009
n
Chem 311
5
Multidentate Ligands for
Complex Formation
• Chelate Effect - Formation of rings
– 5 or 6 member rings are best.
N
N
O
O
Cu
N
O
Ni
N
8/3/2009
Chem 311
O
6
12-
2
Multidentate Ligands for
Complex Formation
• Entropy effects enhance stability of
multidentate ligands.
• M(H2O)6 + 6 L <===> ML6 + 6H2O
– 7 <===> 7 entropy change small
• M(H2O)6 + L <===> ML + 6H2O
– 2 <===> 7 large increase in entropy
– greater entropy change for the latter reaction.
8/3/2009
Chem 311
7
Complexation Titration
• For titrations, 1:1 complexes best
• Intermediate equilibria make titration
breaks less sharp for higher No. of ligands.
14
ML6
pM
ML
7
8/3/2009
Chem 3110
8
EP
Volume Titrant
AMINO POLYCARBOXYLIC
ACIDS
• Most common and useful polydentate
ligands.
– They are used extensively for titrations
– Tie up metal for a variety of applications
• Mayonnaise
• Available with 4, 6, 8 and 10 coordination
sites
• Match to Maximum Coordination No. of
8/3/2009
Chem 311
metal
9
12-
3
AMINO POLYCARBOXYLIC
ACIDS
• EDTA - Ethylenediamine
tetraacetic acid.
H
O
H
– This has 6 Lewis base sites, 4
oxygen and 2 amine electron
pairs.
– designated as H4Y and its anion as
Y4– All six complexation sites are able
to bind to a single metal ion for
many metals.
8/3/2009
O
O
N
O
O
N
H
O
H
O
O
Chem 311
10
AMINO POLYCARBOXYLIC
ACIDS
• NTA - Nitrilotriacetic acid.
– Tetradentate - this is best for small metals.
• DETPA - Diethylenetriamine pentacetic
acid.
– Best for 8 coordinate metals such as the 3rd
Transition series and the Lanthanides.
• TTHA - Triethylenetetramine hexacetic
acid.
8/3/2009
– This is for 10 coordinate metals such as the
Chem 311
actinides.
11
ACID-BASE CHEMISTRY OF
LIGANDS
• Virtually all ligands are Bronsted bases,
– strong or weak
– For weak base ligands, the pH of the solution
determines how much of the total concentration
of the ligand is free to form the complex.
H
O
H
O
O
N
O
O
N
H
8/3/2009
Chem 311
O
H
12
O
O
12-
4
ACID-BASE CHEMISTRY OF
LIGANDS
• Use EDTA as an example:
• H4Y Primary standard but relatively
insoluble
• Na2H2Y .2H2O Not a true primary standard
but soluble to more than 0.05 m/l .
• At low pH most EDTA is in the form H2Y28/3/2009
Chem 311
13
ACID-BASE CHEMISTRY OF
LIGANDS
• At low pH most EDTA is in the form H2Y2-pK '1
-pK '2
0
-pK '4
-pK '3
-2
log alpha
-4
-6
H2Y2-
HY3-
-8
-10
Y4-
H3Y-
-12
H4Y
-14
0
8/3/2009
2
4
6
8
10
12
14
+
]
p[H3O311
Chem
14
ACID-BASE CHEMISTRY OF
LIGANDS
• M+n + H2Y-2 <===> MYn-2 + 2 H+
• Normally titrations must be buffered to
keep pH constant.
• A further complication lies in the fact that
the reaction of this form with metal liberates
H+.
8/3/2009
Chem 311
15
12-
5
Conditional Formation
Constants
• Titrations. These are useful for describing
the formation constant under a specific set
of experimental conditions.
– pH
– Auxillary Ligands
• Titrations always buffered to hold pH
constant
8/3/2009
Chem 311
16
Control pH to Control [Y]
8/3/2009
Chem 311
17
Conditional Formation
Constants
• M + Y-4 <===> MY
[CaY]
Kf
•
[Ca 2  ][Y4  ]
• [Y4- ] = 4 CEDTA
K 'f  K f  4 
[CaY]
[Ca 2  ]C EDTA
– NOTE The conditional formation applies in this
case at only the pH used to calculate  4 for
EDTA.
8/3/2009
Chem 311
18
12-
6
EXAMPLE
• Using conditional formation constants to
predict feasibility of titration.
• 50.00 ml of 0.0100 m Cu2+ is titrated with
0.0100 m EDTA at pH 3.00
• Kf = 6.3x1018
– Note this is a large POSITIVE exponent.
8/3/2009
Chem 311
19
EXAMPLE
• Calculate  4 at pH = 3.00
•  4 = 2.5 x 10-11
• Calculate Kf' = 6.3 x 1018 * 2.5 x 10-11
• = 1.6 x 108
•
•
8/3/2009
Kf’= [CuEDTA]
[Cu]CEDTA
Chem 311
20
Example
• Initial pCu = -log 0.0100 = 2.00
• Before equivalence point:
[Cu 2  ] 
•
moles Cu untitrated
total volume
• moles CuEDTA dissociated = moles EDTA not reacted
• During most of the titration the excess Cu
suppresses the second term until close to the
endpoint. Common ion effect
8/3/2009
Chem 311
21
12-
7
Example
• 40.00 ml of titrant added:
•
[Cu+2] = 0.0500 * 0.0100 - 0.0400 * 0.0100 = 0.0011
•
•
0.0400 + 0.0500
pCu = 2.96
8/3/2009
Chem 311
22
Example
• At equivalence point. Since Kf' is so large
we know the reaction will lie far to the
right.
• Cu+2 + Y-4 ====> CuY-2
• [CuEDTA] ≈ C0 V0
=
•
V0 + VT
0.0100 * 0.0500
0.0500 + 0.0500
=
• =0.0050M
• [Cu2+ ] = C EDTA
8/3/2009
Chem 311
23
Example
•
•
•
•
8/3/2009
Kf' = 1.6x108
=
[CuEDTA]
[Cu2+ ]C EDTA
[Cu2+ ] = 5.5x10-6
Chem 311
=
0.00500
[Cu2+ ]2
pCu = 5.26
24
12-
8
Example
• After the Equivalence point• EDTA is now in stoichiometric excess
60.00 ml of titrant:
• moles EDTA = stoichiometric excess +
dissociation of CuEDTA
• C EDTA = CT VT - C0 V0
•
V0 + VT
8/3/2009
Chem 311
25
Example
• C EDTA= 0.0100 * 0.0600 - 0.0100 * 0.0500
•
0.0500 + 0.0600
• = 0.000910
• [CuY2- ] = C0 V0
= 0.000500
V 0 + VT
0.110
• = 0.00450
8/3/2009
Chem 311
26
Example
• [Cu2+ ] = 0.00450
= 3.1x10-8
•
0.000910 * 1.6x108
• pCu = 7.51
• Kf' determines sharpness of titration
break.For Cu+2
– pH = 2.00 Kf' = 2.3x105
– pH = 3.00 Kf' = 2.1x1010 larger Kf' gives
sharper break.
8/3/2009
Chem 311
27
12-
9
How large a Kf’ is Needed
• Rule of thumb - 1 ppt of sample untitrated
at the end point and a consequent 1 ppt
excess of titrant.
• For CY m/l EDTA we can do the following
calculation:
K 'f 
0.999 xCm 0
[ MY ]
106


[ M ]C EDTA 0.001xCm 0 x 0.001xCY CY
CY  0.01
8/3/2009
Chem 311
28
K 'f  108
Auxillary Ligands
• Problems
– High pH required and metal not soluble
– Two metals with similar Kf and we want to
titrate just one
• Add auxillary ligand - MASKING AGENT
8/3/2009
Chem 311
29
Auxillary Ligands
• [M] =  m Cm where  m refers to the
auxiliary ligand.
Kf 
[ MY ]
[ MY ]

