Page 369 - Physical Chemistry

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350
q
500 atm. Note: For H , to improve the fit of the observed fu- (d) Use (11.32) and the result for (c) to show that H° c,i H i
2
2
gacity coefficients to the law-of-corresponding-states graphs, RT a for i A.
A
one uses T/(T 8 K) and P/(P 8 atm) in place of the usual
c
c
expressions for reduced temperature and pressure. (Hint: The 11.42 For which of the following reactions is the equilibrium
2
quartic equation obtained in solving this problem can be re- constant a function of pressure? (a) N (g) 3H (g) ∆
2
3
2
3
3
duced to a quadratic equation by taking the square root of both 2NH (g); (b) CaCO (s) ∆ CaO(s) CO (g); (c) NH (aq)

4
2
sides.) H O ∆ NH (aq) OH (aq).
Section 11.6 Section 11.9

11.36 Using the approximation log g 0.1I /m° for un- 11.43 Show that G°
G° 16.118n(H )RT, where
10
m
i
charged solutes in aqueous 25°C solutions, redo Examples 11.1 G°
is defined by (11.37).
and 11.2 in Sec. 11.3, starting from the solutions already found. 11.44 For NH , G° 500 is 4.83 kJ/mol. For a mixture of
3
f
4.00 mol H , 2.00 mol N , and 1.00 mol NH held at 500 K and
2
3
2
Section 11.7
3.00 bar, find ( G/ j) T,P for the reaction N (g) 3H (g) ∆
2
2
11.37 Measured CO equilibrium pressures above mixtures 2NH (g). Assume ideal gases. For this mixture, will the reac-
2
3
of CaCO (s) and CaO(s) at various temperatures are tion proceed spontaneously to the right or to the left?
3
P/torr 23.0 70 183 381 716
General
T/K 974 1021 1073 1125 1167
11.45 We saw in Sec. 6.6 that the constant-T-and-P addition
(a) At 800°C (1073 K), find G°, H°, and S° for CaCO (s) of a reactant to a gas-phase equilibrium might shift the equilib-
3
∆ CaO(s) CO (g). Do not use Appendix data. (b) Estimate rium so as to produce more of the added species. For a single
2
the CO pressure above a CaCO –CaO mixture at 1000°C. reaction in a dilute liquid solution, could the addition of a solute
2 3
shift the equilibrium to produce more of that solute? (Assume
11.38 The molality-scale ionization constant of water can be that activity coefficients can be approximated as 1 and use the
represented as the following function of temperature:
result for Prob. 6.50.)
log K° w 948.8760 24746.261K>T2 405.8639 log 1T>K2
11.46 (a) Verify that G° for the process i(sln) → i(g) satis-
0.487961T>K2 0.00023711T>K2 2 fies G° RT ln (K /P°), where K is the Henry’s law
i
i
constant for substance i in the solvent. Thus K /P°, which
i
[See H. L. Clever, J. Chem. Educ., 45, 231 (1968) for a review equals (P /P°)/x for an ideally dilute solution [Eq. (9.63)], can
l
i
i
of experimental work on K .] Calculate G°, S°, and H° for be viewed as the equilibrium constant for i(sln) → i(g).
w
the ionization of water at 25°C. Do not use Appendix data.
(b)Given the following G° /(kJ/mol) data from the NBS ta-
f
298
q
11.39 Use the 25°C estimated V i values 5.4 and 1.4 bles, calculate K i,m for O in water and for CH in water at 25°C
4
2

3
cm /mol for H (aq) and OH (aq), respectively, and the H O and 1 bar: 16.4 for O (aq), 50.72 for CH (g), 34.33 for
2
2
4
3

density 0.997 g/cm to estimate K° for H O ∆ H (aq) CH (aq). Because the molality-scale standard state is used
4
w
2

OH (aq) at 25°C and 200 bar. Take H O as a species in solution, for solutes in aqueous solution, the calculated Henry’s law
2
so that H O contributes to V° . State any approximations constant is K , where P K m (Sec. 9.8).
2
i,m
i
i,m
i
soln
made. Compare with the experimental value 1.18 10 14 .
11.47 True or false? (a) The addition at constant T and V of a
11.40 For acetic acid in water at 25°C, the ionization-constant
ratio K°(400 bar)/K°(1 bar) is 1.191 [D. A. Lown et al., Trans. chemically inert gas (for example, He) to a gas-phase mixture
a
a
Faraday Soc., 64, 2073 (1968)]. (a) Find V° for the in reaction equilibrium will never shift the equilibrium. (b) For
CH COOH ionization. State any approximations made. (b) Esti- a closed-system reaction mixture held at constant T and P, the
3
mate the pressure needed to double K°. sign of ( G/ j) T,P determines in which direction the reaction
a
proceeds; if ( G/ j) T,P 0, the reaction proceeds in the
11.41 (a) Use (11.32) to show that forward direction, whereas if ( G/ j) T,P 0, the reaction pro-
ceeds in the reverse direction. (c) A weak acid is completely
q
0 ln K m ° n A H* ¢H q
m,A i A n i H i
a b dissociated in the limit of infinite dilution in aqueous solution.
0T P RT 2 RT 2 (d) If G° for a reaction is positive, no reaction whatever will
where A is the solvent. (b) Show that K /K r , where b occur when reactants are mixed and held at constant T and P.
b
A
c
m
i A n . (Use a result from Prob. 10.23.) (c) Use the results for (e) The standard state of a species is always chosen as a pure
i
(a) and (b) to show that substance. ( f) G°always refers to a transition from pure
standard-state reactants to pure standard-state products.
0 ln K c ° ¢H q
a b a A a n i (g) S° H°/T.
r
r
0T P RT 2 i A