# Infrared spectroscopy lab report

Infrared RedSpectroscopy
An investigation into light absorption by small molecules.
Quantitative Models for Molecular
Vibration
 Hook’s Law Model
 The system constitutes a physical model for a chemical
bond.
 If chemical bonds may be regarded as springs then:
F = -kx
 The magnitude of the restoring force, F is directly
proportional to spring elongation.
 The strength of a chemical bond should be analogous to
the force constant, k, of the spring.
Measurements for Hook’s Law
 Determine the units of force and use your data to
calculate the force.
 Plot Force along the y-axis versus spring extension (in the
proper units) along the x-axis.
 The force constant, k, is provided directly by the slope.
Simple Harmonic Motion
 Galileos relationship
 The relationship between the period of vibration (T) of a
spring and the mass (m) suspended from it is given by:
𝑚
𝑇 = 2𝜋
𝑘
 The frequency of vibration (v) is measured by the number
of oscillation per second.
 A plot of (I/v)2 versus the mass on the spring (in grams)
should yield line with a slope of:
2𝜋 2
𝑠𝑙𝑜𝑝𝑒 =
𝑘
 Determine k and compare it with the spring constant from
Hook’s Law (% difference).
Presentation of Results
 Two plots should be provided in the lab results:
 Application of Hook’s Law
Force vs. Spring Extension
 Galileo’s relationship
Period of vibration squared (I/v)2 vs mass
 Conduct a linear regression analysis and display the
equation of the line on each graph.
 Determine the force constant, K from each plot and
compare them through a calculation of % difference.
Tabulated Data
 Two separate data tables are required.
 For Hook’s Law, one should show some version of the
following table.
Trial
1
2
3
Mass (units)
Extension (units)
Force (units)
Simple Harmonic Motion
 The data table for Galileo’s relationship:
Trial
Mass (units)
Oscillations
Frequency (units)
Period 2 (units)
1
2
3
4
5
Oscillations were measured over a time interval of 5 seconds.
Application the IR Spectra
 Obtain a spectrum of chloroform, CHCl3. Present this with your report.
 Use the observed frequency of C-H stretch in chloroform to predict
the C-D stretch in deuterated chloroform, CDCl3.
 Calculations are required (see lab handout)!
 Use the measured frequency of vibration (v) and the following
equation to calculate the force constant for the C-H stretch
𝑐
1
𝑣 = 𝜆 = 2𝜋
𝑘
𝑚
 The masses of both hydrogen and deuterium are provided in the
handout.
 Use the force constant to calculate the frequency of vibration for the
C-D stretch.
 Measure or literature search the frequency of vibration for the C-D
bond.
 Report % Error in your determination.
Experimental Determinations
Force Constant by
Hook’s Law
Calculated C-D
Frequency
Force Constant by
Galileo’s Relationship
Actual C-D
Frequency
Percent Difference
Percent Error
An Investigation
into the Absorption
of Infrared
Light by Small Molecules
This experiment is a two-part classroom/laboratory
perspective on spectroscopy.
In Part I, qualitative models for molecular vibration and the mechnaism
by which such vibrations may be excited by infrared light are developed through class discussion. By
stressing the direct analogy between harmonic motion on the macroscopic scale and ont the molecular
scale, this discussion presents complex concepts in an intuitive manner. Part II involes a series of
quantitative
experements
in which you first explore the physics of harmonic mothion on the
laboratory scale and then use their results to predict the vibrational behavior of a molecular system
as probed by a simple IR experiment. By demonstrating the successful application of a macroscopic
physical model to a molecular system, and by experimentally confirming that infrared absorption
frequencies do in fact correlate with the frequencies of molecular vibration.m the laboratory
investigation validates two key concepts from the pre-lab discussion.
Part I: Pre-Lab Discussion
Open discussion own ideas of. how energy is transferred from the radiation source to the
matter and where the energy “goes” in each case considered.
Discuss the mechanism of resonant
energy transfer from the electromagnetic wave to molecular motions.
Part H: Laboratory
Investigation
Explore factors governing the vibrational frequency of a simple spring oscillator. Appy the
quantitative results to a molecular system by drawing an analogy between the spring and a chemical
bond.
Hooke’s Law
Consider the apparatus provided by the instructor.
It should consist of a varible mass
suspended from a spring, one end of which is fixed to a stationary support. This system is assumeed
to constitute a physical model for a chemical bond, and if chemical bonds may be regarded as springs,
then the strength of a chemical bond should be analogous to the force constant, k, of the spring: A
measure of the “stiffness” of the spring, k is defined by the proportionality
between the elongation
of the spring from its equilibrium position, x, and the magnitude to the restoring force, F:
F=-kx
(1)
This relationship, known as Hook’s Law, is readily verified and the numerical value ofk (along with
appropriate units) for a specific spring evaluated by measuring the elongation produced by different
masses. The applied force in newtons, calculated as the product of the mass times the acceleration
due to gravity (9.80 rn/s’), is equal in magnitude but directionally opposed to the restoring force; thus,
a plot of applied force vs. extension of a series of masses yields a straight line with a positive slope
= k.
