Absorption Spectrum of Iodine

P-Chem II lab

Tianna Drew

Absorption Spectrum of Iodine

Abstract

The high-resolution UV-Vis spectrophotometer was used to obtain the spectra of iodine in its excited state along with bromine water. Spectrum peak values were analyzed using a Birge-Sponer extrapolation to see energy differences of absorption peaks and quantum vibrational states. The iodine experiment produced data concluding in results very close to literature values. The ground state bond dissociation energy was found to be 155.88 kJ/mol and the excited state dissociation energy was found to be 57.4944 kJ/mol.

Introduction

In this experiment the visible absorption spectrum of iodine was used to find the dissociation

energy among other useful values that can be determined with this spectrum, such as:

1. Difference in the wavelength of adjacent peaks in the absorption spectra.

2. Potential well depths of each state.

3. Dissociation energies of each state.

Electrons make transitions from a lower state [indicated with a double prime (“)] to a higher

state (‘), when excited by the UV-Vis absorption Spectrophotometer. These transitions, which

are vibrational, are observable because iodine vapor absorbs electromagnetic radiation in the

visible light region. (2) This is why we can see the purple color of vaporous iodine fumes.

Absorption Spectrum of Iodine

P-Chem II lab

Tianna Drew

The potential energy diagram labeling all values determined by this transition is shown here. (3)

Figure 1.

A Morse potential energy diagram (Figure 1) can be used to describe the behavior of a molecule

as that molecule becomes excited. The vibration movements can be demonstrated with a

harmonic oscillator model, but this does not account for the fact that the molecule can break

apart when excited, and jump to a higher state.

Internal energy and translational energy are combined to form the total energy of a diatomic

molecule. Because there is no translational energy of a diatomic molecule, only the internal

energy will be considered from here on. This energy is comprised of the electronic, vibrational,

and rotational energies, as shown:

(1)

To calculate the dissociation energy of iodine, approximations must be made because one

cannot access the states near the dissociation energy. This is due to the states’ low intensities.

Absorption Spectrum of Iodine

P-Chem II lab

Tianna Drew

One approximation/ technique is to use the Birge-Sponer treatment. Two adjacent transitions,

and υ +1, are plotted against each other to make a Birge-Sponer plot. The plot is a straight

line with the function: (1)

. (2)

The second order anharmonicity constant ( ) was neglected, and the y-intercept is

. The

slope is [

], where is the first order anharmonicity constant. Next, the area under the

plot is used to determine the dissociation energy ( of the lower state.

and are found

using and

. These constants are portrayed in figure 1. To find the upper state dissociation

energy ( ) the following equation is used:

(3)

In this equation, ∆E(I*) is a constant (given to be 7603.15cm-1 ) and E* is the convergence limit,

given by the equation:

(4)

where is the frequency of where the extrapolation of the Birge-Sponer plot first begins

and is the area under the curve from to the x-intercept. Then can be calculated using

this equation:

(5)

where is a constant (given at 215cm-1). Now the oscillator strength of I2 can be found:

(6)

where is the reduced mass of the molecule, is the speed of light, and = which is

defined above.

The Morse parameter, which enables us to graph the Morse potential curve, is defined as:

Absorption Spectrum of Iodine

P-Chem II lab

Tianna Drew

Experimental

A high-resolution UV-Vis spectrophotometer with a resolution of 0.2nm or better is required in

order to draw out the detailed spectrum necessary to analyze vibrational processes in this

experiment. (1) A sample of solid iodine is placed in a sealed 100mm sample cell, in which its

fumes can be scanned by the spectrometer at room temperature, or at higher temperatures

using a heat gun. The higher temperature makes the iodine vapor much easier to get an

impressive spectrum from. Bromine water (3%) was also used in the spectrometer in order to

contrast the practicality of running the electronic spectrum of a condensed phase.

Results Plot of the electronic absorption spectrum of I2 vapor (raw data)

Figure 2.

Absorption Spectrum of Iodine

P-Chem II lab

Tianna Drew

Plot of the electronic absorption spectrum of liquid Br2 (raw data)

Figure 3

Graphing the spacing between the vibrational energy levels of the I2 vapor spectrum against

the quantum vibrational numbers v’ of the excited electronic state produces a Birge-Sponer

plot.

Figure 4.

The linear regression of the Birge-Sponer plot gives the vibrational constants for the excited

state energy expression and the total number of vibrational states.

= 6.1001x10-3

max = 84

Absorption Spectrum of Iodine

P-Chem II lab

Tianna Drew

The bond dissociation energy of the excited state was found using the spectral data in

conjunction with the Birge-Sponer plot. Then the dissociation energy of the ground state could

be calculated using D0’, data from the spectrum, and the known atomization energy of iodine.

