Page 222 - Physical Chemistry

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determines whether K° increases or decreases as T increases.
P 6.67 True or false? (a) If G° 0, then no amount of prod-
Who is right? What error did the other person make?
ucts can be formed when the reaction is run at constant T and P
6.65 Which of the following quantities can never be negative? in a closed system capable of P-V work only. (b) In any closed
(a) G°; (b) K°; (c) G°; (d) j . system with P-V work only, G is always minimized at equilib-
eq
f
P
r
rium. (c) If the partial pressure P increases in an ideal gas mix-
6.66 When asked to consider what determines the high- i
ture held at constant T, then m increases in the mixture. (d) Addi-
temperature magnitude of K° for an ideal-gas reaction for i
P tion of a reactant gas to an ideal-gas reaction mixture always
which H° and S° are each of significant magnitude and each
shifts the equilibrium to use up some of the added gas. (e) S of
change only slowly with T (except at very low T, where S° → 0), a closed system is always maximized at equilibrium. ( f ) It is
Joel says that the van’t Hoff equation d ln K°/dT H°/RT 2
P possible for the entropy of a closed system to decrease sub-
shows that if H° is positive, ln K° and K° continually increase
n
P P stantially in an irreversible process. (g) n ca c n a .
as T increases and so K° must eventually become very large at i 1 i i 1 i
P (h) The equilibrium position of an ideal-gas reaction is always
high-enough T; similarly, if H° is negative, K° must eventu-
P independent of pressure. (i) G° for an ideal-gas reaction is a
ally become very small at high-enough T. Thus Joel concludes
function of pressure. ( j) G° for an ideal-gas reaction is a func-
that H° determines the high-temperature magnitude of K°.
P tion of temperature. (k) For an ideal-gas reaction with n 0,
Clementine says that at sufficiently high T, the absolute value
the change in standard-state pressure from 1 atm to 1 bar
of the T S° term in the relation G° H° T S° becomes
changed the value of K° but did not change the value of K .
much larger than the absolute value of the H° term, so that at P P
(l)For an ideal-gas reaction at temperature T, S° H°/T.
high-enough T, G° is approximately equal to T S°. Thus r r
(m) The chemical potential m of substance i in a phase is a
the high-T value of G° is determined largely by the value of i
function of T, P, and x , but is always independent of the mole
S°. Since K° is found from G° RT ln K°, the high-T i
P P fractions x . (n) The chemical potential m of component i of
value of K° is determined mainly by S°. Which student is j i i
P an ideal gas mixture is a function of T, P, and x , but is always
right, and what error did the other student make? i
independent of the mole fractions x .
j i
REVIEW PROBLEMS
R6.1 For a certain ideal-gas reaction, K° is 0.84 at 298 K and librium must always shift so as to decrease the mole fraction of
P
is 0.125 at 315 K. Find H° and S° for this reaction, and the added reactant. (c) The chemical potential of a pure sub-
298
298
state any approximation made. stance is equal to its molar Gibbs energy.
R6.2 Find expressions for each of the following in terms R6.8 State which one of each of the following pairs of sub-
of easily measured quantities: (a) 10S /0T2 P ; (b) 10G /0P2 T ; stances has the lower chemical potential. In all cases, the tem-
(c) 10H /0T2 P ; (d) 10G /0T2 P ; (e) 10S /0P2 T ; ( f ) 10H /0P2 T . perature and pressure of the two substances is the same. In
some cases, the chemical potentials might be equal. (a) Solid
R6.3 Write the equation that defines the chemical potential sucrose and sucrose in a supersaturated aqueous solution of su-
of substance i (a) in a one-phase system; (b) in phase b of a crose. (b) Solid sucrose and sucrose in a saturated aqueous so-
several-phase system.
lution of sucrose. (c) Liquid water at 120°C and 1 atm or water
R6.4 The standard enthalpy of combustion of liquid propan- vapor at 120°C and 1 atm.
1-ol to CO (g) and H O(l) at 298 K is 2021.3 kJ/mol. Find R6.9 Give the SI units of each of the following: (a) A; (b) G ;
2
2
H° and U° of this substance. (c) K° (d) H°; (e) S°; ( f ) m . i m
298
298
f
f
r
P
r
R6.5 The equilibrium composition for an ideal-gas reaction
(a) never depends on the pressure; (b) always depends on the R6.10 For the freezing of 1.00 mol of water at 0°C and 1 atm,
pressure; (c) depends on the pressure for some reactions and is find H, S, A, and G. Densities of ice and liquid water at
3
3
independent of pressure for some reactions. If your answer is 0°C and 1 atm are 0.917 g/cm for ice and 1.000 g/cm for liq-
(c), state what determines whether the equilibrium composition uid water. Specific heats are 4.19 J/(g K) for liquid water,
depends on P. nearly independent of T, and 2.11 J/(g-K) for ice at 0°C. The
heat of fusion of ice is 333.6 J/g.
R6.6 If 0.100 mol of NO (g) is placed in a container held at
2
25°C and the equilibrium 2NO (g) ∆ N O (g) is established, R6.11 Replace each question mark in the following state-
2
2
4
use Appendix data to find the equilibrium composition (a) if V ments with one or more words so as to produce a true statement.
is held fixed at 3.00 L; (b) if P is held fixed at 1.25 bar. (a) For a closed system with P-V work only that is held at
constant ?, the Gibbs energy reaches a ? at material equilibrium.
R6.7 True or false? (a) If a reactant is added to an ideal-gas (b) For a (an) ? system, the entropy can never ?. (c) The entropy
reaction that is in equilibrium, the equilibrium must always of the ? is ? at equilibrium. (d) Whether the equilibrium con-
shift to use up some of the added reactant. (b) If a reactant is stant of an ideal-gas reaction increases or decreases as T in-
added to an ideal-gas reaction that is in equilibrium, the equi- creases is determined by the sign of ?.