Physical Chemistry Third Edition

342 7 Chemical Equilibrium

c.Assuming that∆C◦Pconstant, findKat 1000 K.

d.Assuming that∆H◦constant, find the temperature at

whichK 1 .000.

7.56 The solubility product constant of AgCl is equal to

1. 8 × 10 −^10. Silver ions form the complex AgCl− 2 with a
   formation constant

Kf

γ

(

AgCl− 2

)

meq

(

AgCl− 2

)

m◦

γ

(

Ag+

)

meq

(

Ag+

)

γ

(

Cl−

) 2

meq

(

Cl−

) 2

 2. 5 × 105

a.Find the molality of this complex and the molality of

Ag+ions in a saturated solution at equilibrium with

solid AgCl. Does the presence of the AgCl− 2 com-

plexes affect the molality of Ag+to a significant extent?

Does it affect the total amount of AgCl that dissolves?

b.Find the molality of this complex and the molality of

Ag+ions in a solution containing 0.100 mol kg−^1 of

Cl−and saturated with AgCl. Does the presence of the

AgCl− 2 complexes affect the molality of Ag+to a

significant extent? Does it affect the total amount of

AgCl that dissolves?

7.57 Find the value ofKat 750 K for the reaction:

2SO 2 (g)+O 2 (g)
2SO 3 (g)

a.Use the van’t Hoff equation, Eq. (7.6-8).

b.Use the interpolated values of the

−

(

G◦m−Hm,298◦

)

T

function to find∆G◦and findKfrom that value.

7.58 At 298.15 K the solubility product constant of Ag 2 Sin
water is equal to 8× 10 −^58. The S^2 −ion hydrolyzes with
water:

S^2 −+H 2 O
HS−+OH−

The acid ionization constant of HS−is equal to

1. 0 × 10 −^19.

a.Find the molality of Ag+ions and of S^2 −ions in a

saturated aqueous solution of Ag 2 S. Does the presence

of the hydrolysis reaction affect the solubility

significantly?

b.Find the molality of Ag+ions and of S^2 −ions in a

saturated solution of Ag 2 S that also contains 0.100 mol

of OH−per kg of water.

7.59 Find the value ofKat 750 K for the reaction

N 2 (g)+2O 2 (g)
N 2 O 4 (g)

a.Use the van’t Hoff equation, Eq. (7.6-8).

b.Use the interpolated values of the−(G◦m−Hm,298◦ )/T

functions to find∆G◦and findKfrom that value.

7.60 a.Find∆G◦andKfor each of the following reactions at

1000.0 K:

N 2 (g)+O 2 (g)
2NO(g)

2NO(g)+O 2 (g)
2NO 2 (g)

b.Using the results of part a, find∆G◦andKfor the

reaction at 1000.0 K:

N 2 (g)+2O 2 (g)
2NO 2 (g)

c.Find∆G◦andKfor the reaction at 1000.0 K:

2NO 2 (g)
N 2 O 4 (g)

7.61 Miller and Murphy^5 give the following values for the

distribution coefficient of nicotine between hexane and

water at pH 11, where

Kd

[nicotine](hexane)

[nicotine](water)

t/◦C 5 10 15 20

Kd 0.26 0.41 0.58 0.70

and where the molar concentration of nicotine is denoted

by[nicotine].Find the value of∆G◦,∆H◦, and∆S◦at

15 ◦C for the process of transferring nicotine from water to

hexane, using the concentration description.

7.62 Find the value of∆G◦at 750 K for the reaction

PCl 5 (g)
PCl 3 (g)+Cl 2 (g)

a.Use interpolated values of∆fG◦values.

b.Use the interpolated values of the−(G◦m−Hm,298◦ )/T

function.

c.Use the Gibbs–Helmholtz equation.

(^5) D. L. C. Miller and W. R. Murphy,Ind. Eng. Chem. Res., 33 , 3239
(1994).