[ M ] 4CY  mCm 4CY
K 'f'   m 4 K f
8/3/2009
Chem 311
30
12-
10
EXAMPLE
• Titration of Cd2+ with EDTA at pH 9.24 in
a NH3
• NH4+ buffer which also serves to mask Cd
to prevent precipitation.
• Both NH3 and NH4+ are 0.100 m/l
• Kf for CdEDTA = 3.16x1016
• Cd2+ + 5 NH3 <===> Cd(NH3)52+
8/3/2009
Chem 311
31
Example
• Cd2+ + 5 NH3 <===> Cd(NH3)52+
• K1 = 398 K2 = 316 K3 = 24.5 K4 = 7.59
K5 = 2.09
1
m 
m 
1  K1[ L]  K1 K 2 [ L]2  K1 K 2 K 3[ L]3  ...
1
 1.4 x10  4
1  39.8  1258  3018  2291  479
•  4 = 0.087
• Kf' = 3.16x1016 * 1.4x10-4 * 0.087 = 3.8x1011
8/3/2009
Chem 311
32
Example
• Titration should work well.
• But note that the titration break is not as
great as in the absence of NH3.
• You could not do it without NH3 due to
precipitation of Cd(OH)2.
8/3/2009
Chem 311
33
12-
11
End Point Detection
• Colored Complexes.
– CuEDTA is bright blue and can be monitored
with a spectrometer.
– a colored complex with a substantially lower
Kf' can be used to monitor the endpoint of a
colorless complex. eg. Cu and Fe(III) can be
titrated together.
8/3/2009
Chem 311
34
End Point Detection
•
Cu titration with EDTA
Abs.
Vol. Titrant
8/3/2009
Chem 311
35
End Point Detection
•
Cu and Fe titration with EDTA
Cu E.P.
Abs.
Fe E.P.
Vol. Titrant
8/3/2009
Chem 311
36
12-
12
End Point Detection
• Electrochemical.
– Endpoints have been monitored by change in
pH
– mercury electrode
– ion selective electrodes.
•
8/3/2009
Chem 311
37
End Point Detection
• Indicators.
• metallochromic indicators
• Serendipity science.
– 1945 - a group of Swiss chemists headed by
Swartzenbach accidentally synthesized the
compound Murexide (Roman purple) which
proved to be an indicator for metals.
8/3/2009
Chem 311
38
Murexide
-O
N
O
O
N
N
N
O
O
8/3/2009
N
Chem 311
O
39
12-
13
EBT
• This lead to the development of Eriochrom
Black T
– note nitro and sulfito groups
O
O
N
N
N
O
HO
S
8/3/2009
OH
O ChemO311
40
Calmagite
• N,N,O,O tetradentate complexes
N
N
O
HO
S
O
8/3/2009
OH
O
Chem 311
41
Indicator equilibria
•
pK = 6.3
pK = 11.5
• H2In- <========> HIn-2 <========> In-3
• |
|
|
• red
blue
yellow-orange
• In-3 + M <====> MIn RED
•
with Mg, Ca, Zn, Cd, Hg,
Al,
Ga, In, Pb, Fe, Ti, Co, Ni, Cu, Pt, Rare earth
8/3/2009
Chem 311
42
12-
14
Indicator reaction
• KfEDTA >> KfIn
– Before endpoint there is excess metal so the
indicator is present as M-In complex. Solutions
are red.
• At end point, EDTA strips the metal from
the indicator complex and the solution
becomes blue. This only works well if the
reaction is fast.
8/3/2009
Chem 311
43
Indicator reaction
• For slow reactions the best approach is a
back titration
– excess EDTA is added and allowed to react.
Then the solution is back titrated with a
standard Mg+2 solution to the reverse endpoint.
8/3/2009
Chem 311
44
Ca titration - most common
• Direct EDTA Titration work
– The addition of Mg to the titrant normally
makes the Ca determination better
– Ca binds more tightly to EDTA than Mg, the
indicator should be stripped of Ca near the
endpoint and be present in the MgIn complex
form.
– This then gives a sharp endpoint just after the
Ca equivalence point.
8/3/2009
Chem 311
45
12-
15
Back Titration
• Used when complex formation is slow
• Add excess EDTA
• Titrate with Mg2+ or Mn2+
8/3/2009
Chem 311
46
Displacement Titration
• Useful when indicator is lacking for specific
metal titration.
• Add excess MgY complex (standardized
amount)
• Allow the metal of interest to displace the
Mg from the complex
• Titrate the Mg released with EDTA
8/3/2009
Chem 311
47
Back titration Example
• A 50.0 ml solution containing Ni2+ and Zn2+ was
treated with 25.0 ml of 0.0452 M EDTA to bind all
the metal. The excess EDTA was titrated with
0.0123 M Mg2+ and required 12.4 ml to reach the
endpoint. An excess of the reagent 2,3-dimetcapto2-propanol was then added to the solution to
displace the EDTA from the Zn2+. The solution was
then titrated with additional Mg2+ and 29.2 ml of
the titrant was required to reach the new endpoint.
Calculate the molarity of Ni2+ and Zn2+ in the
original solution.
8/3/2009
Chem 311
48
12-
16
Back titration Example
•
•
•
•
Moles EDTA added= 1.130 mMol
Moles Mg to titrate excess=0.152 mMol
Moles Zn + Ni= EDTA-Mg = 0.978 mMol
Moles Mg after Zn displaced = moles Zn=
0.359 mMol
• Moles Ni= total - moles Zn =0.619 mMol
8/3/2009
Chem 311
49
Example 2
• A mixture of Mn2+, Mg2+, and Zn2+ was analyzed as follows: A 25.00
ml sample was treated with 0.25 gm of hydroxylamine hydrochloride ,
a reducing agent to keep the Mn2+ from being oxidized. The solution
was buffered at pH 10.0 by the addition of 10 ml of ammoniaammonium buffer. A few drops of Eriochrom Black T indicator were
added and the sample was diluted to 100 ml. It was warmed to 40oC
and titrated with 39.98 ml of 0.04500 M EDTA to the blue endpoint.
At this point 2.5 gm of NaF were added to displace Mg2+ from its
EDTA complex. The solution was titrated with 10.26 ml of 0.02065
M Mn2+ to a red endpoint, indicating all EDTA was now complexed.
After this endpoint is reached, 5 ml of 15 % (w/w) aqueous KCN was
added to displace the Zn2+ from its EDTA complex. It required 15.47
ml of the standard Mn2+ solution to reach the third endpoint. Calculate
the number of milligrams of each metal in the initial 25 ml sample of
unknown.
8/3/2009
Chem 311
50
Example 2
•
•
•
•
8/3/2009
Moles EDTA = total moles metal = 1.799 mMol
moles Mn to 2nd EP = moles Mg=0.211 mMol
moles Mn to third EP = moles Zn=0.319 mMol
Moles Mn in initial = total - (Mg + Zn)=1.269
mMol
Chem 311
51
12-
17
Applications
•
•
•
•
8/3/2009
Spot Tests
Test Strips
Flow Injection Analysis
Immunoassays
Chem 311
52
12-
18
Chem 311
Chapter 14
Electrochemistry
8/3/2009
Chem 311
1
Oxidation - Reduction
• Electrons transferred coulomb (q)
– 1 coulomb = 1 amp for 1 sec
• Electricity
– q= nF coulombs = number of electrons x F
• F= 96,500 electrons/coulomb
• ΔG= -nFE = -Eq
8/3/2009
Chem 311
2
Ohm’s Law
• E=IR
• Voltage = current(amps)x resistance (ohms)
8/3/2009
Chem 311
3
14-
1
Electrochemical Cell
• 2 Half Cells
• Salt Bridge
• Potential = E
eV
Salt Bridge
Pt
Pt
OX
8/3/2009
Chem 311
Ce (IV) 1.0
m/l
RED
Fe (II) 1.0
m/l
4
Chemical Analysis
• A variety of chemical analyses involve
electrochemical cells.
–
–
–
–
–
–
8/3/2009
Potentiometry 311
voltametry 312
amperometry
chronopotentiometry
coulometry
others
Chem 311
5
Electron Energy Levels
• Electron Flow in Metals
– Band Theory
– Electrons Move in Conducting Band
• Electron Levels in Metal Electrodes
– Fermi Level
– If Fermi Level > Empty Orbital of Ion
Reduction occurs
– Vice Versa
8/3/2009
Chem 311
6
14-
2
Electron Transfer
• Fermi level of
electrons in electrodes
shown
• Fe2+ filled orbital
• Ce4+ empty orbital
8/3/2009
Chem 311
7
Electron Transfer
• Potential is difference
in energy of two
electrodes.
• Measure with no
electron flow
• Thermodynamic
potential
• ΔG = -nFE
8/3/2009
Chem 311
8
Measuring Potential
• Operational amplifiers
8/3/2009
– measure potential while allowing little current
flow.
– The input of the Op Amp appears to the cell as
a simple resistor with resistance ranging from
1010 to possibly as high as 1015 ohms depending
on quality and cost. This value is often called
the input impedance of the op amp.
– We can calculate the rate of the reaction
occurring for any given cell EMF and input
impedance
Chem 311
9
14-
3
Potentiometer Circuit
Voltmeter
Voltage Follower
Amp
Salt Bridge
8/3/2009
Chem 311
10
Measuring Potential
• Ohm's Law E = IR.
– E= EMF volts
– R = impedance or resistance ohms
– I = current amps
• For R=1012, if the cell EMF is 1.00 volts
then I = 1x10-12 amps.
8/3/2009
– For n=1, the application of Faraday's law
(moles reacted = it/nF t in seconds) yields a
rate of reaction of 1.04x10-17 moles/sec or
about 600000 atoms/sec reacting. This is really
Chem 311
slow.
11
Example of a Cell
• This cell is constructed without a salt bridge. It uses a
porous membrane. The [H+] is the same on both sides of
the membrane, hence no concentration potential develops.
V
Porous
membrane
8/3/2009
Pt
electrode
with H2
bubbler
1.0 M
HCl
Chem 311
Ag electrode
with AgCl
12
14-
4
Line Notation of Cell
• Pt, H2 (1 atm.)/ H+ (a = 1.0)/AgCl/Ag
•
Anode
Cathode
•
OX
RED
• LEFT side is the ANODE-OXIDATION
The cell reaction will have as reactants the
REDUCED form of the material in the
LEFT half cell and the OXIDIZED form of
the material in the RIGHT half cell.
8/3/2009
Chem 311
13
Half Reactions
• H2 ==> 2H+ + 2 eOxidation
• AgCl + e ==> Ag + ClReduction
•
•
•
•
8/3/2009
H2 + 2AgCl ==> 2H+ + 2 Ag + 2ClRedox Couple
Conjugate oxidation- reduction pair
E=0.2222 volts at STP
Chem 311
14
Conventions for the
Description of Electrochemical
Cells.
+2
+4
• Pt / Fe (1.0 M) // Ce (1.0 M) / Pt
• Fe2+ =====> Fe3+ + e- and Ce4+ + e- ====> Ce3+
– All concentrations and partial pressures are
listed in parenthesis.
– Phase boundaries are shown with a single '/’
– Gaseous reactants are normally show in the
same phase as the electrode material. eg.
Pt, H2 (1.0. atm) / H+ (1.0 M)
8/3/2009
Chem 311
15
14-
5
Conventions for the
Description of Electrochemical
Cells.
• Every phase boundary has a potential
difference associated with it.
• Salt bridge or phase boundaries assumed to
generate no potential is designated by the
double '//'.
– These are constructed from a tube filled with a solution of an inert
electrolyte. Normally the tube is closed with glass frits or are made from
an electrolyte in agar to minimize the mixing of the bridge solution with
the cell solutions. In many commercial batteries, porous membranes
(paper or cardboard are often used) are employed in place of a traditional
8/3/2009 salt bridge.
Chem 311
16
Half Reactions
• Can’t measure just One half
• Need a Standard Reference
• Normal hydrogen Electrode
• This is made from a Pt electrode in 1 M H+ in 1
atm H2. The Pt electrode must be carefully coated
with Pt black. The potential of this HALF CELL is
defined as exactly 0.00000 volts at STP. The
operation of this electrode is also hazardous due to
the use of hydrogen.
8/3/2009
Chem 311
17
1953 IUPAC Conventions
• 1. Standard Potential Eo all reactants and
products at 1.0 M activity.
• 2. Std.Potential for a 1/2 cell is the cell
EMF of that 1/2 cell coupled with the NHE.
• 3. The sign of the Std. Potential is the sign
of the 1/2 cell electrode where the NHE is
operating as the ANODE in the reaction.
(Galvanic cells thus have + Std.Potentials
and Electrolytic cells have - Std.Potentials.
8/3/2009
Chem 311
18
14-
6
Tables of Std.Potentials
• Appendix - Standard Potentials Eo
• Formal Potentials - Ignore Activity Eo’
• Oxidized form on left will transfer electrons
to the reduced form of anything with lower
potential it on the right (similar to acid base
half reaction table)
8/3/2009
Chem 311
19
8/3/2009
Chem 311
20
Nerst Equation
• Nerst eq. applies equally well to 1/2 RX and
cell RX.
E  Eo 
8/3/2009
ac ad
0.05916
log Ca Db
n
a A aB
Chem 311
21
14-
7
Calculate EMF of CELL RX
• From Cell Schematic (Shorthand Notation)
• Fe/Fe2+(1.0) // Sn4+(1.0), Sn2+ (1.0) /Pt
• Fe + Sn4+ =====> Fe2+ + Sn2+
• Fe2+ + 2e ====> Fe
Eo Fe2+,Fe = - .447
reduction
• Sn4+ + 2e ===>Sn2+ Eo Sn4+ +,Sn2+ = + .151
– More negative potential will be oxidation –
reverse reaction will occur
8/3/2009
Chem 311
22
Calculate EMF of CELL RX
•
•
•
•
Ecell = EFe,Fe2+ - ESn2+,Sn4+
0.151 – (-0.447) = 0.598 volts
Ecell = EoCathode- EoAnode
NOTE E does not depend on how much
we use. (intensive property) 1 mole, 2
moles etc. Measured under conditions of
No Reaction.
8/3/2009
Chem 311
23
Calculate E1/2 using Nerst At non-standard conditions
•
Fe3+(.200)//Mn04-(.010),
+
, H (1.0)/Pt
look for 1/2 Rx in table
Fe3+====> Fe2+ + eE Fe3+,Fe2+ = 0.771
EFe3+,Fe2+ = 0.771
Mn04- + 8H+ + 5e- ====> Mn2+ + 4H20
E Mn04-,Mn2+ = 1.51
Pt/Fe2+(.100),
Mn2+(1.0x10-4)
•
•
•
•
•
8/3/2009
•
Chem 311
24
14-
8
Calculate E1/2 using Nerst At non-standard conditions
• As oxidation
• EFe3+,Fe2+ = Eo - 0.0591 log [Fe2+]
•
1
[Fe3+]
• E = 0.771 - 0.0591 log 0.100 = 0.771 + 0.0178
•
1
0.200
•
= 0.789 volts
8/3/2009
Chem 311
25
Calculate E1/2 using Nerst At non-standard conditions
• EMn04 ,Mn2+ = 1.51 - .0591 log [Mn2+]H20
•
5
[Mn04-][H+]8
• = 1.51 -.0591 log 1.0 x 10-4
•
5
0.010x(1.0)8
•
potential very sensitive to [H+]
•
= 1.51 + .026 = 1.536
8/3/2009
Chem 311
26
Calculate E1/2 using Nerst At non-standard conditions
• Balanced RX
• 5Fe2+ + Mn04- + 8H+ + 5e-  5Fe3+ + Mn2 +
4 H20 + 5e-
• Ecoll = 1.536 -(0.789) = + 0.747
• Note Potential of 5 Fe2+ =
as for 1
8/3/2009
Chem 311
5Fe3+ same
27
14-
9
Methods of Analysis
• Direct Potentiometry
– Nerst Eq. activity measurements
– Calibration Curve conc. Measurements
– Standard Addition
• Potentiometric Titration
8/3/2009
Chem 311
28
14-
10
Chem 311
Chapter 15
Potentiometry
8/3/2009
Chem 311
1
Reference Electrodes
• Ag/AgCl reference electrode is also
popular. 0.2222 v
• Most common
– No Hg
8/3/2009
Chem 311
2
Reference Electrodes
• Saturated Calomel electrode SCE
Hg,Hg2Cl2/ Hg2+2 (sat.), KCl (sat.)// E =
+0.2415 volts
8/3/2009
Chem 311
3
15-
1
Junction Potentials
• Can be a major problem 1-3 mV
• Both positive and negative ions must be
equally mobile through junction.
• Leaky electrodes - allow free passage of
solution
• Salt Bridge 8/3/2009
Chem 311
4
Junction Potentials
• K+ and Cl –
• Best choice
8/3/2009
Chem 311
5
Errors
• Error due to 1 mV inaccuracy =
– 4% rel conc. n = 1
– 8%
n=2
– etc.
• Accuracy of direct potentiometry limited by
junction pot. Typical salt bridge can have up to 23 mV.
• Not a problem in titrations and std. add
• calibration curves can be a problem – matrix
• See Rainwater example in text
8/3/2009
Chem 311
6
15-
2
Indicator Electrodes
• Electrodes of the 1st kind (Probe the
primary reactant metal)
• Metal electrodes• don't work very well
– Contamination
– Interferences
• Rarely used for Direct Analysis
8/3/2009
Chem 311
7
Indicator Electrodes
• Electrodes of the 2nd kind (probe a
secondary reactant)
– Ag/AgCl - potentiometric titration of Cl
– Quinone/hydroquinone pH electrode
8/3/2009
Chem 311
8
MEMBRANE INDICATOR
ELECTRODES
•
•
•
•
•
8/3/2009
Glass electrode (pH) is good example.
If only one type of charged ion can move
Emem = - RT ln a2
nF
a1
activity. of solutions on two sides of
membrane
Chem 311
9
15-
3
MEMBRANE INDICATOR
ELECTRODES
• If a1 is a constant
• Emem = K - RT ln a2
•
nF
•
• Glass membrane
– Si02 Li20 or Na20 Ca0
8/3/2009
Chem 311
10
Glass Membrane Electrode
• Need
solutions for
electrical
contact with
membrane
Dry Glass
External
Solution
8/3/2009
Internal
Solution
Chem 311
11
Hydrated gel
pH electrode
Volt
meter
• Total Potential
includes potential
of electrode on
both sides of the
membrane.
• pHunk = pHs +
•
.0591
Eunk-Es
8/3/2009
Reference
Solution
External
Electrode
Internal Solution
and Electrode
Chem 311
Porous Junction
12
15-
4
Glass Electrodes
• Glass electrodes with Na20 Al203 B203
respond to Na+, Li+, & K+ to some extent.
• Useful as selective electrodes for these ions
• (also respond to H+ so [H+] must be kept
low)
8/3/2009
Chem 311
13
Ion SELECTIVE Electrodes
• If electrode responds to several different
ions (most electrodes do)
• relative response described by selectivity
coefficient kx,y
– relative response to ion x in presence of ion y
ns
 0.05916  
 log [ X ]   k x , y [Y ] n y
E  constant   

