The Foundations of Chemistry

more H 2 O to ionize, an excess of OHbuilds up. So the solution becomes basic. The

net result of the preceding equations can be written as a single equation. This equation

describes the hydrolysis of acetate ions.

CH 3 COO
H 2 O 34 CH 3 COOH
OH

The equilibrium constant for this reaction is called a (base) hydrolysis constant, or Kbfor

CH 3 COO.

Kb (Kbfor CH 3 COO)

We can evaluate this equilibrium constant from other known expressions. We multiply

the preceding expression by [H 3 O
]/[H 3 O
] to give

Kb

We recognize that

Kb

which gives

Kb5.6 10 ^10

We have calculated Kb, the hydrolysis constant for the acetate ion, CH 3 COO.

We can do the same kind of calculations for the anion of any weak monoprotic acid

and find that KbKw/Ka, where Karefers to the ionization constant for the weak mono-

protic acid from which the anion is derived.

This equation can be rearranged to

KwKaKb (valid for any conjugate acid–base pairin aqueous solution)

If either Kaor Kbis known, the other can be calculated.

EXAMPLE 18-18 Kbfor the Anion of a Weak Acid

(a) Write the equation for the reaction of the base CNwith water. (b) The value of the ioniza-

tion constant for hydrocyanic acid, HCN, is 4.0 10 ^10. What is the value of Kbfor the

cyanide ion, CN?

Plan

(a) The base CNaccepts H
from H 2 O to form the weak acid HCN and OHions. (b) We

know that KaKbKw. So we solve for Kband substitute into the equation.

Solution

(a) CN
H 2 O 34 HCN
OH

(b) We are given Ka4.0 10 ^10 for HCN, and we know that Kw1.0 10 ^14.

[CH 3 COOH][OH]



[CH 3 COO]

1.0 10 ^14



1.8 10 ^5

Kw



Ka (CH 3 COOH)

Kw



1

1



Ka (CH 3 COOH)

[H 3 O
][OH]



1

[CH 3 COOH]



[H 3 O
][CH 3 COO]

[H 3 O
]



[H 3 O
]

[CH 3 COOH][OH]



[CH 3 COO]

[CH 3 COOH][OH]



[CH 3 COO]

This is like the reaction of a molecular
weak base

NH 3 
H 2 O 34 NH 4 

OH

(excess OHis produced; the solution
becomes basic)

Just as we can write a Kbexpression
to describe the extent of ionization of
NH 3 , we can do the same for the
acetate ion.

778 CHAPTER 18: Ionic Equilibria I: Acids and Bases

Base hydrolysis constants, Kb’s,
for anions of weak acids can be
determined experimentally. The values
obtained from experiments agree with
the calculated values. Please note that
this Kbrefers to a reaction in which
the anion of a weak acid acts as a base.

Small Ka

Large Ka

Large Kb

Small Kb

Stronger

conjugate acid Stronger

conjugate base

For conjugate acid–base pairs