BirgeSponer plots are generally made using G for n values far from the dissociation limit. If the data include n values close to the dissociation

Birge–Sponer plots are generally made using ΔG for n values far from the dissociation limit. If the data include n values close to the dissociation limit, deviations from a linear relationship between ΔG and n + 1/2 are observed. Taking these deviations into account allows a more accurate determination of the n value corresponding to dissociation and D₀ to be made. A student determined the following values for ΔG versus n for the ground state of H₂:

n………………………………………. ΔG (cm⁻¹)

0………………………………………. 4133

1………………………………………. 3933

2………………………………………. 3733

3………………………………………. 3533

4………………………………………. 3233

5………………………………………. 3000

6………………………………………. 2733

7………………………………………. 2533

8………………………………………. 2267

9………………………………………. 2000

10………………………………………. 1733

11………………………………………. 1400

12………………………………………. 1067

13………………………………………. 633

a. Construct a Birge–Sponer plot (ΔG versus n + 1/2) using the above data, and fit the data assuming a linear relationship between ΔG and n. Determine the value of n where ΔG = 0. This is the H₂ ground-state vibrational level at dissociation.

b. The area under the Birge–Sponer plot is equal to the dissociation energy, D₀. This area is 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 your best-fit expression ΔG (n) from zero to the n value corresponding to dissociation. Compare your result with the value shown in Table 19.3.

c. Determine the value of n where ΔG = 0 and D₀, assuming a quadratic relationship between ΔG and n, ΔG = a + b (n + 1/2) + c (n + 1/2)2. Which fit gives better agreement with the value for D₀ shown in Table 19.3?