y
 nx  
8/3/2009




Chem 311
14
Ion SELECTIVE Electrodes
ns
 0.05916  
 log [ X ]   k x , y [Y ] n y
E  constant   

y
 nx  




• β is measure of how closely the slope
follows the Nerst type behavior (Nerstian).
Should be approx = 1
• Use sign on n - Positive ions give positive
slope, negative ions give negative slope.
8/3/2009
Chem 311
15
15-
5
Example of Selectivity
• Na+ glass electrode 11% Na20 18% Al203 71%
Si02
• Specific example for sodium electrode and
potassium interference
•
KK/Na = 2800
• Na+ response is = 2800 x K+ response
• KK/Na = 1/KK/Na = 1/2800 = 3.57x10-4
8/3/2009
Chem 311
16
Example of Selectivity
• For interference < 1% of concentration
• [X] > 0.01 * Kx,y [Y]
• [K+] would have to be 2800 x[Na+] to give
an equal potential
•
1% error if K+ = 28 x Na+
• useful to establish working conditions
8/3/2009
Chem 311
17
Liquid Ion Exchange
Membranes
• Immiscible organic phase
interposed between
internal reference solution
and external solution.
• Organic phase contains
some substance which will
transport one ion
preferentially across
membrane. Porous to one
type of ion.
8/3/2009
Chem 311
18
15-
6
Liquid Ion Exchange
Membranes
• Ca didecylphosphate neutral (org. soluble)
• overall E = Q + .0591 log [ Ca2+]
•
2
• Note N = 2 sensitivity only 1/2 that for N = 1
8/3/2009
Chem 311
19
Liquid Ion Exchange
Membranes
• Other Liquid exchanges
• Macrocyclics
– penicillin
– Aureomycin
– Valinomycin
• Crown Ethers K+ 16 crown 5
• Alkyl phosphates Ca2+
• Bidentate ligands (transition metals)
8/3/2009
Chem 311
O
O
O
O
O
20
Liquid Ion Exchange
Membranes
• Ion Pair Formation
– Tetraalkyl ammonium salts
– Alkyl amines
– 1,10 phenanthroline Fe (III) salts
8/3/2009
Chem 311
21
15-
7
Liquid Ion Exchange
Membranes
• Liquid exchangers somewhat limited
• Generally work only down to 10-3 or 10-4 M
– Limited by solubility of exchanger and of
organic solvent in water.
– Slow response - depends on viscosity and
diffusion rate
• 2-20 micron capillary
• measurements in
• single living cells
8/3/2009
KCl
filling
solution
Chem 311 Organic ion
Exchanger
Tungsten wire
22
Treated Tip
Solid State Membranes
• LaF3 single crystal (doped with Eu)
– very conductive - F- ions mobile
– Linear potential from 1 M to 1x10-5 (1x10-7)
– 0H- interferes pH must not be too high.
• But no response to HF
• HF <===> H+ + F- KA = 6.8x10-4
• pH must be controlled (5.5 typical)
8/3/2009
Chem 311
23
Solid State Membranes
• also F- + Mn+  MF metal complexes
• add NTA or EDTA to free F• Other Solid State Electrodes
– AgS
+ AgCl AgBr AgI AgSCN
• Rapid and selective
8/3/2009
(Ag+, S2-, Cl-.)
Chem 311
24
15-
8
Solid State Membranes
• Linear response limited by Ksp (solubility
of exchange crystal)
•
10-10 10-12 M solutions often give good
values
• lower solubility ===>lower limit of
linearity
– I<Br<Cl
8/3/2009
Chem 311
25
Solid State Membranes
• Shape of
curve
E
Slope= 0.0592/ z
Solubility limit
Log_Conc entration
8/3/2009
Chem 311
26
Heterogenous membranes
• Silicone polymer + precipitate
of some insoluble salt.
• PVC
• Coated wire electrodes
• Tungsten wire - treated to
become pH electrode
8/3/2009
Chem 311
27
15-
9
Gas Sensing Electrodes
• Gas permeable membrane
• Ammonia Electrode
•
NH3 + H+ <===> NH4+
• pH electrode or NH4+ electrode
• Also available for CO2, S02,
H2S & N02
8/3/2009
Chem 311
28
Enzyme Electrodes
• ISE, pH, or gas electrode
• Urease <===>NH3
•
• Decarboxylazes===>H+
pH Electrode
Enzyme in
acrylamide gel
• 2 enzyme sandwich 8/3/2009
– cholesterol electrode
Chem 311
29
Enzyme Electrodes
• Nerve gas electrode (& phosphate
pesticides) - Cholinesterase inhibitors
– enzyme film
– add substrate to sample
– monitor reduced activity
• Vitamin D electrode etc.
• Nick Schmit with Gary Rechnitz
8/3/2009
Chem 311
30
15-
10
State Of The Art
• Electrochemical sensors are often fabricated
like integrated circuits with multiple sensors
in a very small space.
– Field Effect Transistors and other semiconductor circuits (Metal Oxide
semiconductors) now used as sensors.
• Mechanical nose - sensor array
– spoiled food, ripe fruit, mine detection
8/3/2009
Chem 311
31
Semiconductor Electronics
• Silicon (4 e) doped with
• Al 3 e p-type
• P 5 e n-type
8/3/2009
Chem 311
32
Diode
• Allows electron flow only np
8/3/2009
Chem 311
33
15-
11
FET
• 2 PN Junctions
8/3/2009
Chem 311
34
Analysis using FET
8/3/2009
Chem 311
35
FET and MOS-FET
•
•
•
•
Sensors for Solution
Sensors for vapors
Made in arrays 10x10 etc
Each FET with different Chemical sensor
– Multiple sensitivities
8/3/2009
Chem 311
36
15-
12
Problems with ISE's
• Slow response (minutes) for Liquid
Junction
• Short life ISE's months
• Enzymes days or hours
• High resistance - good pH meters required
8/3/2009
Chem 311
37
Methods of Application of
ISE's
• Calibration Curves
– Standards and samples of similar ionic strength
– Keep Ejunct similar
– Interfering ions minimized
• N=1
59 mV/log C
• N=2 28 mV/log C
• N=3 20 mV/log C
8/3/2009
Chem 311
38
Methods of Application of
ISE's
• Standard Addition
– Measure sample
– E = Q - .0591 log Cx
•
n
• Measure sample + Std.
– E = Q - .0591 log (Cx+Cs)
•
n
• Assumes linear portion of response.
8/3/2009
Chem 311
39
15-
13
Methods of Application of
ISE's
• If addition causes little volume change Ej
will stay the same
• Std. allows compensation for unknown
matrix
8/3/2009
– eg. ionic strength and Ej effects minimized
– Ex = Q + .0591 log Cx
–
n
– Es = Q + .0591 log VsCs+VxCx
–
n
Vs+Vx
Chem 311
40
Methods of Application of
ISE's
n( E x  E s )
V C  Vx C x
 log C x  log s s
Vs  Vx
0.05916
n(E E)
• Take inverse log
• rearrange
x s
Cx(Vs Vs)
100.0592 
VsCs VxCx
Cx 
8/3/2009
Cs Vs
n(E E )0.0592
(Vx  Vs ) 10
x
s
Chem 311
 Vx
41
Methods of Application of
ISE's
•
•
•
•
•
•
Graphical treatment of std. addition
Log C on X axis
Put Cx at 0
Plot Standards
Extrapolate to
Y=0
Potential
8/3/2009
Chem 311
-Cx
42
Unk.
Unk+S1
Unk+S2
15-
14
Methods of Application of
ISE's
• Potentiometric Titration
– Very precise and accurate
– but not applicable at such low conc. as direct
potentiometry
• 1st and 2nd Derivatives used for end point
determination.
8/3/2009
Chem 311
43
Clinical Analyzers
• Electrochem on a Chip
– Disposable
– ISE’s
8/3/2009
Chem 311
44
Resurgence of ISE’s
• New Techniques
– Ppb level analysis
– Pb in drinking water < 5 ppb
• Add EDTA to filling
– Free metal very low
• Prevent transfer to analyte
8/3/2009
Chem 311
45
15-
15
Chem 311
Chapter 18
Fundamentals of
Spectrometry
8/3/2009
Chem 311
1
Electromagnetic Radiation
• Electronic Vector
• Magnetic Vector at 90 deg
• Characteristics
– Wavelength () crest to crest distance
• 10-9 NM ==> 100 Km
– Speed (c) speed of light
8/3/2009
• vacuum 3.00 x 108 m/sec
• slower in all other media - slowed by electronic
interactions
Chem 311
2
Electromagnetic Radiation
•  = Refractive index = speed in vac
speed in medium
• >1.00
– function of wavelength
– light of different energy moves at different rates
in medium other than vacuum.
– Fiber Optics separate wavelengths of a pulse
8/3/2009
Chem 311
3
18-
1
Electromagnetic Radiation
•  (wave number) = waves/cm = cm-1 = 1/ 
in vacuum
• Frequency ( ) = waves passing fixed
point/sec.
• period (p) time per wave crest  = 1/p
• all are related
= c
•

