Which of the following statement(s) is/are correct? (A) The pH of 1 10-8 M HCl solution is 8. (B) The conjugate base of…

Step 1 — Evaluate each statement:

(A) pH of $10^{-8}$ M HCl = 8: ✗ Incorrect. At such low concentration, the contribution of water's own $\mathrm{H^+}$ ($10^{-7}$ M) cannot be ignored. Total $[\mathrm{H^+}] = 10^{-8} + 10^{-7} \approx 1.1 \times 10^{-7}$ M $\rightarrow$ pH ≈ 6.96, not 8.

(B) Conjugate base of $\mathrm{H_2PO_4^-}$ is $\mathrm{HPO_4^{2-}}$: ✓ Correct. Removing one $\mathrm{H^+}$ from $\mathrm{H_2PO_4^-}$ gives $\mathrm{HPO_4^{2-}}$.

(C) $K_w$ increases with temperature: ✓ Correct. Dissociation of water is endothermic; increasing T shifts equilibrium forward $\rightarrow K_w$ increases.

(D) At half-neutralisation, pH = $\frac{1}{2}\mathrm{pK_a}$: ✗ Incorrect. At half-neutralisation, [acid] = [salt], so by Henderson-Hasselbalch: pH = pKa + log(1) = pKa (not $\frac{1}{2}$pKa).

Correct statements: B and C

Answer: Option (1) — (B), (C)