Chemistry 131, Fall 2007
Solutions to Homework No. 5
Problem 1.
See Levine, problem 6.2.
(a) True. This one of the two properties of an ideal gas mix
ture (Levine, top of p. 176), the other property being that
the ideal gas equation applies to the mixture.
(b) True.
Follows from the expression for the chemical po
tential of a pure ideal gas (Levine eq. 6.2), which is plotted
in Levine Fig 6.1.
(c) True. Each of the extensive properties
U
,
H
,
S
,
G
, and
C
P
of an ideal gas mixture can be found by adding the same
property calculated for each pure gas at the same tempera
ture and volume as the mixture (Levine, bottom of p. 176).
The definition of ideal gas mixture implies that the pressure
of each pure gas is equal the partial pressure of the gas in
the mixture when the temperature and volume of each pure
gas are the same as those of the mixture. So statement (c)
is true even though it does not explicitly define the pressure
of each pure gas.
Problem 3.
See Levine, problem 6.9.
(a) True. Each factor (
P
i,
eq
/P
◦
)
ν
i
in the product giving the
standard pressure equilibrium constant
K
◦
P
(Levine eq. 6.13)
is the quotient of two pressures elevated to some power
ν
i
.
The units of pressure in each factor cancel out so the final
product is dimensionless.
(b) False. In this case, each factor in the product giving the
pressure equilibrium constant
K
P
(Levine eq. 6.19) has di
mensions of pressure, so the whole product is dimensionless
only if the sum of the exponents is zero, i.e., if
∑
i
ν
i
= 0
(Levine p. 179), in which case the units of pressure cancel
out in the overall product rather than in each factor, as was
the case in part (a).
(c) False. See part (b).
(d) False. In the reverse reaction, the roles of reactacts and
products are exchanged, so the signs of the stoichiometric
coefficients
ν
i
(Levine p.
132) are reversed.
Reversing the
signs of the
ν
i
’s effectively swaps the numerator with the
denominator in the product giving
K
◦
P
(Levine eq.
6.13).
Therefore,
K
◦
P
for the reverse reaction is the reciprocal of
K
◦
P
for the forward reaction.
(e) True. See part (d).
(f) False.
Each stoichiometric coefficient
ν
i
appears as the
exponent of a ratio of partial pressure to standard pres
sure,
so doubling each
ν
i
effectively raises the standard
pressure equilibrium constant
K
◦
P
to the power of 2.
For
example, for the reaction 2
A
B
the equilibrium con
stant is
K
◦
P
=
(
P
B
/P
◦
)
/
(
P
A
/P
◦
)
2
,
but for 4
A
2
B
the equilibrium constant is
K
◦
P
= (
P
B
/P
◦
)
2
/
(
P
A
/P
◦
)
4
=
[(
P
B
/P
◦
)
/
(
P
A
/P
◦
)
2
]
2
.
(g) True. See part (f).
(h) True. The idealgas equilibrium constant depends on tem
perature only (Levine p. 182). The temperature dependence
of
K
◦
P
is described by the van’t Hoff equation (Levine eq.
6.36). Although each equilibrium partial pressure
P
i,
eq
de
pends on the initial composition of the reaction mixture, the
product giving the standard pressure equilibrium constant
K
◦
P
(Levine eq.
6.13) is always equal to exp(

Δ
G
◦
/RT
)
(Levine eq.
6.15), where Δ
G
◦
is a property of the reac
tion that does not depend on the initial composition of the
mixture. Therefore,
K
◦
P
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 Fall '08
 Lindenberg
 Physical chemistry, Thermodynamics, Equilibrium, Partial Pressure, pH

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