•
E = h  = hc/ = hc 
8/3/2009
Chem 311
4
Electromagnetic spectrum
•
8/3/2009
Chem 311
5
Interaction of matter and
Electromagnetic Radiation
• Electronic vector Interactions
• X-rays- ionize atoms eject inner shell e• UV-VIS - energy charges in valence e• IR - molecular vibrations
• microwave - molecular rotations
Rotational Transition
Vibrational Transition
Electronic Transition
8/3/2009
Chem 311
6
18-
2
Energy Levels Diagrams
•
_____3s ____ 3p ____ 3d
• 
• E ____ 2s ____ 2p
•
____1s
– Emission occurs when e- state drops.
• Studied for atoms. Chemland
– Absorption occurs when photon of exactly the
energy of the transition strikes the atoms.
8/3/2009
• Studied for molecules (hard to exited enough to
emit.)
Chem 311
7
Molecular Energy Levels
•    orbitals
• Bonding and Antibonding orbitals
• CAChe and Spartan calculate these
8/3/2009
Chem 311
8
Molecular Energy Levels
•
•
•
•
•
8/3/2009
Computation chemistry
Compute energy of all MO’s
Predict UV-Vis spectra
Predict IR Spectra
Predict NMR Spectra
Chem 311
9
18-
3
Quantitative aspects of
Absorption
• Beer's Law
Beer-Lambert Law
– (Harry Gray's version)
• The taller the glass, the darker the brew, the less
amount of light comes through.
• Absorption depends on probability of a
photon striking and being absorbed by a
molecule.
8/3/2009
Chem 311
10
Quantitative aspects of
Absorption
dx
P(o)
P(x)
P
• if each thin segment (dx) absorbs some
fraction of all of incident light (Px)
•
dP = -k Px C dx
8/3/2009
Chem 311
11
Quantitative aspects of
Absorption
• dP = -k Px C dx
– k= constant for absorbing species
• cross section area of absorbing region of molecule (0rbital or
conjugated system
• Probability of transition occurring (0 => 1 )
– PX =Incident radiation power
– C = Concentration
• -dP/Px = kC dx
• Integrate over entire path length x= 0 to b
8/3/2009
Chem 311
12
18-
4
Quantitative aspects of
Absorption
•
•
•
•
log(P0/P) = k/2.303 Cb =  bC
or (abC)
P = Transmittance (T)
Po
-log T = A Absorbance - A is dimensionless
– A = abc
– A= bc
C in gm/l
C in moles/l
• bC = cm*mol/1000 cm3 = mol/1000 cm2
• a units cm2/gm
 unit = cm2/mol
• (old literature often dm2/gm)
8/3/2009
Chem 311
13
Limitations on Beer’s Law
• Light must be monochromatic
• Parallel
• Enter at a right angle.
8/3/2009
Chem 311
14
Accuracy
Deviations from Beers Law
• Instrumental Deviations
– Non-monochromatic light
• value of  or a not constant across bandwidth of
spectrometer.
–
–
–
–
8/3/2009
Negative deviation at high conc.
Concentration error
lower sensitivity.
A
Need more standards.
Chem 311
15
Conc.
18-
5
Deviations from Beers Law
• Wide slits give lower A values • Value measured on ST320 (7nm band) or
Spec 20 (20 nm band) will be less than for
HP diode array (1 nm band) which may be
less than PE 330/Hitachi (0.1-10 nm band)
8/3/2009
Chem 311
16
Bandwidth effects
8/3/2009
Chem 311
17
Bandwidth effects
8/3/2009
Chem 311
18
18-
6
Deviations from Beers Law
• Chemical Deviations
•
Equilibria - acid base pH control
•
Activity coef.
•
Temperature
•
Solvent effects - concentration changes
dielectric constant of solution
• Refractive Index change due to Conc.
8/3/2009
Chem 311
19
Deviations from Beers Law
• Diagnostic Tool for Deviations
– Plot A vs path length.
• Beers Law - straight line (deviations must
be chemical)
• Stray Light - negative deviations
– Reflections inside instrument
– Higher orders from a grating
– slit diffraction around entrance slit
8/3/2009
Chem 311
20
Concentration Errors- Precision
• Assume error is a constant value of
Transmittance (T)
• A=abC A= -log T
• C = - log(T)/ab
• take derivative of C with respect to T
• dC/dT = -0.4343/T(ab)
8/3/2009
Chem 311
21
18-
7
Concentration Errors- Precision
• Want relative concentration error dC/C so
divide by
0.4343
dC C
• C= -log(T)/ab

T
log(T)
dT
• ab term cancels
dC
dT 0.4343

x
C
T
log(T)
• dC/C has a minimum at T=0.368 (36.8%)
8/3/2009
Chem 311
22
Concentration Errors- Precision
•
•
•
•
Error as f(%T)
Working Range
very short
factor of 5-10
error
36.8%T
%T
8/3/2009
Chem 311
23
8/3/2009
Chem 311
24
18-
8
Chem 311
Chapter 19
Applications of
Spectrometry
8/3/2009
Chem 311
1
Applications of
Spectrophotometry
• Direct determination of a chromophoric
compound
– anything that absorbs strongly.
– Absorptivities range from 0 to 500,000 , wide
range of sensitivities.
8/3/2009
Chem 311
2
Applications of
Spectrophotometry
• Form a chromophore with non-absorbing species
– metals react with ligands to form colored complexes large number of analytical methods developed to use
this
– organic derivatives - 2,4-dinitrophenyl hydrozones
– azo coupling- make azo dye -acid rain nitrate
– vanillate ion in lab
– breath-a-lizer alcohol detn.
8/3/2009
Chem 311
3
19-
1
Methods of Quantitation
• Direct Use of Beer’s Law –
– Least Precise and Accurate (one point
calibration) assumes blank=0.00
• Using a Standard Curve
–
–
–
–
Known concentrations vs Abs. – Least Squares
Intercept need not be Zero
Identify non-linearity if present
Subtract Blank or Zero instrument with Blank
8/3/2009
Chem 311
4
Methods of Quantitation
• Standard Addition Method
– Prepare solutions by adding known amounts of
analyte to the unknown
– one or more different additions
– For one addition
Cunk 
8/3/2009
C stdVstd
Aunk  std
(Vstd  Vunk )  Vunk
Aunk
Chem 311
5
Standard Addition
• Useful if matrix of sample has background
absorbance which cannot be accounted for
in a blank or calibration curve
• Quick if only one or two samples are to be
run
8/3/2009
Chem 311
6
19-
2
Extensions to Beer’s Law
• Multi-component Systems
• A 1 =  1bC1 +  2bC2 +  3bC3 +.....
– Total abs. = sum of absorbencies of individual
absorbing species.
• Measure at several wavelengths solve
simultaneous equations.
– Calc. conc. of all species.
8/3/2009
Chem 311
7
Spectrophotometric
Titration
A-Titrant only absorbs
.B-Product of Reaction
absorbs
C- Sample only absorbs
D-Two successive
absorbing species are
formed eg. ML then ML2
.E- Colored analyte is
converted to colorless
product by colored titrant.
(brominate a red dye)
F- Similar to D but second form
absorbs less
8/3/2009
Chem 311
8
Spectrophotometry to study
reaction stoichiometry
• Used for - metal complexes, enzyme
substrate complexes, etc.
• Continuous variation - Job’s Method
– Use where ratio is close to 1:1
– Make series of solutions where Total moles of
two reactants constant.
– Plot Mole ratio vs A
8/3/2009
Chem 311
9
19-
3
Job’s Method
8/3/2009
Chem 311
10
Scatchard Plot
• Measure Equilibrium Constant
– Biochemists
8/3/2009
Chem 311
11
Scathcard Plot
8/3/2009
Chem 311
12
19-
4
Scatchard Plot
• Slope = - K
• K=4.0x109
8/3/2009
Chem 311
13
Instrumentation for Optical
Spectroscopy
Source of
monochromatic
radiation
8/3/2009
Sample
Detector
Readout
Chem 311
14
Sources of Radiation
• Black body radiators – Tungsten lamp 2870oK - 1.5 micron peak
• visible only - 330 nm minimum
–
8/3/2009
Chem 311
15
19-
5
Monochromators
• Filters
– Glass 30-50 nm band width 5-20% T at max
– Interference Filters 10-20 nm bandwidth 40% T
• Prisms - Quartz for UV-VIS
• Gratings - parallel lines on glass
– Most common dispersion device
• Fourier Transform instruments - Nondispersive (IR’s) - Details in Chem 312
8/3/2009
Chem 311
16
Dispersion by a Grating
8/3/2009
Chem 311
17
Wavelength Selectors
• Definition of effective bandwidth
8/3/2009
Chem 311
18
19-
6
Cells
• Glass or Plastic - Vis only
• Quartz - UV-VIS-NIR $60-100 each
• Flat parallel windows best
– Cylindrical cells must always be in the same
position
– (mark on spec 20 cells)
• Flow Cells
• Fiber Optic Probes
8/3/2009
Chem 311
19
Solvents - must be transparent
UV cutoff
•
•
•
•
•
•
•
•
•
•
•
•
Solvent
Acetone
Acetonitrile
Benzene
Carbon disulfide
Chloroform
Dichloromethane
Ether
Ethyl Acetate
Hexane
Methanol
Water
8/3/2009
UV Cutoff
330
210
280
380
245
233
220
260
210
210
200
Chem 311
20
Detectors
• Photo-tube
• Photo emissive surface
A
– Work function -photon energy needed to eject
e-'s
– photo cathodes designed for various regions of
the spectrum.
– each photon produces 1 or more e– some thermal e- also produced
– shot noise
– dark current function of temp.
8/3/2009
Chem 311
21
19-
7
Detectors
• Solid State Detectors
– Photodiodes
– Change Couple Devices.
• Photodiodes - pn junction conduct in
reverse direction due to photon flux.
8/3/2009
Chem 311
22
Detectors
• Linear photodiode Arrays
– 512 diodes - detect 512 wavelengths at once complete spectrum not scanned. HP
Spectrometer
•
•
•
• .
8/3/2009
Good visibility sensitivity
Rapid response
high linearity
Chem 311
23
Instrument Designs
Photodiode array spectrophotometer
8/3/2009
Chem 311
24
19-
8
Fiber Optic Dip Probes
• No cell required
• Mirror reflects
8/3/2009
Chem 311
25
Flow Injection Analysis
• Inject pulse of sample with valve
• Mix with reagents
• Pass through detector cell
8/3/2009
Chem 311
26
FIA
• Calibration Data
• Autoanalyzers
• Common in Clinical
8/3/2009
Chem 311
27
19-
9
ELISA
8/3/2009
Chem 311
28
ELISA
• Requires specific antibody for each analyte
• Antibody bound to substrate
– Magnetic particles
– Solid supports
– Etc
y = -0.6456Ln(x) - 0.8658
2
R = 0.9886
2.000
logit % B/Bo
1.500
1.000
0.500
0.000
-0.500
8/3/2009
-1.000
0.01
Chem
311
0.1
Conc. (ug/L)
29 1
19-
10
Chem 311
Chapter 23
Separations
General Chromatography
8/3/2009
Chem 311
1
A little History
• Precipitation - Liq - Solid Sep.
– Quantitative Analysis
– Qualitative Analysis
– Purification of synthetic products
• Precipitation often does not produce a very
pure product - Inclusion and Occlusion, Coprecipitation.
8/3/2009
Chem 311
2
A little History
• To get a multi-stage separation required
much time - weeks - years.
•
Rare earth separation
•
precipitation
•
L
S
•
L
SL
S
•
L
SL
SL
S
• 1000 stages Ph.D. Thesis
8/3/2009
Chem 311
3
23-
1
A little History
• Solvent Extraction Research
– Alternative to Alternative to Precipitation
– Easier to remove contamination
• Craig Counter Current Extraction
– Multistage solvent extraction
• Chromatography - Continuous Extraction
8/3/2009
Chem 311
4
SEPARATIONS AND
EXTRACTION
• Separation necessary when measurement
technique not adequately selective
• Contact between two immiscible phases
– Separation of phases
8/3/2009
Chem 311
5
Phase Combinations
•
•
•
•
•
•
•
8/3/2009
16 possible phase combinations
G L
S
SCF
G *
*
*
L
*
*
*
S
*
*
SCF
*
Each represents 1 or more separation
methods depending on how phases are
brought together.
Chem 311
6
23-
2
Mechanisms for phase contact
• Bulk separations - recognizable volumes of
each phase.
– Solvent Extraction
– Distillation
• Thin - layer separations - 1 phase present as
a 2 dimensional layer.
– GC
– HPLC
Thin layer G-L
Thin layer L-L or L-S
8/3/2009
Chem 311
7
Solvent Extraction
• Equilibrium of solute Z between two
immiscible phases:
•
Z(Aq) <===> Z(org)
•
Keq = Kp = [Z]or
•
[Z]Aq
• Partition Coefficient
– Activity coef, rarely known - use conc.
8/3/2009
Chem 311
8
Solvent Extraction
• Multiple equilibria often occur
– major advantage of extraction methods.
•
•
•
•
•
•
M+ + L- <====> MLAq
+X
+H+
||
||
||
V
V
V
MX+
HL(Aq
ML(org) + B <===> ML . B(org)
||
V
HL(0rg)
8/3/2009
Chem 311
9
23-
3
Solvent Extraction
• Most useful information - total conc of all
forms.
•
•
D = Cor =
[ML]or + [ML.B]or
•
Caq
[MX+] + [M+] + [ML]Aq
•
• Distribution Ratio
8/3/2009
Chem 311
10
Fraction Extracted
• Calculation of fraction of total in each
phase.
– Start with all solute in Aq - phase.
• q = fraction remaining in Aq phase = CAq
•
Co
• Cor = (CoVAq - CAqVAq)/Vor = (Co-CAq) VAq
•
Vor
• D = Cor = (CoVAq - CAq VAq)/Vor=Vaq x Co - CAq
•
CAq
CAq
Vor
CAq
8/3/2009
Chem 311
11
Fraction Extracted
Co  Vor 
 1
xD
Caq  Vaq 
• Co = initial conc.
q
Caq
Co

