Physical Chemistry Third Edition

25.4 The Calculation of Molecular Partition Functions 1079

and so on. Repeat the calculation including states up to

and including then5 level. Compare your answers

with each other and with those of parts a and b.

25.47 a.Calculate the rotational partition function forpara-H 2
at 500.0 K, using the formula in Eq. (25.4-13).
b.Repeat the calculation using the formula in
Problem 25.31.
c.Repeat the calculation using direct summation.
25.48Find the ratio of the populations of thev1,J1 state
and thev0,J0 state at 298 K for
a.H 2
b.HD, where D is deuterium,^2 H
c.D 2
25.49Find the ratio of the populations of thev1,J1 state
and thev0,J0 state at 298 K for:
a.^1 H^35 Cl
b.^1 H^37 Cl
c.^2 H^35 Cl

d.^2 H^37 Cl

25.50 a.For a temperature of 298 K, find the ratio of the

population of thev1 vibrational state to the

population of thev0 vibrational state of H 2.

b.For a temperature of 298 K, find the ratio of the

population of thev1 vibrational state to the

population of thev0 vibrational state of I 2.

c.Explain why the values in parts a and b are so

different.

25.51 a.Calculate the ratio of the population of thev 1

vibrational state of HF to thev0 vibrational state at

(a) 298.15 K, (b) 500 K, (c) 1000 K, and (d) 5000 K.

What is the limit as T→∞? Data are found in

Table A.22 in Appendix A.

b.Calculate the ratio of the population of theJ 1

rotational level of HF to theJ0 rotational level at

(a) 298.15 K and (b) 1000 K. What is the limit as

T→∞?

c.Find the value ofJthat has the largest population for

HF at 298.15 K and at 1000 K.