Question

A 0.400 M solution of weak base has a pH of 9.85. What is the base hydrolysis constant, Kb for the weak base?

Answer 1

Calculate [H3O+]

In order to calculate hydronium ion concentration we use following expression

pH= - log [H3O+]

Therefore

[H3O+]= antilog (-pH)

10^(-9.85)=1.41E-10

Using hydronium ion concentration, calculate hydroxide ion concentration

[OH-]=1.0E-14/hydronium ion concentration=1.0E-14/1.41E-10=7.1E-5

Now show dissociation reaction of given base.

Lets B is the base

B(aq)     + H2O(l)   ----> BH+(aq)      +   OH-(aq)

I         0.400                              0                         0

C           -x                             +x                        +x

E     (0.400-x)                           x                    x

We know x = [OH-] = 7.1E-5 M

Equilibrium concentration of B(aq) = 0.400-7.1E-5=0.3999 M

[BH+]=x=7.1E-5 M

Use kb expression

Kb = [BH+][OH-]/[B]

(7.1E-5)^2/0.3999=1.25 E-8

So the kb of this base is 1.25 x 10^-8