1
1

Vor
1

V
RD
1
D
Vaq
• VR= Vor/Vaq
• fraction in org. phase = p
8/3/2009
Chem 311
p  1 q 
VR D
1  VR D
12
23-
4
P’s and q’s
• Special case VR = 1
• q= 1
p=
D
•
1+D
1+D
– % Extracted = 100p
8/3/2009
Chem 311
13
Simple extraction
• p = fraction in organic phase D VR
•
1+DVR
• q = fraction in aqueous phase
•
1
1+DVR
• Extract efficiency depends on D & VR
• For small values of D it becomes necessary to
increase VR to get complete extraction. Practical
limits to VR about 1000
8/3/2009
Chem 311
14
Repeated - Stepwise Extraction
• Use several organic portions to extract
aqueous phase (Vanilla Experiment).
• p1 = DVR
•
1+DVR
• p2 = DVR
•
1+DVR
•
•
8/3/2009
q1 =
*
1
1 + DVR
1
= DVR
= pq
1+DVR (1+DVR)2
q2 = 1
* 1
= 1
= q2
1+DVR 1+DVR (1+DVR)2
Chem 311
15
23-
5
Repeated - Stepwise Extraction
• Third ext.
•
p3 = p*q2 = DVR
* 1
=
D VR
•
1+DVR
(1+DVR)2
(1+DVR)3
•
q3 = 1
. 1
=
1
= q3
•
1+DVR (1+DVR)2
(1+DVR)3
•
org phase
pqN-1
•
Aq phase
qN
• total solute if all organic layers combined = (1-qN)
• pT = p1 + p2 + p3 = p + pq + pq2 = total fraction
• Total quantity = pT CoVAq = (1-qN) CoVAq
8/3/2009
Chem 311
16
Example
• Extraction of Acetanilide from water into ether
• D = 3.0
• Single Ext VR = 1
ptotal =
D
= 3/4 = 0.75
•
1+D
• Final Conc = 0.75*Co = 0.75
• Single Ext VR = 10 ptotal = D =
•
1+D
• ptotal =3*10/(1+3*10) = 0.97
• Final Conc = 0.97 * Co/10 = 0.097
8/3/2009
Chem 311
17
Example
• Extraction of Acetanilide from water into eth
• 5 ext. VR = 1
•
pt = 1- (1 /1+D) 5 = 1-(1/4)5
ptotal = .999
• Final conc = 0.999*Co/5 = 0.1998 = 0.2
•
much more efficient to do multiple extractions
• Max possible extraction efficiency
– limit where Vaq divided into infinite no. of portions
•
8/3/2009
pT = 1 - q∞
 Dc
Chem 311
q  e
Vor
Vaq
18
23-
6
Multiple extractions
• In general N = 5 is optimum gets within a factor of
5 of max. possible efficiency.
8/3/2009
Chem 311
19
Separation of 2 solutes
• Separation factor depends on ratio of
DcA/DcB
• Ratio must be very large to obtain high
purity 106.
• Optimum conditions for separation
•
VR = (DcA/DcB)1/2
8/3/2009
Chem 311
20
Solvent Extraction
• Extraction of Organic Molecules
• Acids, bases, and neutral molecules
•
•
•
•
•
8/3/2009
Only Neutral form partitions into Org.
Acids extract at low pH
Bases extract at high pH
Neutrals unaffected by pH
Used for separation of chemical classes
Chem 311
21
23-
7
Vanilla Experiment
• Vanillin is neutral molecule
– Partitions into organic phase with high D
• Add Base
– De-protonated form of vanillin is anion
– Soluble in aqueous phase
– anion form not soluble in organic phase
• Very efficient separation
• Selective for neutral molecules with acidic
functional group
8/3/2009
Chem 311
22
Solvent Extraction
• Extraction of Organic Molecules
Dc   HA K p'
• Text uses only case for monoprotic but
equation applies to all. Use alpha for neutral
form.
8/3/2009
Chem 311
23
Solvent Extraction
• Metal separations-common use of Ext.
• Extraction has several advantages over
precipitation.
– Less contamination (entrapment or adsorption
on precipitate is a problem).
– More variables in Equilibrium. - exploited to
give separation.
– Organic extractants - fine tune for specific
separation.
8/3/2009
Chem 311
24
23-
8
Simplest Metal Ext. Case
•
bn
• Mn+ + nL- <===> MLn(Aq]
•
+H+
 KpML
•
 KA
MLN(or)
•
HL(Aq)
•
 KpHL
•
HL(or)
8/3/2009
Chem 311
25
Distribution
• D=
[ML]or
•
[M+]Aq + [ML]Aq
bn = [MLn]Aq
•
[M+N][L]n
• KpML= [MLn]or
•
[ML]Aq
8/3/2009
KA= [H+][L-]
[HL](Aq)
KpHL = [HL]or
[HL]
Chem 311
26
Distribution
• [MLn]or = KP[MLn]Aq [MLn]Aq = Bn[Mn+][L-]n
• [MLn]or = KPBn[Mn+][L-]n
•
•
[HL]A = [HL]or
KPHL
•
• [L-] = KA[HL]or
•
[H+ ]KPHL
8/3/2009
[L-] = KA[HL]A
[H+]
Chem 311
27
23-
9
Distribution
 K HL] 
[ MLn ]or  K pML  n [ M n  ] a or 
[ H ]K pHL 
n
• D = [MLn]or
• [M+]Aq + [MLn]Aq
– assume complex not water soluble [Mln]Aq =0
– Generally [MLn]Aq is very small except acetyl
acetonates and water soluble ligands with
additional charged sites
8/3/2009
Chem 311
28
Metal Distribution
Dc
K
pML
 n ( K a ) n [ HL ] n or
(K
) n [H
pHL
D c  ( constant
8/3/2009
] naq

) n [H

 n
] aq
Chem 311
29
Metal Distribution
• Variables to control
– pH
– Organic Solvent (Changes Kp)
Dc
K
n
pML
 n ( K a ) [ HL ]
(K
pHL
D c  ( constant
8/3/2009
Chem 311
) n [H

) n [H
n
or
] naq

 n
] aq
30
23-
10
Metal Distribution
• Multidentate
ligands give
sharper pH
extraction
breaks
n=2
n=3
n=1
% Ext.
pH
8/3/2009
Chem 311
31
Metal Extraction
• Control of pH allows separation of species
with different B's and different KPML's.
• Extraction Eq. also may be effected by
auxiliary ligands (masking agents) which
change conditional 's
– i.e. Reduce extraction of masked ion.
• Use of Adduct forming organic phases also
has an effect
8/3/2009
– MLn[org] + B <====>
increase extraction
MLn . B[org]
Chem 311
32
A little History
• Solvent Extraction Research - Alternative to
Precipitation
• Craig Counter Current Extraction
• Chromatography - Continuous Extraction
8/3/2009
Chem 311
33
23-
11
CHROMATOGRAPHY AND
SEPARATIONS
• Problems with difficult separationsCounter current extraction was slow.
• Tswett – Russian/Italian worked in Russian
Poland
•
•
•
•
Russian Japanese war and WW I problems
Made enemies of leaders of field before publication
Finally published in 1906 – German Botanical
Chromatography
– Color-writing or tsvet-writing
8/3/2009
Chem 311
34
CHROMATOGRAPHY AND
SEPARATIONS
• Lederer's work in 1930's
Germany - also lost.
• AJP Martin - Silica gel
has surface layer of bound
water.
• Packed column with silica and
passed CHCl3 through (mobile
phase) worked for fatty acids.
8/3/2009
Chem 311
35
CHROMATOGRAPHY AND
SEPARATIONS
• Then invented Gas chromatography and the
common detectors for GC
• Martin and Synge - Nobel Prize 1952
– Developed extension of counter current math to
describe chromatography.
– Not best treatment (ignores kinetics) but worth
some time.
• Three types of chromatography - Elution,
Frontal, and Displacement
8/3/2009
Chem 311
36
23-
12
Elution chromatography - most
common
• Solute placed at top of column.
• Eluted until each component reaches the
end (detector).
8/3/2009
Chem 311
37
Elution chromatography - most
common
• Mobile phase velocity is the fastest possible
rate of movement through the columns.
• solutes retarded - based on time spent in
stationary phase.
• TLC - Elute till solvent reaches top and
look for position of peaks
8/3/2009
Chem 311
38
Elution chromatography - most
common
• Change elution data to linear velocity in the
column
• 10 cm HPLC column x4.6 mm ID with 2.0 ml/min
flow
– if mobile phase moves through in 0.50 minutes - linear
velocity = 20 cm/min
• Vel = length/to
– 10 cm length must contain 1.00 ml of mobile phase
• Vol mobile phase = to x Flow Rate
8/3/2009
Chem 311
39
23-
13
Elution chromatography
•
•
•
•
•
•
•
•
Total column volume 4.6 mm diameter
x 10 cm
2
Vt = pr h = 1.66 ml.
Mobile phase volume
Vm = 1.00 ml
Stationary phase volume
Vs = Vt- Vm = 1.66-1.00 = 0.66 ml
Phase Ratio F = Vs/Vm = .66/1.0 = 0.66
8/3/2009
Chem 311
40
Elution chromatography
• time ratio in phases Tstationary
Tmobile

