Chapter 11: Measurement and data analysis
A. Uncertainty in Measurement:
-IN ANALOG INSTRUMENTS:+- Half the smallest division
-IN DIGITAL INSTRUMENTS: THE SMALLEST SCALE
DIVISION
Additional sources of uncertainty:-reaction time of
experimenter (for time measurements), judging color
change, voltage of an electrochemical cell at any given
time
-SIGNIFICANT FIGURES: DIGITS IN THE MEASUREMENT UP
TO AND INCLUDING THE FIRST UNCERTAIN DIGIT
B. Experimental Error
DIFFERENCE BETWEEN RECORDED VALUE AND GENERALLY
ACCEPTED OR LITERATURE VALUE
-CAN BE RANDOM OR SYSTEMATIC
a. RANDOM ERROR- equal probability of being too high or
too low on a reading
Caused by: readability of the instrument
Changes in the surroundings which affect the reading
(temp variations, air currents)
Insufficient data
Misinterpretation of the reading by the observer
CAN REDUCE RANDOM ERROR THROUGH REPEATED
MEASUREMENT- balance too high and too low readings
MUST DUPLICATE EXPERIMENTAL RESULTS TO REDUCE
RANDOM ERROR
REPEATABLE RESULTS: same person duplicates the
experiment with the same result
REPRODUCIBLE RESULT- several experimenters
duplicate result
If given several results to take an average- report result
as +- range
SMALLER RANDOM ERROR= GREATER PRECISION
b. SYSTEMATIC ERROR: DUE TO POOR EXPERIMENTAL
DESIGN OR PROCEDURE, CANNOT BE REDUCED BY
REPITITION
Due to: misreading the volume in a graduated cylinder
(always from the top of the meniscus)
Overshooting the volume of liquid in a titration—leads
to volumes too high
Using the wrong acid-base indicator with wrong
endpoint
Heat loss in An exothermic reaction
CAN BE REDUCED BY IMPROVING EXPERIMNENTAL
DESIGN
SMALLER SYSTEMATIC ERROR= GREATER ACCURACY
PRECISE MEASUREMENTS HAVE SMALL RANDOM
ERROR AND ARE REPRODUCIBLE WITH REPEATED
TRIALS
ACCURATE MEASUREMENTS HAVE SMALL SYSTEMATIC
ERROR AND ARE CLOSE TO ACCEPTED VALUE
C. Percentage Uncertainties
-helpful to express uncertainty as a fraction of the total
measurement or as a percentage of the total
measurement to show how significant it is
Fractional uncertainty = uncertainty/total measured value
Percentage uncertainty= absolute uncertainty/toatal
measured value x 100
THIS IS NOT PERCENTAGE ERROR WHICH EQUALS
ACCEPTED VALUE-EXPERIMENTAL VALUE/ACCEPTED
VALUE x 100
D. HOW TO PROPAGATE UNCERTAINTIES:
-ADDITION AND SUBTRACTION:
SUM THE ABSOLUTE UNCERTAINTIES
-MULTIPLICATION AND DIVISION:
Find the percentage uncertainty of each individual
measurement and add them
E. SIGNIFICANT FIGURES
-MULTIPLICATION ANDD DIVISION: ANSWER QUOTED TO
SAME NUMBER OF SIG FIGS AS LEAST PRECISE DATA
-ADDITION AND SUBTRACTION: SMALLEST NUMBER OF
DECIMAL PLACES
B. Graphical Techniques:
-independent variable: horizontal axis, dependent
variable- vertical axi
RULES FOR PLOTTING GRAPHS:
-TITLE
-LABEL AXES WITH Quantities and Units
-USE SENSIBLE SCALES- no big jumps
-DRAW A LINE OF BEST FIT
-IDENTIFY POINTS WHICH DO NOT AGREE WITH THE
TREND
a. Often best procedure is to find a way of plotting data in
a straight line
b. EXTRAPOLATION- extending line beyond the range of
measurements
c. INTERPOLATION: assuming that trend line applies
between two points
d. TWO IMPORTANT PROPERTIES OF A STRAIGHT LINE=
GRADIENT AND INTERCEPT
e. Y= mx +c x=indepent variable, y= depent variable, m=
slope (gradient), c is intercept on vertical axis
f. M= change in y/change in x- should have units (y units/x
units)
g. THE GRADIENT OF A CURVE AT ANY POINT IS THE
GRADIENT OF A TANGENT TO THE CURVE AT THAT
POINT
CHOOSING WHAT TO PLOT TO PRODUCE A STRAIGHT
LINE:
P=1/v (P and V are inversely proportional)
USING LOG SCALES: allow straight lines for some
relationships
Rate = k (A)n
C. Spectroscopic ID
THREE TYPES OF ANALYSIS
-QUALITATIVE: detection of the presence but not the
quantity of a substance in a mixture
-QUANTITATIVE: measurement of the quantity of a
given substance
-STRUCTURAL- analysis of how atoms are arranged in
molecules
THREE INSTRUMENT FOR STRUCTURAL ANALYSIS:
- IR SPECTROSCOPY- to identify bonds in a molecule
- MASS SPECTROMETRY- to determine relative atomic
and molecular masses
- NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY- to
show the chemical environment of isotopes of C, H, P,
