Calculate the pH of a 0.20 M aqueous solution of diethylamine $(C H_{3} C H_{2})_{2} N H$ at 25°C. Given $K_{b} = 5.6 \times 1 0^{- 4}$ .

medium 2 marks Class 12 · Chemistry · Amines

Answer

pH = 11.34

The correct answer is pH = 11.34 — Rounded to two decimal places, the pH is 12.02.

Step-by-step solution

Write the base‑dissociation equilibrium: $(C H_{3} C H_{2})_{2} N H + H_{2} O ⇌ (C H_{3} C H_{2})_{2} N H_{2}^{+} + O H^{-}$ .
Assume the change in concentration is $x$ for $[O H^{-}]$ and $[(C H_{3} C H_{2})_{2} N H_{2}^{+}]$ .
Set up the expression: $K_{b} = \frac{x ^{2}}{C - x}$ where $C = 0.20$ M.
Because $K_{b}$ is relatively small, $x ≪ C$ ; approximate $C - x \approx C$ .
Solve for $x$ : $x = K_{b} \times C = 5.6 \times 1 0^{- 4} \times 0.20 = 1.12 \times 1 0^{- 4} = 1.058 \times 1 0^{- 2}$ M.
Thus $[O H^{-}] = 1.058 \times 1 0^{- 2}$ M.
Calculate pOH: $pO H = - lo g [O H^{-}] = - lo g (1.058 \times 1 0^{- 2}) = 1.98$ .
Finally, $p H = 14 - pO H = 14 - 1.98 = 12.02$ .
Rounded to two decimal places, the pH is 12.02.

Common mistake: Using the approximation

x \approx C

instead of

x ≪ C

, which overestimates

[O H^{-}]

Concept tested: Basicity of aliphatic amines – pH calculation