18.27.Use statistical thermodynamics to determine
H°(25°C) and S°(25°C) for the reaction
H 2 (g) D 2 (g) →2HD (g)You should be able to calculate vibrational and rotational tem-
peratures for D 2 and HD using the values for H 2 and the
changes in the reduced masses of the other gaseous species.
18.28.Use statistical thermodynamics to determine H° and
S° for the reaction
2H 2 (g) O 2 (g) →2H 2 O (g)Compare this with the value of fS° for H 2 O (g) from Appendix
- Note the phase label on the product.
18.29.Verify the expressions for Ein Table 18.5 (except for
vibrations).
18.9 & 18.10 Equilibria and Crystals
18.30.The chapter uses the right side of equation 18.61 to
argue that the overall expression must be a constant at equi-
librium. Support such an argument using the leftside of equa-
tion 18.61 for a reaction at equilibrium.
18.31.Show that the isotope exchange reaction below should
ideally have high-temperature equilibrium constant of 4.
(^14) N 2 15 N 2 2 14,15N 2
Assume that the dissociation energies of the molecules are the
same.
18.32.Determine the equilibrium constant for the following
reaction at 1000 K and 1 atm pressure for each species:
2H 2 (g) O 2 (g) →2H 2 O (g)
equals 2 for H 2 O, H 2 , and O 2. De(H 2 ) 431.8 kJ/mol,
De(O 2 ) 493.7 kJ/mol, and De(H 2 O) 917.6 kJ/mol. Compare
it with the equilibrium constant at 1000 K determined using
classical thermodynamic means (that is, GHTS,
with T1000 K, then find the equilibrium constant Kfrom
G) and explain the difference in the equilibrium constants.
Which one do you think is closer to the experimental value?
18.33.In Chapters 17 and 18 we have derived expressions
for the absolute amounts of the energies Hand G. However,
in tables of thermodynamic data, we always tabulate Hand
G(that is, changesin enthalpy and Gibbs free energy). How
do you explain this apparent discrepancy?
18.34.The Einstein-Debye suggestion that atoms in crystals
“vibrate” has some validity. In fact, the vibrations of atoms in
solids are treated as if they were caused by real particles called
phononsthat have characteristic vibrational frequencies. For
solid Al, the frequency of the phonons is about 4.5
1012 s^1.
If this phonon were approximated as a stretching type of vi-
bration of a single Al atom, what would be (a)the equivalent
JQPJ
force constant of this “stretch,” and (b)the wavenumber of
light that this phonon would absorb? (c)Many solid materi-
als are very good absorbers of low-energy infrared light. Does
your answer to part b agree with this generality?
18.35.The law of Dulong and Petit states that the CVof ma-
terials approaches 3Nk(which equals 3R) at high tempera-
tures. Can you show that both Einstein’s and Debye’s expres-
sions for the heat capacity of crystals agree with this
generalization at high temperatures?
18.36.Diatomic hydrogen has a vibrational frequency of
4320 cm^1. Evaluate the vibrational partition function at dif-
ferent temperatures and determine the temperature above
which the high-temperature limit for qvib, given by equation
18.20, is valid.
18.37.The rotational temperature of molecular iodine is 310 K.
Evaluate qrotat T298 K term by term, listing the cumula-
tive value of qrotfor every term. At what number of terms does
the change in qrotbecome negligible? Repeat the evaluation
for T1000 K.
18.38.Write a set of equations (or a small program) to eval-
uate the constant-volume heat capacity for a molecule. Use
this algorithm to determine the heat capacity versus temper-
ature (say from 298 K to 1000 K) for H 2 O and CH 4.
18.39.Silver metal is a very good conductor of heat. The fol-
lowing are heat capacities at different temperatures. Using
equation 18.66, determine a value for the Einstein tempera-
ture E that best fits this data.
T(K) C[J/(gK)]
1 7.2
10 ^6
2 2.39
10 ^5
3 5.95
10 ^5
4 1.24
10 ^4
6 3.9
10 ^4
8 9.1
10 ^4
10 0.0018
15 0.0064
20 0.0155
25 0.0287
30 0.0442
40 0.078
50 0.108
60 0.133
70 0.151
Source:D. R. Lide, ed., CRC Handbook of Chemistry and Physics,82nd ed., CRC
Press, Boca Raton, Fla., 2001.
650 Exercises for Chapter 18
Symbolic Math Exercises