Question

The first and second dissociation constants of an acid $H_2A$ are $1.0 × 10^{−5}$ and $5.0 × 10^{−10}$ respectively. The overall dissociation constant of the acid will be

• A. $5.0 × 10^{−5}$
• B. $5.0 × 10^{15}$
• C. $5.0 × 10^{−15}$
• D. $0.0 × 10^{5}$

Answer 1

Answer: (C)

$H_2A \rightleftharpoons HA^- +H^+\,\, K_{1}=\frac{\left[HA^{-}\right]\left[H^{+}\right]}{\left[H_{2}A\right]}$
$HA^{-} \rightleftharpoons H^+ +A^{2-}\,\, K_{2}=\frac{\left[H^{+}\right]\left[A^{2-}\right]}{\left[HA^{-}\right]}$
For the reaction
$H_2A \rightleftharpoons 2H^+ +A^{2-}$
$K=\frac{\left[H^{+}\right]^{2}\left[A^{2-}\right]}{\left[H_{2}A\right]}=\,\,K_{1}\times K_{2}$
$=1\times10^{-5}\times5\times10^{-10}$
$=5\times10^{-15}$
Hence, (3) is correct.