(i) $\mathrm{H}_3 \mathrm{PO}_4(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{H}_2 \mathrm{PO}_4^{-}(a q)$
(ii) $\mathrm{H}_2 \mathrm{PO}_4^{-}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{HPO}_4^{2-}(a q)$
(iii) $\mathrm{HPO}_4^{2-}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{PO}_4^{3-}(a q)$
The equilibrium constants for the above reactions at a certain temperature are $K_1, K_2$ and $K_3$ respectively. The equilibrium constant for the reaction $\mathrm{H}_3 \mathrm{PO}_4(a q) \rightleftharpoons 3 \mathrm{H}^{+}(a q)+\mathrm{PO}_4^{3-}(a q)$ in terms of $K_1, K_2$ and $K_3$ is
$K_1+K_2+K_3$
$\frac{K_1}{K_2+K_3}$
$\frac{K_3}{K_1 K_2}$
$K_1 K_2 K_3$
Solution
Required relation
$\begin{aligned}
& \mathrm{H}_3 \mathrm{PO}_4(a q) \rightleftharpoons 3 \mathrm{H}^{+}(a q)+\mathrm{PO}_4^{3-}(a q) \\
& K=\frac{\left[\mathrm{H}^{+}\right]^3\left[\mathrm{PO}_4^{3-}\right]}{\left[\mathrm{H}_3 \mathrm{PO}_4\right]}
\end{aligned}$
For reaction $(i)$
For reaction (ii)
For reaction (iii)
On multiplying $(i),(i i)$ and $(i i i)$ $K=K_1 \times K_2 \times K_3$
