Question

$\underset{C(1 - \alpha)M}{HA} \rightleftharpoons \underset{C\alpha M}{H^{+}} + \underset{C\alpha M}{A^{-}}$

$K_{a} = \frac{C\alpha.C\alpha}{C(1 - \alpha)} = \frac{\alpha^{2}.C}{1 - \alpha} \approx \alpha^{2}.C \Rightarrow \alpha = \sqrt{\frac{K_{a}}{C}} $$${\text{Now, }K_{a} = \frac{\left\lbrack H^{+} \right\rbrack.C\alpha}{C(1 - \alpha)} = \frac{\left\lbrack H^{+} \right\rbrack.\alpha}{1 - \alpha} \Rightarrow \alpha = \frac{K_{a}}{K_{a} + \left\lbrack H^{+} \right\rbrack} }{= \frac{1}{1 + \frac{\left\lbrack H^{+} \right\rbrack}{K_{a}}} = \frac{1}{1 + 10^{\left( P^{K_{a} - P^{H}} \right)}}}$$