Simple Harmonic Motion
Once the force constant of the spring has been determined, consider Galileos
between the period of vibration (T) of a spring and the mass (rn) suspended from it:
r = 2nvm/k
(2)
relationship
~
_.
,/i
or in terms of the frequency
of vibration,
v
V,
= ~ = _I vklm
T
Taking into account
the mass contribution
(3)
211
of the spring itself this becomes:
k
v =
211
m
JIl
(4)
+ f11 S
where rn, and 11;1, represent the effective. mass of the spring and the mass suspended
respectively.
Inverting both sides and squaring yields:
_1
( v)
2
= (211)2″
m
+ m
III
S
m
= (211)2 ” ~
k
k
+ (211?
m
” _s
k
from it,
(5)
Consequently,
a plot of (I/v)? vs. the mass on the spring should yield line with slope = (2n) /k
Verify this relationship using your experimental setup and calculate the percent deviation between the
values ofk obtained using eqs 1 and 5.
IR Absorption
Spectrum
of CHCI3 and CDClJ
Having developed a quantitive relationship between the mass, force constant, and vibrational
frequency of a one-dimensional
spring oscillator, you will now investigate what this model can tell
us about vibrational harmonic motion at the molecular level by observing the effects of deuterium
substitution
on the infrared absorptions of chloroform
Record the IR spectrum of CHCl~ first.
Calculate the force constants for the presumed strectching and bending vibrations of the C-H bond
by substituting the observed absorption frequencies into eq 3:
1 rtr:
v = -c = -yklm
A
211
where c is the velocity oflight (2.9979 x IOllJ cm/s) and mIl = 1.6735 x 10’27 kg. Now, if the model
is valid on a molecular scale, it should be possible for one to use these calculated force constants to
accurately predict the frequencies for the corresponding C-D absorptions of CDCl3 by substituting
mD = 3.3443 X 10-27 kg into the above equation. Record the spectrum of CDq
and compute the
percent deviation between the predicted and the observed values. Finally, notice the existence in both
spectra of several additional low-frequency bands (the C-CI symmetric and asymmetric strecthes)
Propose an assignment for these absorptions that is consistant with the model just developed.
Discuss
Hook’s law
trial
mass(g)
1
2
3
4
5
50
150
250
350
450
extension(m) force(N)
0.024
0.030
0.039
0.047
0.055
490
1470
2450
3430
4410
Galileo’s relationship
trial
mass(g)
oscillaatons
frequency(O/s)
1
250
27
2.7
2
350
24
2.4
3
450
21
2.1
4
550
20
2
5
650
19
1.9
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Standard Error
Observations
0.972598
0.945946
0.918919
36.76073
4
ANOVA
df
Regression
Residual
Total
Intercept
SS
MS
F
1 47297.3
47297.2973
2 2702.703 1351.351351
3
50000
35
CoefficientsStandard Error
t Stat
P-value
-128.378 107.7939 -1.190960942
0.355850249
0.14 2702.703 456.8401
5.916079783
RESIDUAL OUTPUT
Observation
1
2
3
4
Predicted 250
Residuals Standard Residuals
331.0811 18.91892 0.630315236
493.2432 -43.2432 -1.44072054
547.2973 2.702703 0.090045034
628.3784 21.62162
0.72036027
0.027402475
Chart Title
5000
y = 123674x
R² = 0.997
4500
4000
3500
3000
2500
2000
1500
1000
500
0
0.000
period(
0.14
0.17
0.23
0.25
0.28
0.010
0.020
0.030
0.040
Chart Title
0.35
0.3
y = 0.0004x + 0.052
R² = 0.973
0.25
0.2
0.15
0.1
0.05
0
0
100
200
300
400
500
0.14 Residual Plot
30
20
10
0
-10
Significance F
0.027402
0
0.05
0.1
0.15
-20
-30
-40
-50
Lower 95% Upper 95% Lower 95% Upper 95%
-592.178 335.4215 -592.178 335.4215
Series1
737.0782 4668.327 737.0782 4668.327
y = 123674x – 2373.3
R² = 0.997
0.050
0.060
y = 0.0004x + 0.052
R² = 0.973
500
600
700
sidual Plot
0.2
0.25
0.3
0.17
0.23
0.25
0.28
0.17
0.23
0.25
0.28
18.91892
-43.2432
2.702703
21.62162
331.0811
493.2432
547.2973
628.3784
0
0
0
0
350
450
550
650

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