What is the pH of a solution that results from mixing together equal volumes of a 0.060 M solution of ammonia and a 0.030 M solution of hydrochloric acid? (pKa of NH4+ = 9.25)

Question

What is the pH of a solution that results from mixing together equal volumes of a 0.060 M  solution of ammonia and a 0.030 M  solution of hydrochloric acid? (pK_a of NH₄⁺ = 9.25)

Answer 1

When we mix equal volumes of 2 solutions, the concentrations (molarities) of each are halved.

Reaction is as follows:

NH₃ + HCl ==> NH₄⁺ + Cl^-

0.03 M...0.015M....0...............Initial

-0.015...-0.015....+0.015........Change

0.015 M.....0.........0.015 M.....Equilibrium

Note that this creates a buffer consisting of a weak base (NH₃) and the conjugate acid (NH₄⁺).

For a basic buffer such as this, we can use the following form of the Henderson Hasselbalch equation:

pOH = pKb + log [conj.acid]/[base]

Since the ratio of [conj.acid]/[base] = 0.015/0.015 = 1, that means the pOH = pKb since log 1 = 0

pOH = pKb and the pKb for NH3 = 14 - the pKa for NH₄⁺ = 14 - 9.25 = 4.50

pOH = 4.50

From pOH, we can simply find pH...

pH = 14 - pOH

pH = 14 - 4.50

pH = 9.50