Question

The first and second dissociation constant of an acid $H_{2}A$ are $1.0\times {10}^{-5}$ and $5.0\times {10}^{-10}$ respectively. The overall dissociation constant of the acid will be:

• A. $5.0\times {10}^{-5}$
• B. $5.0\times {10}^{15}$
• C. $5.0\times {10}^{-15}$
• D. $0.2\times {10}^{-5}$

Answer 1

The correct option is C $5.0\times {10}^{-15}$

$H_{2}A\rightleftharpoons H{A}^{-}+H^{+}\therefore K_1=1.0\times {10}^{-5}=\frac{\left[H^{+}\right]\left[H{A}^{-}\right]}{H_{2}A}H{A}^{-}\rightleftharpoons H^{+}+A^{2-}\therefore K_2=5.0\times {10}^{-10}=\frac{\left[H^{+}\right]\left[A^{2-}\right]}{\left[H{A}^{-}\right]}$
Overall reaction: $H_{2}A\rightleftharpoons 2H^{+}+A^{2-}$ $K_{overall}=\frac{\left[H^{+}{]}^2\right[A^{2-}]}{H_{2}A}=K_1\times K_2{K}_{overall}=5\times {10}^{-15}$