= 4806.20 cm-1 or 57.494 kJ/mol

= 13027 cm-1 or 155.88 kJ/mol

Discussion

After assigning the quantum number v’=25 to the absorption line at 18312.50 cm-1 in Figure 2,

the rest of the quantum numbers were assigned accordingly.(4) Because the iodine was heated

in the experiment, the population of I2 molecules shifted. It went from being mostly populated

in the ground state to a large increase in the population in a vibronic state, which made it

difficult to assign specific wavenumbers to each vibrational state. ()

This increase in population of molecules in the v”=1 and v”=2 states intensifies the spectral lines

created by the transitions.(5) These “hot bands” increase the complicatedness of the iodine

absorption spectrum (Figure 2). The interference of the hot bands was intense enough to skew

the exact locations of the v’’=0 to v’= n transition band heads. To make things easier, the

transition locations within each peak region were labeled consistently, the ratio of the location

of the absorption line at 18312.50 cm-1 to the width of its peak was calculated, then

superimposed on the other peaks to give specific wavenumber values for each v’’=0 to v’= n

transition.

To prove a point, it was instructed that the spectra of bromine water be taken. The results were

a whole lot of nothing. UV-Vis spectroscopy does not pick up the peaks for Br2 water because

liquids and solids do not give vibrational information. This is because the condensed phases

collide with each other often enough to give their peaks lifetime broadening. Lifetime

broadening is when collisions between particles shorten the life of their quantum states.

According to the uncertainty relation , as the lifespan of a state decreases, its energy

uncertainty increases which means broad absorption peaks are observed.(6) A large, single

peak represents all transitions in the case of liquid bromine (Figure 3).

According to calculations, using in equation (2) shows 84 total vibrational states in

the excited electronic state of I2. A literature value found at the University of Rhodesia

calculated 86 quantum vibronic levels in the excited state of I2.

Due to the noise in the absorption spectrum (Figure 2), direct measurements of the spacing of

transitions could only be made with from v’= 0 to v’= 33, which represents only 2% of the

Absorption Spectrum of Iodine

P-Chem II lab

Tianna Drew

energy summed from v’= 0 to v’= 33. It can be inferred that Δṽ(v’) for values of v’ > 33 will be

small enough to disregard, in comparison to the partial sum. This means the remaining energy

changes to be totaled can be expressed as an integral from v’=33 to v’max=84. The expression

for the sum of energies that total the bond dissociation energy D0’ of the excited state then

becomes:

dv’ (8)

Evaluation of equation (8) gives D0’ = 4806.20 cm-1 or 57.494 kj/mol. The literature figures for

D0’ and D0 are 4046 cm-1 and 152.532 kj/mol, respectively.(7,8) The value of Do differs by 16%,

and the two figures for Do differ by 2.1%.

Conclusion

The values of bond strength of the diatomic molecuse iodine (I2) calculated in this experiment (

155.88 kJ/mol for the ground state and 57.4944 kJ/mol for the excited state) were in close

agreement with published values. This is true for the number of vibrational states (84) in the

exited electronic state as well. The main goal to find the dissociation energy of the I2 molecule

was successful in that the data and results were again close to the literature results. Using a

high-resolution UV-Vis spectrophotometer, it is a fairly simple method to obtain a spectrum

which can be interpret and manipulated to find many values relative to one’s field of research.

The UV-Vis spectrophotometer was used because Iodine vapor absorbs radiation at

wavelengths corresponding to yellow light.()

References

1. Brittain, E. F. (1970). Introduction to molecular spectroscopy. (pp. 80-83). New York:

Academic Press Inc.

2. Garland, C. (2003). Experiments in physical chemistry. (pp. 423-432). New York: McGraw Hill.

3. Google Images

4. Steinfeld, J. (1965). Spectroscopic constants and vibrational assignment for iodine. The

Journal Of Chemical Physics, 42(1), 25-33.

5. Chapman, D. (2012, March 22). The electronic spectrum of iodine. Retrieved from

http://home.sou.edu/~chapman/ch445/Iodine.htm

6. Hiereth, M. (2005, January 20). Lifetime broadening. Retrieved from http://www.pci.tu-

bs.de/aggericke/PC4e_osv/Spectroscopy050119/node7.html

Absorption Spectrum of Iodine

P-Chem II lab

Tianna Drew

7. McNaught, I. (1980). The electronic spectrum of iodine revisited. Journal of Chemical

Education, 57(2), 101-105.

8. Barrans, R. (2002, December 10). Fluorine, iodine, and bond energy. Retrieved from

http://www.newton.dep.anl.gov/askasci/chem00/chem00945.htm