Consider the following statements: (a) The pH of a mixture containing 400 mL of 0.1 M H2SO4 and 400 mL of 0.1 M NaOH…

Step 1 — Evaluate each statement:

(a) pH of mixture of 400 mL 0.1M $\mathrm{H_2SO_4}$ + 400 mL 0.1M NaOH: Moles $\mathrm{H^+}$ from $\mathrm{H_2SO_4}$ = $2 \times 0.1 \times 0.4 = 0.08$ mol Moles $\mathrm{OH^-}$ from NaOH = $0.1 \times 0.4 = 0.04$ mol Excess $\mathrm{H^+}$ = $0.08 - 0.04 = 0.04$ mol in 800 mL $[\mathrm{H^+}] = 0.04/0.8 = 0.05$ M $\rightarrow$ pH = $-\log(0.05) = 1.3$ ✓ Correct

(b) $K_w$ is temperature dependent: ✓ Correct — $K_w$ increases with temperature.

(c) $K_a = 10^{-5}$, pH = 5, degree of dissociation = 50%: If pH = 5, $[\mathrm{H^+}] = 10^{-5}$ M $K_a = \frac{\alpha^2 C}{1-\alpha}$; if $\alpha = 0.5$: $K_a = \frac{0.25C}{0.5} = 0.5C$ For $K_a = 10^{-5}$: $C = 2 \times 10^{-5}$ M, $[\mathrm{H^+}] = \alpha C = 10^{-5}$ ✓ Correct

(d) Le Chatelier's principle NOT applicable to common-ion effect: ✗ Incorrect — Le Chatelier's principle IS the basis for the common-ion effect.

Correct: a, b, c

Answer: Option (4) — (a), (b) and (c)