F in a molecule
1. Mass Spectrometry:
- Can be used to find the mass of individual atoms and
the abundance of isotopes- also can be used to find
the relative molecular weight of a compound- IF
EMPIRICAL FORMULA KNOWN FROM
COMPOSITIONAL ANALYSIS, MOLECULAR FORMULA
CAN BE DETERMINED
- Mass spectrometer works by electron from electron
gun hitting the species to remove an electron
X (g) + e-  X+(g) + 2eCollision can break the molecule up into fragments
LARGEST MASS PEAK= PARENT ION ESCAPING
THROUGH UNSCATHED, all fragments are also
detected
Mass/charge
15
17
18
28
or C double bond O +
29
31
C. 45
CH3+
OHH2O
CH2 double bond CH2
CH3CH2+
CH3O+
COOH
C. Degree of unsaturation (IHD),
-INDEX OF HYDROGEN DEFICIENCY PROVIDES CLUE TO
STRUCTURE OF MOLECULE IF ITS FORMULA IS KNOWN
CHO+
-A MEASURE OF HOW MANY MOLECULES OF H2 NEEDED TO
CONVERT MOLECULE TO THE CORRESPONDING SATURATED
NON_CYCLIC MOLECULE
Cyclohexane and hex-1-ene—have same formula (C6H12) so
same IHD (same amount of unsaturation)
One molecule of hydrogen needed to convert both to hexane
(C6H14)
Ethene (C2H4) also has IHD = 1
Ethyne (C2H2) IHD = 2
C2H5OH has an IHD of 0 because only one H atom is needed—
so does C2H5Cl
D. DIFFEDRENT REGIONS OF THE EMS GIVE DIFFERENT INFO
ABOUT THE STRUCTURE OF ORGANIC MOLECULES
There is a type of spectroscopy for each main region of the EMS
EMS= waves characterized by wavelength and frequency (v)
V x lamba (wavelength) = c speed of light 3.0 a 10-8 m/s
IN IR (INFRARED SPECTROSCOPY) THE FREQUENCY IS
MEASURED IN WAVES PER CENTIMETER. THIS IS CALLED THE
WAVENUMBER
DIFFERENT PARTS OF EMS INTERACT WITH SUBSTANCES IN
DIFFERENT WAYS:
-radio waves are absorbed by certain nuclei and make them
reverse their spin (NMR)
-microwaves: increase rotational energy in molecules , can give
info about bond lengths
-IR is absorbed by certain bonds causes them to stretch or bend
-Visible light and UV light can produce electron jumps
(transitions)- tell us about electron energy levels in an atom
-XRAYS: are produced when e- jump between energy levelshave wavelengths of the same order of magnitude as interatomic distances—tell us about molecular/crystal structure.
F. IR SPECTROSCOPY:
-a chemical bond is like a spring- each one vibrates at its
own natural frequency—depends on the bond strength
and the masses of the atoms
LIGHT ATOMS VIBRATE AT HIGHER FREQUENCY THAN
HEAVIER ATOMS, MULTIPLE BONDS VIBRATE AT HIGHER
FREQUENCY THAN SINGLE BONDS
-simple diatomic molecules, HCl, HBr, HI only vibrate when
the bond stretches (HCl vibrates the fastest of the threehigh bond strength, lightest halogen
BENDING CAN ALSO OCCUR IN MORE COMPLEX
MOLECULES
-ENERGY TO MAKE BONDS VIBRATE AND STRETCH
COMES FROM IR REGION- MOLECULE MUST BE POLAR TO
INTERACT WITH IR- WHEN IT VIBRATES A CHANGE IN THE
DIPOLE MOMENT OF THE MOLECULE OCCURS, INTENSITY
OF IR ABSORPTION DEPENDS ON POLARITY OF BOND
SYMMETRICAL NONPOLAR BONDS (N-double bondN or O
double bond O do not vibrate)
-Stretching and bending in a polyatomic molecule- (like
H2O)- stretching and bending occurs more for the whole
molecule than for each bond
WATER VIBRATES AT THREE FUNDAMENTAL FREQUENCIES
(3650 cm, 3760 cm, 1600 cm)
CO2- 4 frequencies but one bend causes no change in
dipole moment (so doesn’t count)- 2350, twoat 670
THE ABSORPTION OF PARTICULAR WAVENUMBERS HELPS
TO IDENTIFY THE BONDS IN A MOLECULE—USUALLY A
RANGE OF WAVENUMBERS BECAUSE PRECISE
ABSORPTION DEPENDS ON THE BOND ENVIRONMENT
C-O 1050-1410 strong
C double bond C 1620-1680 medium-weak, multiple
bonds
C double bond O 1700-1750 strong
C triple bond C 2100-2260 variable
O-H, hydrogen bonded in carboxylic acids 2500-3000
strong
C-H 2850-3090 strong
O-H, hydrogen bonded in alcohols and phenols 3200-3600
strong
N-H 3300-3500 strong
H bonds will broaden the absorption at a specific
frequency
MOLECULES WITH DIFFERENT BONDS WILL VIBRATE IN
SEVERAL WAYS AT DIFFERENT FREQUENCIES—MAKE
THEIR OWN FINGERPRINT, CAN ALSO BE COMPARED TO
KNOWN COMPOUNDS FOR AN UNKNOWN
E. NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY:
-NMR depends on combo of nuclear physics and chemistry
-NUCLEI OF ATOMS WITH AN ODD NUMBER OF PROTONS,
H, C13, F19, P31 SPIND AND BEHAVE LIKE BAR MAGNETS.
