Physical Chemistry Third Edition

328 7 Chemical Equilibrium

7.33 Calculate the pH of a solution from 0.0500 mol of
cacodylic acid in 1.000 kg of water at 298.15 K. The acid
dissociation constant is equal to 6. 4 × 10 −^7. Include the
hydrogen ions from water and use the Davies equation to
estimate activity coefficients.

7.34 The three acid ionization constants of citric acid are
K 1  7. 20 × 10 −^4 ,K 2  1. 68 × 10 −^5 , and
K 3  4. 11 × 10 −^7.
a.Find the pH at 25◦C of a solution made from 0.100 mol
of citric acid and 1.000 kg of water.
b.A solution is made from 0.100 mol of citric acid,
1.000 kg of water, and enough solid NaOH to make the
pH equal to 6.00. Find the equilibrium molality of citric
acid and of each anion of citric acid.

7.35 The acid ionization constant of hydrocyanic acid (HCN) is
equal to 4× 10 −^10 at 298.15 K.
a.Find the pH of a solution made from 0.100 mol of HCN
and 1.000 kg of water at 298.15 K.

b.Find the value of the equilibrium constant for the

hydrolysis reaction CN−+H 2 O
HCN+OH−.

c.Find the pH of a solution made from 0.100 mol of KCN

and 1.000 kg of water at 298.15 K.

7.36 The two acid ionization constant ofortho-phthalic acid are

K 1  1. 3 × 10 −^3 andK 2  3. 9 × 10 −^6. Find the pH of a

solution made from 0.100 mol ofortho-phthalic acid and

1.000 kg of water.

7.37A solution is made from 0.0100 mol of ammonium

benzoate and 1.000 kg of water. It is maintained at 25◦C.

For benzoic acidKa 6. 46 × 10 −^5 at 25◦C, and for

ammonia is equal toKb 1. 774 × 10 −^5 at 25◦C.

Aguirre-Ode^3 gives an approximate formula (assuming

that all activity coefficients equal unity):

meq(H+)/m◦

(

KaKw

Kb

) 1 / 2 (

Kb+m/m◦

Ka+m/m◦

) 1 / 2

wheremis the stoichiometric molality. Find the pH using

this formula.

7.4 Equilibria in Solutions of Strong Electrolytes

Hydrochloric acid, HCl, is one of a half-dozen strong acids, which means that its acid

ionization constant is too large to measure accurately. We must find a way to handle

the activity of unionized species such as HCl in spite of their unmeasurably small

concentrations. Since aqueous HCl has an appreciable vapor pressure we assume that

aqueous unionized HCl in an aqueous solution of HCl is at equilibrium with gaseous

HCl. From the fundamental fact of phase equilibrium

μ(HCl,aq)μ(HCl,g) (7.4-1)

The aqueous unionized HCl is also at equilibrium with H+and Cl−in the solution:

HCl(aq)
H++Cl− (7.4-2)

The condition for equilibrium of this reaction is

μ(HCl,aq)μ(H+)+μ(Cl−) (7.4-3)

For the unionized HCl, we use a new molality description, in whichm◦is replaced

bym′, a small constant molality. We will not be able to determine the value ofm′, but

will be able to eliminate it from our equations. We write

μ(HCl)μ◦(HCl)+RTln[a(HCl)]

μ◦(HCl)+RTln

[

γ(HCl)

(

m(HCl)/m′

)]

(7.4-4)

(^3) F. Aguirre-Ode,J. Chem. Educ., 64 , 957 (1987).