chemistry Formal Report FOR A-PLUS WRITER

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Electronic Spectrum of I2

Overview

In this experiment, the student will record and analyze the vibrational structure of

the B – X electronic transition in molecular iodine to determine the dissociation energy of

I2 in the B 3 Π state. The student will record the spectrum at several temperatures at low

resolution to observe the gross effects of temperature on the overall structure of the

spectrum and then record the spectrum at higher resolution for the analysis of the

spectrum. Bands will be assigned and the dissociation energy calculated using a Bïrge-

Sponer method.

Theory

The total energy of a molecule (under the Born-Oppenheimer approximation) can

be expressed as a sum of electronic and vibrational energies.

ETotal = Eelectronic + Evibrational

A simplified energy level diagram is shown below for two electronic states of the

hypothetical diatomic molecule A2.

Rotational energies are small enough that they are no resolved in this experiment and are

thus ignored. The “term” value for a given quantum state is measured relative to the

bottom of the potential energy well for the ground electronic state. By analyzing the

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transitions between the two states, once can determine the energy differences labeled as

Te’ (the electronic excitation term value of the excited electronic state), E* (the term

value for the excited atomic state of A*), De” and De’ (the dissociation energy of the

lower and upper electronic state respectively as measured from the potential well

minima) and D0” and D0’ (the dissociation energy of the lower and upper electronic state

respectively as measured from the v = 0 energy levels of the respective states).

The analysis in this experiment will focus on the energy levels of the upper state,

so let’s write down an expression for these levels based on electronic and vibrational

contributions to the total energy. For the purposes of this discussion, all energies will be

expressed as term values which are really energies divided by the factor hc.)

Tv = Te + Gv’

Taking the difference between successive levels gives the following result.

Tv+1 – Tv = Gv+1 - Gv

The difference Gv+1 - Gv is given the symbol ∆Gv+½. The vibrational term value can be

expressed in terms of the vibrational constants ωe and ωexe and the vibrational quantum

number v.

Gv = ωe(v + ½) - ωexe(v + ½) 2 + ωeye(v + ½)

3 + …

Neglecting any terms higher than ωexe, the total expression for ∆Gv+½ can be derived as

follows:

∆Gv+½ = Gv+1 – Gv = ωe(v + 1 + ½) - ωexe(v + 1 + ½) 2

- ωe(v + ½) - ωexe(v + ½) 2

∆Gv+½ = ωe – 2ωexe(v+1)

According to theory, the dissociation limit occurs when the spacing between successive

vibrational levels (∆Gv+½) is zero. Fitting ∆Gv+½ as a function of (v+1) should yield a

straight line with slope -2ωexe and intercept ωe.

The dissociation energy can be determined from the constants ωe and ωexe using

the Birge-Spöner extrapolation. In this method, one plots ∆Gv+½ vs. (v+1). The area

under the curve gives the dissociation energy (the sum of all of the vibrational spacings

up to the dissociation limit – where ∆Gv+½ becomes zero.) The method typically over

estimates the dissociation energy by approximately 15% (more for some molecules) due

to neglecting higher-order terms in the vibrational term energy expression. The figure

below shows an example of a Birge-Sponer plot. The deviation from the linear

relationship occurs if high order terms such as ωeye or ωeze become important for a given

molecule.

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Finally, the dissociation energy of the lower state can be determined from Te, De’ and E*

by noting that

Te + De’ = De” + E*

Experimental Method

The experimental data is taken on two different spectrometers. One is equipped

with a temperature control and the other provides higher resolution.

1. Record the visible absorption spectrum of I2 at 30 o C, 40

o C and 50

o C using

the Varian Bio 50 spectrophotometer. Use the highest resolution obtainable.

2. Record the same band system using the Perkin-Elmer Lambda 9 spectrophotometer. Seek the best possible signal to noise ratio and resolution

combination on this instrument.

Analysis

Organize your data into a table leaving room to report the wavenumber, vibrational

assignment for each assignable transition. Also include a column for and ∆Gv+1/2 for the spacing

between each pair of transitions.

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Assign vibrational quantum numbers to the bands in the spectrum. Use the following

assignments to get yourself started. These assignments are taken from J. Chem. Ed. 57, 101

(1980).

v’ – v” λ (nm)

27-0 541.2

28-0 539.0

29-0 536.9

Birge-Spöner Method

• Prepare a graph of ∆Gv+1/2 vs (v+1) and report the best-fit line to your data. • From the fit, calculate values for ωe and ωexe. • Find vmax from this data. • Calculate the dissociation energy for the excited electronic state of I2.

∫ = += maxv

0v 2/1v0 dv∆GD

• Also determine a value for De’ by calculating G(vmax). • From your fit of the data, calculate Te – the electronic excitation energy of the B

state.

• The value if E* is 7603 cm -1

(4). This is the energy of excitation for I* ( 2 P1/2)

compared to I ( 2 P3/2). Use this information in conjunction with your above results

to find a value for De” – the ground electronic state dissociation energy.

Error Analysis

• Determine the uncertainties of the spectroscopic constants you report and compare all of your findings to values found in the literature. (A good

source of literature values is the table of Constants of Diatomic Molecules

found at http://webbook.nist.gov/.)

Post Laboratory Questions

1. Explain the differences between the three spectra recorded on the Bio 50 instrument.

2. Derive the expression ∆Gv+½ = ωe – 2ωexe(v+1). 3. What would be the theoretical dissociation limit of a molecule that can be treated

as a true harmonic oscillator?

References

1. Experiments in Physical Chemistry, D. P. Shoemaker, C. W. Garland and J. W. Nibler, 7 th

edition,

WCB/McGraw-Hill, New York, (2003)

2. Physical Chemistry: Methods, Techniques, Experiments, R. J. Sime, Saunders College Publishing, San Francisco, CA (1990)

3. Physical Chemistry, R. A. Alberty, R. J. Silbey and M. G. Bawendi, Physical Chemistry, 4 th

ed.,

Chapter 16, John Wiley and Sons, Hoboken, NJ (2005)

4. Atomic Energy Levels, Vol. III (Molybdenum through Lanthanum and Hafnium through Actinium), Charlotte E. Moore, Circular of the National Bureau of Standards 467, U.S.

Government Printing Office, Washington, DC (1958).