JEE Main · 2023 · 15 Apr 2023 · Shift 1 · Equilibrium

A $1\times 10^{-8}$ M HCl solution is still acidic; at such high dilution the ${\mathrm{H}}^{+}$ contributed by the self-ionisation of water cannot be ignored, and the pH works out close to 6.98, not 8, so statement (A) is false. Removing one proton from ${\mathrm{H}}_2\mathrm{P}{\mathrm{O}}_4^{-}$ gives $\mathrm{HP}{\mathrm{O}}_4^{2-}$, which is its conjugate base, so statement (B) is true. The ionisation of water is endothermic, so $K_w$ increases as the temperature rises, making statement (C) true. At the half-neutralisation point of a weak monoprotic acid $[{\mathrm{A}}^{-}]=[\mathrm{HA}]$, and the Henderson-Hasselbalch relation gives $\mathrm{pH}=\mathrm{p}{K}_a+\log 1=\mathrm{p}{K}_a$, not $\frac{1}{2}\mathrm{p}{K}_a$, so statement (D) is false. Only statements (B) and (C) are correct.