Calculate the pH of a 0.05 M solution of ammonia (NH₃). Given that the base dissociation constant Kb for NH₃ is $1.8 \times 1 0^{- 5}$ .

hard 5 marks Class 7 · Science · Acids, Bases and Salts

Answer

pH ≈ 11.0

The correct answer is pH ≈ 11.0 — Determine pH: $p H = 14 - pO H = 14 - 3.02 = 10.98 a pp r o x 11.0$ .

Step-by-step solution

Write the base dissociation equilibrium: $d i s pl a y s t y l ece N H 3 + H 2 O <=> N H 4 + + O H -$ .
Let $x$ be the concentration of $ce O H -$ formed at equilibrium.
Express Kb: $K_{b} = \frac{x ^{2}}{0.05 - x}$ .
Assume $x l l 0.05$ , so $K_{b} \approx \frac{x ^{2}}{0.05}$ .
Solve for $x$ : $x = K_{b} \times 0.05 = 1.8 \times 1 0^{- 5} \times 0.05 = 9.5 \times 1 0^{- 4} M$ .
Calculate pOH: $pO H = - l o g_{10} (9.5 \times 1 0^{- 4}) \approx 3.02$ .
Determine pH: $p H = 14 - pO H = 14 - 3.02 = 10.98 a pp r o x 11.0$ .

Common mistake: Using Kb directly in pOH calculation or neglecting the quadratic nature of the equilibrium

Concept tested: pH of weak base solution