JEE Main 2007 — Ionic Equilibrium Question with Solution

$\begin{array}{ll}{\mathrm{H}}_2\mathrm{A}\rightleftharpoons {\mathrm{HA}}^{-}+{\mathrm{H}}^{+}& {\mathrm{K}}_1=\frac{\left[{\mathrm{HA}}^{-}\right]\left[{\mathrm{H}}^{+}\right]}{\left[{\mathrm{H}}_2\mathrm{A}\right]}\dots (1)\\ {\mathrm{HA}}^{-}\rightleftharpoons {\mathrm{H}}^{+}+{\mathrm{A}}^{2-}& {\mathrm{K}}_2=\frac{\left[{\mathrm{H}}^{+}\right]\left[{\mathrm{A}}^{2-}\right]}{\left[{\mathrm{HA}}^{-}\right]}\dots (2)\end{array}$ For the reaction $\begin{aligned} & \mathrm{H}_2 \mathrm{A} \rightleftharpoons 2 \mathrm{H}^{+}+\mathrm{A}^{2-} \\ & \mathrm{K}=\frac{\left[\mathrm{H}^{+}\right]^2\left[\mathrm{~A}^{2-}\right]}{\left[\mathrm{H}_2 \mathrm{A}\right]}=\mathrm{K}_1 \times \mathrm{K}_2 \\ & =1 \times 10^{-5} \times 5 \times 10^{-10} \\ & =5 \times 10^{-15} \end{aligned}$ Hence, (C) is correct.