Cstationary Vstationary
x
Cmobile
Vmobile
• K = Cs partition ratio
Cm
• =KF
Thermodynamic basis for
retention
8/3/2009
Chem 311
41
Elution chromatography
• Capacity factor k'
- Describes Retention
– Most common for HPLC
– time in stationary phase/time in mobile phase
•
k'
Vr  Vo t r  t o t ' r


Vo
to
to
•
k' varies from 0 to large numbers
• ln k' = D H - D S - ln F
•
RT
R
8/3/2009
Chem 311
42
23-
14
Elution chromatography
• ln k' = D H - D S - ln F
•
RT
R
• Van’t Hoff Plots
• Plots of ln k’ vs 1/T linear
– show contribution of entropy and enthalpy
–
8/3/2009
Chem 311
43
Separation Factor
• Relative Retention α= t’r2 / t’r1 = k’2/k’1
8/3/2009
Chem 311
44
Band spreading in
chromatography
• Inject Sample as a very narrow band square wave pulse of sample
• Three Causes of Band Spreading
• σ2 Injector + σ2 Column + σ2 Detector
8/3/2009
Chem 311
45
23-
15
Band spreading in
chromatography
• Broadening in column
– As it moves through column, it begins to
spread -
•  = std. dev. of peak profile
• Number of theoretical plates N
N= tr2/ 2
peak width at base tw = 4 
8/3/2009
Chem 311
46
Band spreading in
chromatography
• N= 16(Vr/Vw)2 = 5.54(Vr/V1/2)2
– Vr = tr Vw = tw
– use any units time, length, volume
8/3/2009
Chem 311
47
Band spreading in
chromatography
• HETP = L/N
• Plate Theory ===> van Deemter Equation
• H= A + B/v + Cv
– where v= mobile phase velocity
8/3/2009
Chem 311
48
23-
16
Band spreading in
chromatography
• H= A + B/v + Cv
Three Components
– A-Eddy diffusion
– B-Longitudinal
diffusion
– C-Rate of mass
transfer between
phases
8/3/2009
Chem 311
49
Band spreading in
chromatography
• Longitudinal Diffusion of solutes
• D 10-5 to 10-7 function of MW
8/3/2009
Chem 311
50
Band spreading in
chromatography
• Mass Transport between phases
8/3/2009
Chem 311
51
23-
17
Band spreading in
chromatography
• Multiple Flow Paths - Eddy Diffusion
• Not present in Open Tubular Columns
8/3/2009
Chem 311
52
HETP Theory - optimum
conditions
k’=1
•
• small particle diameter
• thin layer of stationary phase
• high diffusion coefficients
– ( high temperature) low viscosity
• Slope of rising portion of van Deemter plot
is function of particle diameter, small
particles flatten the graph allowing efficient
operation at high flow
8/3/2009
Chem 311
53
HPLC vs GC
• Differences due to
– diffusion rates in liquids vs gases
– particle sizes
GC
H
LC
1E-5
8/3/2009
1e-4
1e-3
1e-2
Chem 311
veloc ity c m/ sec
1e-1
1
10
100
54
23-
18
Reduced parameters
• v = dpv/Dm
h = H/dp
• All curves superimpose with h minimum at
about 2dp = 2 particle diameters is the
minimum length of column required for a
theoretical plate. v optimum = 1
• Dm for liquids 10-5 to 10-7
• Dm 10-2 to 10-1
8/3/2009
Chem 311
55
Very High Flow
Prev. Discussion Assumes Laminar Flow
Turbulent Flow Conditions
Faster Mass Transport
HETP Graph comes back down
Not as far as Laminar minimum
Useful for high speed sample prep
8/3/2009
Chem 311
56
Time required for separation
• Plates/second
• Optimum k = 2.0
12
Log tr
10
8
1 year
LC
6
1 day
GC
4
1 hour
2
8/3/2009
1 min
0
Chem 311
2
3
57
4
5
6
7
8
Log N
23-
19
LC vs GC
• LC less plates/sec due to slower mobile
phase velocity
• LC applicable to much wider range of
compounds
• GC always method of choice where both
work equally well. Volatile and low MW.
compounds
8/3/2009
Chem 311
58
Deviant Chromatographic
Behavior
• Non-linear
partition
isotherms
Anti-Langmuir
Isotherm
Ideal behavior
Conc
Stationary
phase
Langmuir
Isotherm
8/3/2009
Chem 311
Conc mobile phase
59
Deviant Chromatographic
Behavior
• Antilangmuir
Anti-langmuir case
– sample acts
as
stationary
phase
• Langmuir
8/3/2009
– Saturate
sites
Langmuir case
Chem 311
60
23-
20
Deviant Chromatographic
Behavior
• Anti-Langmuir
8/3/2009
Chem 311
61
Extra-column Volume
• Broadens the injected band before it reaches
the column
• Broadens the post column bands before the
detector
• For good peak shape
– Vcol >>> Vinlet + Vdetector+ Vconnections
8/3/2009
Chem 311
62
Resolution in Chromatography
• R= Dtr/4 = Dtr/Wav
• = (tr2 - tr1)/0.5(W1 + W2)
• most common equation for determining R
from chromatogram
8/3/2009
Chem 311
63
23-
21
Resolution
8/3/2009
Chem 311
64
Resolution in Chromatography
R

