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 over all 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 $5.0\times {10}^{-15}$

$H_{2}A\stackrel{K_1}{\rightleftharpoons }H{A}^{-}+H^{+}$

$\Rightarrow K_1=\frac{\left[H{A}^{-}\right]\left[H^{+}\right]}{\left[H_{2}A\right]}$ $⟶\left(1\right)$

$H{A}^{-}\stackrel{K_2}{\rightleftharpoons }{H}^{+}+A^{2-}$

$\Rightarrow K_2=\frac{\left[H^{+}\right]\left[A^{2-}\right]}{\left[H{A}^{-}\right]}$ $⟶\left(2\right)$

Overall dissociation constant $K$

$\Rightarrow K=\frac{\left[H^{+}{]}^2\right[A^{2-}]}{\left[H_{2}A\right]}=K_1\times K_2$

$=1\times {10}^{-5}\times 5\times {10}^{-10}$

$=5\times {10}^{-15}$ .