The first and second dissociation constants of an acid $\mathrm{H}_2 \mathrm{A}$ are $1.0 imes 10^{-5}$ and $5.0 imes 10^{-10}$ respectively. The overall dissociation constant of the acid will be

Question

The first and second dissociation constants of an acid $\mathrm{H}_2 \mathrm{A}$ are $1.0 	imes 10^{-5}$ and $5.0 	imes 10^{-10}$ respectively. The overall dissociation constant of the acid will be

Aicharya · Accepted Answer

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

The first and second dissociation constants of an acid $\mathrm{H}_2 \mathrm{A}$ are $1.0 \times 10^{-5}$…

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