When vibrational transitions are observed in an electronic absorption spectrum, these transitions can be used to determine

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When vibrational transitions are observed in an electronic absorption spectrum, these transitions can be used to determine dissociation energies. Specifically, a Birge€“Sponer plot is constructed where the energy difference between successive vibrational transitions n and n + 1 (ΔGn+1/2) (see figure) is plotted versus the vibrational level number. Note that G does not refer to the Gibbs energy in this context.

D. De AG12 AG512 AG312 AG12

The central idea behind the approach is that the dissociation energy is equal to the sum of these energy differences from n = 0 to the dissociation limit:

D-ΔG/2 + ΔG/2+ΔG5/2 ΣΔG+1/2 n=0

a. For the ground state of I2 the following values for ΔG versus n were determined (J. Chem. Phys. 32 (1960): 738.

If the potential function can be described by a Morse potential [Equation (19.5)], ΔG will be a linear function of n + 1/2. Construct a Birge€“Sponer plot (ΔG versus n + 1/2) using the given data, and, using the best fit to a straight line, to determine the value of n where ΔG = 0. This is the I2 ground-state vibrational quantum number at dissociation.

b. The area under the Birge€“Sponer plot is equal to the dissociation energy, D0. This area can be determined by summing the ΔG values from n = 0 to n at dissociation [determined in part (a)]. Perform this summation to determine D0 for ground state I2. You can also integrate the best fit equation to determine D0.

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Physical Chemistry

ISBN: 978-0321812001

3rd edition

Authors: Thomas Engel, Philip Reid

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