(  1 )
1
4
k'
k'
8/3/2009

2
k'
1  k'
N
 separation factor
1
Chem 311
65
Resolution in Chromatography
• 3 Ways to control separation
– Change relative affinity of solutes for stationary
phase – Column Selectivity (α)
•
•
•
•
change stationary phase
change form of solute ( charge or size)
change temperature
Change pH
– Change overall retention by changing k'
• Change temperature in GC
• change mobile phase in LC
– Change N
• flow rate
• change column - particle size or length
8/3/2009
Chem 311
66
23-
22
Types of Columns
• Packed columns
open tubular
coating on walls
Packed column
• For open tubular columns there is no flow
paths term He = 0
8/3/2009
Chem 311
67
General Elution Problem
• Single set of
conditions good
for only 6-8
components
8/3/2009
Chem 311
68
Chem 311
69
Capillary GC
of FAMES
• Isothermal GC at
150 degrees
– Note Tr separation
between even C’s
– almost doubles
8/3/2009
23-
23
Capillary GC of FAMES
Chart Title
5.45
6.98
10.04
16.24
22.02
31.68
45.58
8/3/2009
y = 0.079x - 0.2364
R2 = 0.9963
2.0000
1.5000
Log Tr
C number Tr
12
14
16
18
20
22
24
Log tr
1.0000
Linear (Log tr)
0.5000
0.0000
0
10
20
30
Carbon Number
Chem 311
70
Capillary GC of FAMES
• Temperature Programmed run
8/3/2009
Chem 311
71
General Elution Problem
• Elution parameters must be varied to
separate complex mixtures
– Temperature • GC- column equilibrates quickly.
• LC columns equilibrate very slowly, temp rarely
used
– Mobile phase • GC Mobile phase is inert and doesn’t effect the
separation.
• LC- most commonly varied parameter
8/3/2009
Chem 311
72
23-
24
General Elution Problem
• Initial conditions k' very large most peaks held
at start of column
– Special case in capillary column GC cryofocusing.
• If solvent is a liquid at initial temperature, the peaks
actually focus into a sharper band than the injection
band
• Gradually reduce k' - peaks start to move
• Temperature programming - linear ramps,
sometimes multi-stage ramps
8/3/2009
Chem 311
73
General Elution Problem
• Initial conditions k' very large most peaks held
at start of column
• Solvent programming – solvent strength vs % composition is
exponential curve so programs are often
exponential in shape to produce linear change
in eluting power of mobile phase.
– Vary polarity, pH, salt content
– Ternary and quaternary gradients possible
• Chocolate lab - Methanol, acetonitrile better than
either one alone
8/3/2009
– DryLab Software for
optimization
Chem
311
74
Gradient Elution
• Peaks can be all about the same shape
• No limit to number of components
• N/t approximately constant in programmed
run. N is meaningless as a measure of
quality.
8/3/2009
Chem 311
75
23-
25
Sample Capacity
• Isocratic
– Max sample proportional to tr/2N1/2
• Programmed
– Max sample proportion to tro/2N1/2
– tro = retention time at initial conditions (very
large)
8/3/2009
Chem 311
76
Problems with programmed
elution
• Time to return to initial conditions
•
GC - cool column oven
•
LC- equilibrate column
•
SFC - density gradient - re-equilibrate
8/3/2009
Chem 311
77
Frontal Chromatography
• Mixture used
as mobile
phase
• Great if you
want Solute 1
only
8/3/2009
Chem 311
78
23-
26
Displacement
Chromatograph
• Great for y
Preperative
Separations
–
–
–
–
Gram Quantities on
standard columns
Must have displacer
Must determine
isotherms
8/3/2009
Chem 311
79
Solid Phase Extraction
• Absorb solute on the surface of particles
– Need lots of surface area
– Selective absorption of solute of interest
• Elution
– Different solvent used - solute partitions into solvent
• Solute elutes from column
• Affinity Columns - specific biological interaction antibody-antigen
• Pre-concentration- pass large volume through
• Sample Cleanup – remove interferences
8/3/2009
Chem 311
80
Solid Phase Extraction
• Applications
– Vanillin lab type - hold analyte and wash out
junk
– Put SPE in Sample loop of HPLC
• Flush out contaminants
• Drug and metabolites in plasma
– 96 Well plates – do 96 samples at once
8/3/2009
Chem 311
81
23-
27
Chem 311
Chapter 24
Gas Chromatography
8/3/2009
Chem 311
1
Types of Columns
Column type
Typical
length
Typical
diameter
Preparative
packed
Packed
Analytical
Fused silica
capillary
2-4 meters
¼ to ½ in OD 100
Typical
number of
plates
1-10 meters 1/8 in OD
1000
10-100
meters
10,000100,000
8/3/2009
0.05 – 1 mm
ID
Chem 311
2
Types of Columns
• Capillary columns
–
–
–
–
steel, glass, fused silica.
.067 - 1 mm ID
1000 -100 plates/ft
Columns may be very long due to low pressure
required
• Typical 10 meters - 60 meters (GC Lab 30 meter)
– 30,000 106 plate possible
– 100,000 typical
8/3/2009
Chem 311
3
24-
1
Silicone Phases for GC
Functional Group
Methyl
Polarity
Non-polar
Application
Boiling point
separations
Phenyl
Slightly polar and pi
5% - 100% of silicon
bonding
General application
with more polar
molecules being
retained longer for
same BP
Separation by
polarity
Works when others
don’t
Cyano
Very polar
5% - 100% of silicon
C3F7
Moderately polar
8/3/2009
•
Temp limits 200Chem 311
300oC
4
Liquid Phases for GC
Polymer
Polarity
Application
Poly-ethylene glycol Very polar
Carbowax
HO- [CH2-CH2-0 ]nH
MW’s to 20,000
General separation
by polarity
Ethylene glycol
esters
DEGS di-ethylene
glycol succinate
Fatty acids and other
polar moleucles
Very polar
O
O
8/3/2009
O
O
O
O
Chem
311
O
O
5
n
Solid Supports for GC
• Adsorption on solid surface - Strongest
stationary phase interaction
– Useful for permanent gases
• GSC silica, graphite, firebrick
• 1000 m2/gm surface
• 2-5 gm in a column
• As vapor pressure decreases need less
retention.
– Minimizing Solid Support Interactions
8/3/2009
Chem 311
6
24-
2
Solid Supports for GC
• “Inert”supports with low surface area
– 0.2 - 1 m2/gm surface
• Diatomaceous earths - high surface area
silica
–
–
–
–
Acid wash
remove metals
Calcine
reduce surface
silanize
bond surface hydroxyl groups
Coat with liquid phase
1000 available
8/3/2009
Chem 311
7
Instrumentation for GC
Carrier Gas Supply
Flow Controller
Pressure Controller
Pressure Programming
Injector
Flash Vaporization
On Column
Split- Capillary
8/3/2009
Column Oven
Low Thermal Mass
40 deg/min dT
Chem 311
Detector
Readout
Computer
Integrator
Recorder
8
Split/Splitless
Injector
•
•
•
•
8/3/2009
Constant Pressure
Split vent electrical valve
Expansion of solvent
Inert liner
– quartz
– silanized glass
Chem 311
9
24-
3
Injection
•
•
•
•
•
•
•
Syringe Injection 0.1 to 10 ul +/- 2-3%
Gas samples can be up to 2 ml
Valve injection – gases
SPME – other desorption techniques
Headspace analysis
Purge and Trap
Cold Trapping
8/3/2009
Chem 311
10
Detectors -Thermal conductivity detector
• Hot filament - Resistance is f(Temp)
• Filament temp is varied with thermal
conductivity of gas in cell
– He high TC
– Org low TC
Rr
Rs
Amp
V
Rr
8/3/2009
Rs
Reference
Chem 311
Column
Sample
Column
DC Power
Supply
11
Detectors -Thermal conductivity detector
• Wheatstone Bridge
• If resistances are matched V=O volts
– sample reduces thermal cond.
– increases temp ==>inc. resist
– Voltage appears at V
• Detection limit .1 to 1 microgram injected 10-9 gm/sec
• Linear Range 104
• Detects everything except carrier gas
8/3/2009
Chem 311
12
24-
4
Ionization Detectors- Flame
ionization
Electrode
200 volt DC
Flame
Electrometer
Sample +
Hydrogen
8/3/2009
Chem 311
13
Ionization Detectors- Flame
ionization
• Used for C-H compounds.
Electrode
200 volt DC
Flame
– Gram response approximately constant
– C=0 & C-X lower response
• Formaldehyde H2CO
Electrometer
Sample +
Hydrogen
very low response
• current 10-14 to 10-7 amps.
• 10-12 gm/sec detection
– Total peak 0.1 to 1ng
• linear range 106
• ionization efficiency .1%
8/3/2009
Chem 311
14
ECD Electron Capture Detector
Power
Supply - DC
or Pulsed
-
Electrometer
+
Sample
Beta
source
b e- + carrier establish background standing
current
8/3/2009
Chem 311
15
24-
5
ECD Electron Capture Detector
Standing Current 10-9 to 10-10 amps
Sample + esamplereduces standing current
negative peaks
sensitivity depends on electron affinity
varies by 104
•
•
•
•
•
•
-
Electrometer
Power
Supply - DC
or Pulsed
+
Sample
Beta
source
8/3/2009
Chem 311
16
ECD Electron Capture Detector
• halogenated samples best pesticides PCB's
– CHC13 1 x 10-15 gm/sec
– peaks for 11-14 to 10-12 gm
• Linear range 300-10000 depends on
design
• Sensitivity high due to high ionization Eff.
100%
Power
Supply - DC
or Pulsed
-
8/3/2009
Chem 311
Sample
Electrometer
+
17
Beta
source
GC-MS
• EI or CI ionization
– EI sensitivity like FID
• EI M + e-  M+. + 2 e– M+.  D+ + D.
• Fragments Daughter ions
– Structural Information
– Library Search
8/3/2009
Chem 311
18
24-
6
GC-MS
•
•
•
•
•
CI Chemical Ionization
CH4 + e-  CH5+
CH5+ + M  MH+ + CH4
High efficiency ionization
Few Fragment ions
– Much higher sensitivity
– No Library Search possible
8/3/2009
Chem 311
19
GC-MS
• Selected Ion Monitoring
– Find characteristic ion in each spectrum
– Produce chromatogram of specific ion
• Total Ion Chromatogram
– All ions in each spectrum summed
• MS-MS
– Fragment a Fragment
– Improved S/N ratio
8/3/2009
Chem 311
20
Detector Summary
Detector
FID
ECD
Best case limit
Linear range
of detection
10-12 gm/sec
106
10-11 gm in peak
Applicability
10-15 gm/sec
300-10,000
10-14 gm in peak
Cl and F
molecules
NPD
N or P
FPD
S
Mass
Spectrometer
10-12 to 1015gm/sec
TCD
10-9 gm/sec
10,000
10-7 gm in peak Chem 311
8/3/2009
All
hydrocarbons
100,000
Identification
and
quantitation
Non-destructive
21
24-
7
Photo ionization
•
•
•
•
•
7-12 eV H2 Lyman line - far UV
Ionization Eff 1%
Less background noise than FID
More sensitive by 10 - 50 then FID
Somewhat selective depending on
wavelength
– C1-C4 He N2 not detected
8/3/2009
Chem 311
22
Thermonic Detector
•
•
•
•
8/3/2009
N or P specific FID
alkali metal FID
Bead of CeI placed in flame of FID
Enhances the sensitivity to N and P
Chem 311
23
Flame photometric
• Sulfur specific
• Flame with photodetector
• Useful fo analysis of fuels
8/3/2009
Chem 311
24
24-
8
Microwave Emission
• All elements excited in microwave plasma.
• Select light from one of interest.
• 1x10-12 gm peaks for some elements.
– Multiple channels - several elements empirical
formulas
• Halogen analysis in water samples
• Selenium in garlic
8/3/2009
Chem 311
25
Identification of Peaks
• Plot Log tr vs Carbon Number
• Linear graph for homologous series
• Log plots on two different columns
Identify
compound
log Tr
Col A
8/3/2009
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26
log Tr Col B
Identification of Peaks
• Mass Spectrometry
–
–
–
–
Molecular weight of molecules
Fragmentation pattern for Identification
Library search 300,000 spectra available
Trace analysis sensitivity
• GC-IR
– IR spectrum of peaks
8/3/2009
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27
24-
9
Analysis Methods
• External Standard Method
– make calibration curve
– run sample and compare
– Limited by injection accuracy
• 2-4%
• 1-2%
• 0.5%
manual
auto
valve injections
8/3/2009
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28
Analysis Methods
• Internal Standard Method
– eliminates injection error - only integration
error is left
– add standard to each sample use it to correct for
variation in injection and in sample workup etc.
• Single point - determine peak ratio with one
standard mixture
• Calibration curve - plot area ratio vs mass ratio
8/3/2009
Chem 311
29
Internal Standard Method
• Data from GC experiment
C22:1
C16:0
y = 0.6548x - 0.0804
R2 = 0.9989
5
4
Series1
3
20
Series1
15
10
2
Linear
(Series1)
1
y = 1.0405x 0.3135
R2 = 0.9991
Linear
(Series1)
5
0
0
0
8/3/2009
2
4
6
0
8
Chem 311
10
20
30
24-
10
Chem 311
Chapter 25
HPLC
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1
A little History
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Chem 311
Types of particles
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2
A4
3
25-
1
Slide 3
A4
LC/GC April 2006 p 10
Administrator, 11/13/2006
25-
Columns
• Small particles –
– More pressure
– Harder to pack.
• Pressure required increases
– ΔP=k/dp2
• Small particles reduce C term in HETP
8/3/2009
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4
A5
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Chem 311
Effect of particle size
Xanthines
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Chem 311
5
A6
6
25-
2
Slide 5
A5
LC/GC December 2005 p 1251
Administrator, 11/13/2006
Slide 6
A6
LC/GC April 2006 p 10
Administrator, 11/13/2006
25-
Columns
• Smaller particles ==>faster separation
– 1.5 ml/min x 8 min= 12 ml
– 1.5 ml/min x 1.6 min = 2.4 ml
• Same separation in 20% of time using
20% of the solvent
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7
8/3/2009
Chem 311
8
9 components in < 30 sec
Alkylphenones
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9
25-
3
Columns
• Short Columns
• 3 and 5 cm length Fast HPLC
• Narrow Bore 1 mm and 2 mm ID
– low flow rate for LC-MS
– Use less solvent
– Increased sensitivity
8/3/2009
Chem 311
10
LIQUID
CHROMATOGRAPHY
• Forces which lead to retention
– Ionic force • + and - ions
– Polar Force • Dipole - Dipole attraction
– Dispersive Forces • London forces & Van der Waals
– Size Exclusion
8/3/2009
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11
•
Polar Force
• Normal phase LC
– Silica or Aluminum solid absorbent
– Si02
Al203
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12
25-
4
Polar Force – Normal Phase
8/3/2009
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13
Dispersive Forces -Reverse
Phase London forces & Van der Waals
•
•
•
•
•
•
8/3/2009
Induced dipoles
Reversed phase LC
R = C18 H37
C8 H17
C3H6NH2
C4H9
Chem 311
14
Reverse Phase
• Elutropic Series Weak solvent
•
•
•
•
•
Water lowest eluting power
Acetonitrile
Methanol
THF
CH2Cl2 Great eluting power
» Non-aqueous reverse phase
8/3/2009
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15
25-
5
Reverse Phase
• Solvent Triangle
– ACN, MeOH, THF
– Binary and ternary mixtures
• Lab MeOH + ACN better than either alone
• Computer Optimization – Map space for best
