### Given the pK of a Salt, Calculate the pH of a Solution of the Acid or Base

Typically, when doing this type of problem, you usually see one of two things:

1) You are given the concentration and Ka (or pKa) of an acid, then asked to calculate the pH.
2) You are given the concentration and Kb (or pKb) of a base, then asked to calculate the pH.

In the examples below, you are given (a) the pK of a salt of an acid or base and (b) the concentration, then asked to calculate the pH. There is just one additional step when compared to the technique needed for (1) and (2) just above.

Problem #1: What is the pH of a 0.262 M NH3 solution? The pKa for NH4+ = 9.248.

Solution:

Determine the Kb for ammonia:

KaKb = Kw = 1.00 x 10-14, therefore:
pKa + pKb = 14.000

9.248 + x = 14.000

x = 4.752

Then:

Kb = 10-pKb

Kb = 10-4.752

Kb = 1.77 x 10-5

The step above is the additional step I referred to above. Now, the problem becomes this:

What is the pH of a 0.262 M NH3 solution? The Kb for NH3 = 1.77 x 10-5.

You can see the rest of the solution technique here. The answer to the above problem is 11.333

Problem #2: What is the pH of a 0.262 M HCN solution? The pKb for CN¯ = 4.788.

Solution:

Determine the Ka for HCN:

Since KaKb = Kw = 1.00 x 10-14, we know:
pKa + pKb = 14.000

x + 4.788 = 14.000

x = 9.212

Then:

Ka = 10-pKa

Ka = 10-9.212

Ka = 6.14 x 10-10

The step above is the additional step I referred to above. Now, the problem becomes this:

What is the pH of a 0.262 M HCN solution? The Ka for HCN = 6.14 x 10-10.

You can see the rest of the solution technique here. The answer to the above problem is 4.897