7.3 Chemical Equilibrium in Solutions 327PROBLEMS
Section 7.3: Chemical Equilibrium in Solutions
7.22 Find∆H◦,∆S◦, and∆G◦at 298.15 K for each of the
following reactions, using formation data and absolute
entropy data. Compare the value of∆H◦−T∆S◦with
that of∆G◦to test the consistency of the data.
a.2Fe^2 +(aq)+Sn^4 +(aq)2Fe^3 +(aq)+Sn^2 +(aq)
b.Cl 2 (g)+2Br−(aq)2Cl−(aq)+Br 2 (l)
7.23 Find∆H◦,∆S◦, and∆G◦at 298.15 K for each of the
following reactions, using formation data and absolute
entropy data. Compare the value of∆H◦−T∆S◦with
that of∆G◦to test the consistency of the data.
a.Cl 2 (g)+2I−(aq)2Cl−(aq)+I 2 (s)
b.2Ag+(aq)+Ca(s)2 Ag(s)+Ca^2 +(aq)
7.24 The equilibrium constant for the dissolving of a sparingly
soluble electrolyte is called thesolubility product constant.
The solubility product constant of lithium carbonate is
represented byKsp[
γ(Li+)(meq(Li+)/m◦)] 2
γ(CO− 3 )(meq(CO− 3 )/m◦)where the activity of water is assumed equal to unity.Ksp
for lithium carbonate is equal to 1. 7 × 10 −^3 at 25◦C.
a.Find the solubility in mol kg−^1 of lithium carbonate in
water at this temperature. Use the Davies equation to
estimate activity coefficients.
b.Find the solubility in mol kg−^1 of lithium carbonate in
a solution of 0.100 mol of sodium carbonate in 1.000 kg
of water at 25◦C. Use the Davies equation.
c.Find the solubility in mol kg−^1 of lithium carbonate in
a solution of 0.100 mol of sodium sulfate in 1.000 kg of
water at 25◦C. Use the Davies equation.7.25 a.Find the solubility product constant at 298.15 K for the
reaction
AgCl(s)Ag++Cl−b.Find the molality of Ag+produced by equilibrating
solid AgCl with pure water at 298.15 K. Use the Davies
equation to approximate activity coefficients.
7.26 The solubility product constant of nickel(II) hydroxide is
equal to 2. 9 × 10 −^15 at 25◦C.
a.Find the solubility in mol kg−^1 of nickel(II) hydroxide
in water at this temperature. Use the Davies equation to
estimate activity coefficients.b.Find the solubility in mol kg−^1 of nickel(II) hydroxide
in a solution of 0.100 mol of sodium carbonate in
1.000 kg of water at 25◦C. Use the Davies equation.
c.Find the solubility in mol kg−^1 of nickel(II) hydroxide
in a solution of 0.100 mol of sodium sulfate in 1.000 kg
of water at 25◦C. Use the Davies equation.
7.27 For each of the following weak acids, find the pH of a
solution made from 0.100 mol of the acid and 1.000 kg of
water at 298.15 K. Do each calculation twice: once
assuming thatγ±equals unity, and once using the Davies
equation to estimateγ±. In each case, decide whether
hydrogen ions from water must be included:Acid Ka
a. naphthalene sulfonic 2. 7 × 10 −^1
b. benzoic 6. 46 × 10 −^57.28 For chloroacetic acid,Kais equal to 1. 40 × 10 −^3. Find the
pH of a solution made from 0.100 mol of this acid and
1.000 kg of water at 298.15 K. Do each calculation twice:
once assuming thatγ±equals unity, and once using the
Davies equation to estimateγ±.
7.29 Find the pH at 298.15 K of a solution made from
0.0100 mol of aspartic acid and 1.000 kg of water. Do the
calculation twice, once assuming thatγ±equals unity, and
once using the Davies equation to estimateγ±. For this
acid,K 1 1. 38 × 10 −^4 andK 2 1. 51 × 10 −^10.
7.30 The solubility of Ag 2 SO 4 in pure water at 25◦C is equal to
0.0222 mol kg−^1. Find the value of the solubility product
constant. Use the Davies equation to estimate activity
coefficients.
7.31 Find the molalities of H 2 CO 3 and HCO− 3 in an aqueous
solution at 298.15 K that has been equilibrated with
gaseous CO 2 at 0.0400 atm and in which the pH is equal to
7.40.
7.32 For each of the following weak acids, find the pH of a
solution made from 0.0100 mol of the acid and 1.000 kg of
water at 298.15 K. Do each calculation twice: once
assuming thatγ±equals unity, and once using the Davies
equation to estimateγ±. In part c, decide whether
hydrogen ions from water must be included:Acid Ka
a. periodic 2. 3 × 10 −^2
b.o-phenylbenzoic 3. 47 × 10 −^4
c. hydrocyanic 4 × 10 −^10