Page 191 - Physical Chemistry

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11.49; 110, 11.97; 120, 12.40; 130, 12.83; 140, 13.31; 150, 5.46 Some values of (H° m,2000 H° m,298 )/(kJ/mol) are 52.93 for
13.82; 160, 14.33; 170, 14.85; 180, 15.42; 190, 16.02; 197.64, H (g), 56.14 for N (g), and 98.18 for NH (g). Use these data
2
3
2
16.50. Liquid: 197.64, 20.98; 200, 20.97; 220, 20.86; 240, and Appendix data to find H° 2000 for N (g) 3H (g) →
2
2
20.76; 260, 20.66; 263.1, 20.64. Gas: 263.1, 9.65; 280, 9.71; 2NH (g).
3
298.15, 9.80. (a) Fit the data for the solid to a polynomial in T
using a spreadsheet or another suitable computer program. 5.47 For T 2000 K, some values of (G° H° m,298 )/T in
m,T
Check that you have a good fit. Do the same for the liquid and J/(mol K) are 161.94 for H (g), 223.74 for N (g), and 242.08
2
2
for the gas. (b) Use these polynomials together with the Debye for NH (g). Use these and Appendix data to find G° 2000 of
f
3
3
T law (5.31) to find S° m,298 of SO (g). NH (g).
3
2
5.34 Suppose that instead of the convention (5.22), we had 5.48 Verify Eq. (5.43) for G°.
T
taken S° of graphite, H (s), and O (s) to be a, b, and c, respec- 5.49 (a) If G T bar and G T atm are G° values based on 1-bar
2
2
m,0
T
tively, where a, b, and c are certain constants. (a) How would and 1-atm standard-state pressures, respectively, use Eq. (5.41)
S° m,298 for graphite, H (g), O (g), CH (g), H O(l), and CO (g) be to show that
2
2
4
2
2
changed from their values listed in the Appendix? (b) How
atm
bar
would S° 298 for CH (g) 2O (g) → CO (g) 2H O(l) be ¢G T ¢G T T 30.1094 J>1mol K24 ¢n g >mol
2
2
4
2
changed from its value calculated from Appendix data?
where n /mol is the change in number of moles of gases for
g
5.35 Use data in the Appendix and data preceding Eq. (4.54) the reaction. (b) Calculate this difference for G° of H O(l).
2
f
298
and make certain approximations to calculate the conventional
S of H O(l) at (a) 298.15 K and 1 bar; (b) 348.15 K and 1 bar;
m
2
(c) 298.15 K and 100 bar; (d) 348.15 K and 100 bar. Section 5.10
5.50 (a) Use bond energies listed in Sec. 19.1 to estimate
5.36 For the reactions of Prob. 5.10, find S° from data in H° for CH CH OH(g) → CH OCH (g). Compare with the
298
the Appendix. 298 3 2 3 3
true value 51 kJ/mol. (b) Repeat (a) using bond-additivity val-
5.37 For the reactions in Prob. 5.10, find S° ; neglect the ues. (c) Repeat (a) using group-additivity values.
370
temperature variation in C°. 5.51 (a) Use Appendix data and bond energies in Sec. 19.1
P
5.38 Derive Eq. (5.37) for S° S° . to estimate H° 298 of CH OCH CH (g). (b) Repeat (a) using
f
3
3
2
T 2 T 1
bond-additivity values. (c) Repeat (a) using group-additivity
5.39 (a) Use S° m,298 Appendix data and the expression for values.
C°(T) in Example 5.6 in Sec. 5.5 to find S° 1000 for 2CO(g)
P
O (g) → 2CO (g). (b) Repeat the calculation using C° P,m,298 data 5.52 Look up the Benson–Buss bond contribution method
2
2
and assuming C° is independent of T. (Sec. 5.10) and use it to estimate S° m,298 of COF (g); be sure to
2
P
include the symmetry correction. Compare with the correct
5.40 For reasonably low pressures, a good equation of state value in the Appendix.
for gases is the truncated virial equation (Sec. 8.2) PV /RT
m
1 f(T)P, where f(T) is a function of T (different for different 5.53 The vapor pressure of liquid water at 25°C is 23.8 torr,
gases). Show that for this equation of state and its molar enthalpy of vaporization at 25°C and 23.8 torr is
10.5 kcal/mol. Assume the vapor behaves ideally, neglect the
S m,id 1T, P2 S m,re 1T, P2 RP 3 f 1T2 Tf ¿1T24
effect of a pressure change on H and S of the liquid, and calcu-
late H° , S° , and G° for the vaporization of water; use
298 298 298
Section 5.8 only data in this problem. Compare your results with values
5.41 For urea, CO(NH ) (c), H° 298 333.51 kJ/mol and found from data in the Appendix.
f
2 2
S° m,298 104.60 J/(mol K). With the aid of Appendix data, find 5.54 For CH OH(l) at 25°C, the vapor pressure is 125 torr,
G° of urea. 3
298
f
H of vaporization is 37.9 kJ/mol, H° is 238.7 kJ/mol,
m f
5.42 For the reactions in Prob. 5.10, find G° using (a) the and S° is 126.8 J/(mol K). Making reasonable approximations,
m
298
results of Probs. 5.10 and 5.36; (b) G° 298 values in the find H° and S° m,298 of CH OH(g).
298
3
f
f
Appendix.
5.55 Let D and D be the COC and COH bond energies
CC CH
5.43 For the reactions of Prob. 5.10, use the results of and b CC and b CH be the H° bond-additivity values for these
f
298
Probs. 5.24 and 5.37 to find G° . bonds. (a) Express H° 298 of C H 2n 2 (g) in terms of b CC and
f
n
370
b . (b) Express H° 298 of C H 2n 2 (g) in terms of D , D ,
CC
CH
n
f
CH
5.44 Use Appendix data to find the conventional G° m,298 for H° [H(g)] and H° [C(g)]. (c) Equate the expressions in
f
298
f
298
(a) O (g); (b) H O(l). (a) and (b) to each other and then set n 1 and n 2 to show
2
2
that b CC D CC 0.5 H° [C(g)] and b CH D CH
298
f
Section 5.9 H° [H(g)] 0.25 H° [C(g)]. Substitute these two equa-
f 298 f 298
5.45 Look up in one of the references cited near the end of tions for b CC and b CH into the equation found by equating
Sec. 5.9 G° data at 1000 K to find G° 1000 for 2CH (g) → the expressions in (a) and (b) and verify that this equation is
f
4
C H (g) H (g). satisfied.
2
2
6