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

activity that introduces a broader

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

your results.

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

Adjusted 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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