IF PLACED IN A MAGNETIC FIELD , SOME OF THESE NUCLEI
WILL LINE UP WITH THE FIELD, SOME WILL LINE UP
AGAINST IT
- radio waves provide the energy for the nuclei to reverse
their spin and change their orientation in a magnetic field
- HIGHER ENERGY SPIN STATE: NUCLEUS LINES UP
AGAINST THE MAGNETIC FIELD
-LOWER SPIN STATE: NUCLEUS LINES UP IN THE SAME
DIRECTION AS THE MAGNETIC FIELD
The sample is placed in a magnetic field—radio waves
applied at different frequencies until the nucleus flips over
and spins in opposite direction- RESONANCE- RECORDED
ON A SPECTRUM
- THE CHEMICAL SIGNALS PRODUCED DEPEND ON THE
ENVIRONMENT AROUND THE NUCLEI. THE H
MOLECULES ACT AS SPIES AND GIVE INFO ABOUT
THEIR POSITION IN THE MOLECULE
- SIGNALS MEASURED AGAINST A STANDARD – the 12
H nuclei in tretramethylsilane (TMS)
CH3
CH3
Si
CH3
CH3
THE POSITION OF THE NMR SIGNAL RELATIVE TO THIS
STANDARD IS CALLED THE CHEMICAL SHIFT OF THE PROTON.
HYDROGEN IN PARTICULAR CHEMICAL ENVIRONMENTS HAVE
DISTINCT CHEMICAL SHIFTS
Example NMR shift p 561
G. SPECTROSCOPIC ID OF ORGANIC COMPOUNDS
-NMR ARE MEASURED AGAINT TMS STANDARD- used
because H attached to Si absorbs at a different frequency
than H attached to C- will not overlap
CHEMICAL SHIFT OF A PROTON = (v (freq absorbed by H in
compound) – Vo (frequency absorbed by TMS)/vo x 106
TMS IS CHEMICALLY INERT, SOLUBLE IN MOST ORGANIC
SOLVENTS, CAN EASILY BE REMOVED FROM THE SAMPLE
AS IT HAS A LOW BOILING POINT
HIGH RESOLUTION NMR (for organic compounds)- does
not usually show series of single peaks—peaks are usually
split or resolved intop smaller parts (compared to low
resolution)
THE PEAKS SPLIT BECAUSE THE MAGNETIC FIELD OF EACH
NUCLEUS IS MODIFIED BY THE MAGNETIC FIELD OF
SURROUNDING NUCLEI= SPIN SPIN COUPLING
H. X-RAY DIFFRACTION
-visible light will not reflect off a molecule and show us
how it looks because wavelength is too long—X-rays are
used, when they pass through a crystalline solid they are
scattered- interact with each other to form a DIFFRACTION
PATTERN
WHEN WAVES IN PHASE, INTERFERE CONSTRUCTIVELY—
LARGER WAVE
DESTRUCTIVE INTERFERENCE WHEN OUT OF PHASE- can
also cancel each other out completely
SAMPLE MUST BE IN SOLID STATE- MUST BE AN ORDERLY
STRUCTURE TO GIVE INTERPRETABLE DIFFRACTION
PATTERN
An electron density map is made from the X-ray diffraction
pattern—can be used to determine the identity of atoms
(H ATOMS INVISIBLE—ELECTRON DENSITY TOO LOW)