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

${\mathrm{H}}_2\mathrm{A}\underset{{\mathrm{K}}_1}{\rightleftharpoons }{\mathrm{H}}^{+}+{\mathrm{HA}}^{-}$

${\mathrm{HA}}^{-}\underset{{\mathrm{K}}_2}{\rightleftharpoons }{\mathrm{H}}^{+}+{\mathrm{HA}}^{-}$

${\mathrm{H}}_2\mathrm{A}\underset{\mathrm{K}}{\rightleftharpoons 2}{\mathrm{H}}^{+}+{\mathrm{A}}^{-}$

${\mathrm{K}}_1=\frac{\left[{\mathrm{H}}^{+}\right]\left[{\mathrm{HA}}^{-}\right]}{\left[{\mathrm{H}}_2\mathrm{A}\right]};{\mathrm{K}}_2\frac{\left[{\mathrm{H}}^{+}\right]\left[{\mathrm{A}}^{-}\right]}{\left[{\mathrm{HA}}^{-}\right]}$

We know that, $\mathrm{K}={\mathrm{K}}_1{\mathrm{K}}_2$

$\mathrm{K}=\frac{\left[{\mathrm{H}}^{+}\right]\left[{\mathrm{HA}}^{-}\right]\left[{\mathrm{H}}^{+}\right]\left[{\mathrm{A}}^{-}\right]}{\left[{\mathrm{H}}_2\mathrm{A}\right]\left[{\mathrm{HA}}^{-}\right]}=\frac{{\left[{\mathrm{H}}^{+}\right]}^2\left[{\mathrm{A}}^{-}\right]}{\left[{\mathrm{H}}_2\mathrm{A}\right]}$

${\mathrm{K}}_1=1\times {10}^{-5};{\mathrm{K}}_2=5\times {10}^{-10},\mathrm{K}={\mathrm{K}}_1{\mathrm{K}}_2$

$\therefore \mathrm{K}=1\times {10}^{-5}\times 5\times {10}^{-10}=5\times {10}^{-15}$