18.2 Nuclear and Electronic
Partition Functions
18.1.Using a table of nuclear spin states, determine qnucfor
(a)^12 C atoms, (b)^56 Fe atoms, (c)^1 H atoms, (d)D (D is^2 H)
atoms. Explain your answers for parts c and d.
18.2.How many terms would you recommend for the sum-
mation of the electronic partition function for (a)N 2 gas; (b)
O 2 gas at standard temperature? You may need to consult a
table of electronic energy levels (as in G. Herzberg, Spectra of
Diatomic Molecules,Van Nostrand Reinhold, New York, 1950,
or G. Herzberg and K. P. Huber, Constants of Diatomic Molecules,
Van Nostrand Reinhold, New York, 1979).
18.3.Use equation 18.4 to evaluate the nuclear contributions
to Eand S. How do you justify the answers you get?
18.4.Repeat Example 18.1, but this time for T10,000 K (a
surface temperature of a hot star). Does your conclusion about
the effect of electronic excited states on qelectchange? Why or
why not?
18.5.What is the minimum value of qelect? Why is this so?
18.6.Compare qelectfor Ni atoms at 298 K with qelectfor Ni
atoms at 1000 K (see Example 18.2). Can you explain why
they are so close? Now compare qelectfor Ni atoms at 5.0 K
with qelectat 298 K. Can you explain the difference?
18.3 Molecular Electronic Partition Functions
18.7.The vibrational frequency of H 2 (g) is 4320 cm^1.
What is the change in qelectat 298 K for H 2 if D 0 is used as the
dissociation energy instead of De? The bond energy in H 2
is 432 kJ/mol. Compare your answer with the answer in
Example 18.3.
18.8.What is the electronic partition function for H 2 O (g) at
373 K if it takes 918 kJ to break both O–H bonds?
18.9.Diatomic helium (He 2 ) exists only in very low tempera-
ture gas samples. Upper limits to its bond energy are esti-
mated at 89.8 J/mol. (a)Calculate qelectfor He 2 at 4.2 K, the
normal boiling point of He. (b)Comment on whether or not
you would expect He 2 to exist at room temperature (300 K).
Explain your answer.
18.4 Molecular Vibrational Partition Functions
18.10.Consider two identical planets that are the same dis-
tance from their star. One planet has an atmosphere of argon
gas, and the other has an atmosphere of fluorine gas. Assume
that all other physical descriptions of the planets are the same.
From statistical thermodynamic perspectives, which planet
should have the higher atmospheric temperature? Justify your
answer by citing specific equations from the chapter.
18.11.What is the expected ratio of vibrational partition
functions for H 2 and D 2? Use the high-temperature form of
qvibto estimate your answer.
18.12.Calculate the vibrational partition function for NH 3 (g)
at 250 K, 500 K, and 1000 K. Do the changes in qvibshow the
expected differences? Consult Table 18.2 for necessary infor-
mation.
18.13.Calculate the vibrational partition function of CH 4 (g)
at 298 K. See Table 18.2.
18.14.Use the information in Table 18.2 to calculate the vi-
brational frequencies of carbon tetrachloride in units of cm^1.
How many total vibrational frequencies does CCl 4 have?18.5 & 18.6 Molecular Rotational
Partition Functions
18.15.What are minimum values for qnucand qrotfor a gas-
phase molecule? What about qvib?
18.16.Determine the temperature at which qrotfor HCl equals
the qrotvalue for HBr at 298 K. See Table 18.3 for necessary data.
18.17.What is the expected ratio of rotational partition func-
tions for H 2 and D 2? Compare this ratio with the answer from
exercise 18.11.
18.18.Diatomic oxygen, O 2 , has an antisymmetric ground
electronic state. If oxygen nuclei are bosons (I0), what are
the expected symmetry pairings of the nuclear and rotational
wavefunctions?
18.19.The rovibrational spectrum of acetylene, H–C C–H,
shows intensity variations consistent with expected nuclear de-
generacies. Would you expect D–C C–H to show similar in-
tensity variations? Why or why not?
18.20.What happens to rof a diatomic molecule as Jin-
creases? Why? (Hint:See section 14.5.)
18.21.Determine qrotfor NH 3 (3) and CCl 4 (12) at
298 K. Consult Table 18.4 for the rotational temperatures.18.7 & 18.8 Qand Thermodynamic Properties
18.22.Determine an expression for Cp. (Hint:use equations
18.47 and 18.54.)
18.23.Using the expression you determined from the previ-
ous exercise, answer this: of the heat capacities Cpand CV,
which is larger? Will this always be the case? Why or why not?
18.24.Use equation 18.46 to show that pVNkT.
18.25.Calculate E, H, G, and Sfor HCl at standard pressure
and 25°C. equals 1 for this molecule, and De431.6 kJ/mol.
18.26.Determine E, H, G, and Sfor CH 4 at standard pressure
and 25°C. equals 12 for methane and the atomization en-
ergy of CH 4 is 1163 kJ/mol. Compare your calculated value of
Swith the tabulated (that is, experimentally determined) value
in Appendix 2.Exercises for Chapter 18 649EXERCISES FOR CHAPTER 18