separations
• Drylab Software – Run 4 Chromatograms
– Predict most effects of parameter changes
8/3/2009
Chem 311
16
Reverse Phase
• Advantages over Normal Phase
– samples in aqueous solution
– lower cost mobile phases easy disposal
– rapid equil. of mobile phase
• Disadvantages
– columns more expensive - not much
– Less efficient columns than normal phase
8/3/2009
Chem 311
17
HPLC Instrument
Solvent Supply
Pump
Constant flow
Gradient or Mixture
Injector
Valve
Column
Detector
Readout
Computer
Integrator
Strip Chart
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18
25-
6
Pumps
• Single piston - cheap - need pulse
damper
• Dual piston - most common
8/3/2009
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19
Pumps
• Screw piston - small bore column
• Air pressure - dissolved bubbles a
problem
• Isocratic and Gradient Systems
• Solvent Mixing pumps
– 3 o4 4 Solvent inlets
– Valves proportion in solvent
– Mixes in pump body
8/3/2009
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20
Solvent Preparation
• Bubbles due to cavitations
• Bubbles in detector
– Helium Sparge (LDC in lab)
– Vacuum Degasser (Thermo - LC/MS)
– Intelligent pumps (Hitachi in lab)
• Filter mobile phases to eliminate particles
– Cause damage to check valves
8/3/2009
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21
25-
7
HPLC Instrument
Injector Valve
8/3/2009
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22
Capillary Columns
• Capillary HPLC
– 1mm ID column loosely packed with large
particles
– fused silica capillary coated with liq. phase
– typical separation 0.1 - 24 hrs.
•
8/3/2009
106
107 plates
Chem 311
23
Detectors
• Refractive index - Difference
between solvent and sample solution.
– Universal sensitivity
– 10-9gm/sec best case RI = 1x10-7
– Very temp. sensitive 10-4RI/oC
• 0.001 C stability req.
– Linear Range 3000
– peaks may be + or 8/3/2009
Chem 311
24
25-
8
Absorption UV - Vis
• Flow Cell in Spectrometer
• Diode Array for full spectrum
• 10-12gm/sec sensitivity best case
– Absorptivity 100 - 500,000/mole
– 8l flow cells with 1 cm path length
– 3l flow cell with 0.5 cm path
– 0.1 l flow cell with 0.2 cm path
– 0.03l flow cell with 0.10 cm
• Linear range 3000+
8/3/2009
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25
Detector Volume
• Volume of detector and Injector and
connecting tubes <<< Void volume
• Inj. & Det must have low volume 10
microliter detector volume for 25 cm 10
micron column
• 3 microliter volume for high speed
column
• < 0.1 ml detector volume now available
for capillary columns
8/3/2009
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26
Fluorescence photometry
• Sample absorbs light in UV and emits at
longer wavelength
• Sensitivity 10-15 gm/sec depends on
fluorescence of sample
• very selective - most things don’t
fluoresce
• narrow linear range
• Also used for Chemiluminescence
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27
25-
9
Sample
Electrochemical
Cell
Voltage
source
• Amperometry
-
– biological studies A
– neuroscience
– measure current flow at fixed voltage
– current due to oxidation or reduction of
molecules in solution
– 10-13 moles injected 10-15 moles/sec
– may have very small cell vol. 0.1-3 l
– used for capillary LC
8/3/2009
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28
Other Detectors
Evaporative Light
Scattering
– Sample sprayed
into chamber
– Solute particles
scatter light
– Universal
detector - nonvolatile solutes
8/3/2009
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29
Other Detectors
• LC-MS
– Same advantages as GC-MS
• Identification
• Very high sensitivity
• Very high selectivity
– Electrospray (ESI)
• Polar molecules better
– APCI
• Non-polar molecules better
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30
25-
10
Comparison of Detectors
8/3/2009
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31
Peak integration
• Drop perpendicular
–
–
–
–
Most common method
Simple
Small peak + error
Large Peak – error
8/3/2009
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32
Peak integration
• Valley Method
– Always produces – errors
– Errors can be large
– Useful for
• Multiple peaks
• Complex baseline
8/3/2009
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33
25-
11
Peak integration
• Skim Method
–
–
–
–
Exponential Skim
Linear Skim
R<1
Small peak < 5% of large
8/3/2009
Chem 311
34
Peak integration
• Gaussian Skim
– More Complicated
– Less error than other skim methods
8/3/2009
Chem 311
35
Peak integration
• Errors depend
– Relative Peak areas
– Resolution
– Method used
• Improve Resolution!!!
8/3/2009
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36
25-
12
Ionic forces
• Ion exchange LC
– Polymer Resin -
R
• Styrene- DVB
• PVP-DVB
R
N
R
+
– Bonded Silica
• Anion exchange
• Cation Exchange
R SO3 H
O
R
8/3/2009
OH
Chem 311
37
Ion Exchange
• Uses
– Water purification
– Amino acid analyzers
– Rare earth (RE) separations
•
•
•
•
30 ft columns in series
citrate complexing agent
pH gradient
citrate RE -- Resin RE competition
8/3/2009
Chem 311
38
Ion chromatography
• DIONEX
– 2 Columns - Separator and Ion suppressor
– Conductivity Detector
• for anions - suppressor is cation
exchange
• mobile phase
Na0H or Na2CO3 in
H20
8/3/2009
– NaCl ==> HCl
– NaF ==> HF
Chem 311
– Mobile phase H2O
or H2CO3
39
25-
13
Ion Chromatograph
8/3/2009
Chem 311
40
Ion chromatography
• Sample Range ppb
• Cations
to100%
– alkali metals, NH4+ ,etc
– transition metals + ligand post columns
spectrophotometric
• Anions – NO3-, SO42- halides, S04, PO4, NO3
– inositol phosphates, etc.
8/3/2009
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41
Ion chromatography
• Cr(VI) (Erin Brockovich)
– Toxic form of Cr
– ICP Total
– Cr3+ good
8/3/2009
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42
25-
14
Ion chromatography
• Cation Analysis
– Soils
– Water
8/3/2009
Chem 311
43
Ion chromatography
• Anions
– Water pollution
– Soil Analysis
8/3/2009
Chem 311
44
Stearic Exclusion Ch. 26
• Volume available to each
species depends on its size
• All species elute
"unretained" but void
volume varies with
molecular size.
• Void volume = available
cross section x length
8/3/2009
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45
25-
15
Stearic Exclusion
• Molecular sieves – Zeolite clays
• 4, 5, 13  holes
– Sephadex - dextran polymer
• holes for molecules 100 - 5x105 M.W.
• not rigid enough for high pressure
– Polystyrene beads
• MW 200 - 50 million
• organic mobile phases
• non-polar samples
8/3/2009
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46
Stearic Exclusion
• Molecular sieves – Glass beads
• MW 300 - 1,200,000
• Polymer M.W. distributions
– silica gels.
• MW 400 - 8,000,000
• C8 bonded silica and others
8/3/2009
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47
Stearic Exclusion
• Advantages
• Vo =Vol. of mobile
phase not in pores
• Vi = volume in all
pores
• All peaks elute
between Vo
• and Vo + Vi =
total void volume
8/3/2009
log M.W.
Chem 311
Vo small
molecules
Vo large
log Retention volume
48
25-
16
Steric Exclusion
• Calibrate VR vs log M.W. and determine
unknowns.
• No equilibrium so no eq. band
broadening
• Low separation factor.
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49
25-
17
Chem 311
Chapter 26
IC, GPC and CE
8/3/2009
Chem 311
1
Ionic forces
• Ion exchange LC
– Polymer Resin -
R
• Styrene- DVB
• PVP-DVB
R
N
R
+
– Bonded Silica
• Anion exchange
• Cation Exchange
R SO3 H
O
R
8/3/2009
Chem 311
OH
2
Ion Exchange
• Uses
– Water purification
– Amino acid analyzers
– Rare earth (RE) separations
•
•
•
•
8/3/2009
30 ft columns in series
citrate complexing agent
pH gradient
citrate RE -- Resin RE competition
Chem 311
3
26-
1
Ion chromatography
• DIONEX
– 2 Columns - Separator and Ion suppressor
– Conductivity Detector
• for anions - suppressor is cation
exchange
• mobile phase
Na0H or Na2CO3 in
H20
8/3/2009
– NaCl ==> HCl
– NaF ==> HF
Chem 311
– Mobile phase H2O
or H2CO3
4
Ion Chromatograph
8/3/2009
Chem 311
5
Ion chromatography
• Sample Range ppb
• Cations
to100%
– alkali metals, NH4+ ,etc
– transition metals + ligand post columns
spectrophotometric
• Anions – NO3-, SO42- halides, S04, PO4, NO3
– inositol phosphates, etc.
8/3/2009
Chem 311
6
26-
2
Ion chromatography
• Cr(VI) (Erin Brockovich)
– Toxic form of Cr
– ICP Total
– Cr3+ good
8/3/2009
Chem 311
7
Ion chromatography
• Cation Analysis
– Soils
– Water
8/3/2009
Chem 311
8
Ion chromatography
• Anions
– Water pollution
– Soil Analysis
8/3/2009
Chem 311
9
26-
3
Reagent Free IC
• Electrochemical Generation of mobile
phase
8/3/2009
Chem 311
10
Stearic Exclusion
• Volume available to each
species depends on its size
• All species elute
"unretained" but void
volume varies with
molecular size.
• Void volume = available
cross section x length
8/3/2009
Chem 311
11
Stearic Exclusion
• Molecular sieves – Zeolite clays
• 4, 5, 13  holes
– Sephadex - dextran polymer
• holes for molecules 100 - 5x105 M.W.
• not rigid enough for high pressure
– Polystyrene beads
• MW 200 - 50 million
• organic mobile phases
• non-polar samples
8/3/2009
Chem 311
12
26-
4
Stearic Exclusion
• Molecular sieves – Glass beads
• MW 300 - 1,200,000
• Polymer M.W. distributions
– silica gels.
• MW 400 - 8,000,000
• C8 bonded silica and others
8/3/2009
Chem 311
13
Stearic Exclusion
• Advantages
• Vo =Vol. of mobile
phase not in pores
• Vi = volume in all
pores
• All peaks elute
between Vo
• and Vo + Vi =
total void volume
8/3/2009
log M.W.
Chem 311
Vo small
molecules
Vo large
log Retention volume
14
Steric Exclusion
• Calibrate VR vs log M.W. and determine
unknowns.
• No equilibrium so no eq. band
broadening
• Low separation factor.
8/3/2009
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15
26-
5
Traditional Electrophoresis –
ion migration separation
• Cations migrate toward the negative
electrode and Anions toward the positive
electrode
• Neutral molecules do not migrate in an
electric field.
• Rate of ion migration depends on size and
charge Vep=uepE
– uep= charge/6* pi* viscosity* radius or ion
8/3/2009
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16
Capillary Electrophoresis
• Adds flow of buffer through the capillary
• Buffer migrates toward the Negative
Electrode
• Cations move faster
• Anions swim upstream and may or may
not elute
• Neutrals go with the flow
8/3/2009
Chem 311
17
Capillary Electrophoresis
• Fused silica tube
treated with base to get
free silanol groups
• At high pH, surface is
negative – Layer of
positive buffer ions
forms to counter the
charge.
8/3/2009
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18
26-
6
Capillary Electrophoresis
• Excess cations in the
area near the walls
move toward the
cathode – DRAG THE
SOLVENT WITH
THEM
• At low pH, no charge
on silica and it doesn’t
work well.
8/3/2009
Chem 311
19
Capillary Electrophoresis
• Electroosmotic flow
• Veof = ueof E
dielectric cons * Zeta
4 pi * viscosity
Zeta  k * wall charge * double layer thick
ueof 
8/3/2009
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20
Ion Velocity
• V=Vep + Veof
• Cations both positive
– V> Veof
• Anions Vep negative
– V<Veof
• Neutral Species V=Veof
8/3/2009
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21
26-
7
Separation
•
•
•
•
Depends on Electrophoretic mobility
Different Size
Different charge
Manipulate pH, ionic strength, dielectric
constant to change charge and shape
• Additives to adduct with solutes
– Cyclodextrins
– Micelles
8/3/2009
Chem 311
22
Instrument Diagram
8/3/2009
Chem 311
23
Instrument
• Injection
– Pressure - siphon effect or gas pressure
– Electrophoretic injection – place capillary in
sample and apply voltage to draw sample in.
– Mechanically more complex than HPLC or GC
and not as easy to reproduce.
• Columns - Silica - surface treated
8/3/2009
Chem 311
24
26-
8
Instrument
• Detection – note MW’s in 100’s to 100,000’s
– Fluorescence (Laser induced LIF) – very sensitive
• 10-18 to 10-20 moles injected
– UV-Vis through column - remove polyimide coating –
not very sensitive
• 10-13 to 10-16 moles
– Mass Spec – Electrospray works great
• 10-16 to 10-17 moles
– Electrochemical – works well for electroactive solutes
• 10-18 to 10-19 moles
– Vacancy detection -– add absorbing species to buffer
and look at vacancies.
8/3/2009
Chem 311
25
Example of CE
• DNA fragments
8/3/2009
Chem 311
26
MECC - Micelles
• Micelles trap neutral organics and form
dynamic stationary phase.
• Micelles migrate with or against the flow
depending on charge
8/3/2009
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27
26-
9
MECC - Micelles
• Typical surfactants used
8/3/2009
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28
MECC Micelles
• Example of MECC
8/3/2009
Chem 311
29
Cyclodextrin CE
• Cyclodextrins are basket shaped molecules
which can trap small molecules inside them.
8/3/2009
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30
26-
10
Cyclodextrin CE
• CD’s available with many functional groups
• Added to mobile phase to increase
separation – dynamic mobile phases.
• CD’s are chiral so chiral separations are
possible
8/3/2009
Chem 311
31
Capillary ElectroChromatography
• Silica particles packed in column extend
the Electro-osmotic effect across entire
column
• Packing pumps mobile phase through
column - no pressure drop.
8/3/2009
Chem 311
32
CEC
• Flat flow profile – less
band broadening then
HPLC
8/3/2009
Chem 311
33
26-
11
CEC
• Column packings being developed with
ODS bonded to silica but sufficient
silica surface to pump buffers.
• Chiral separations• Cyclodextrin and other additives
8/3/2009
Chem 311
34
Comparison of HPLC and
CEC
• HPLC column length limited by high
pressure drop for small particle columns.
• CEC has no such limitations.
– CEC and CE devices can be built on microchips
8/3/2009
Chem 311
35
CE on a Chip
• State of the art 96
parallel CE channels on a
chip –
• Detection
– Laser fluorescence
– MS
• Separation in a few seconds
8/3/2009
Chem 311
36
26-
12