A weak acid HA has degree of dissociation x. $\text{ Thus, }\left(\mathrm{pH}-{\mathrm{pK}}_{\mathrm{a}}\right)\text{ is }$

$$\begin{gathered} \mathrm{HA}\rightleftharpoons {\mathrm{H}}^{+}+{\mathrm{A}}^{-} \\ \mathrm{Initial} \mathrm{C} 0 0 \\ \mathrm{After} \mathrm{ionisation} \mathrm{C}-\mathrm{Cx} ? \mathrm{Cx} \end{gathered}$$

$$\begin{gathered} {\mathrm{K}}_{\mathrm{a}}=\frac{\left[{\mathrm{H}}^{+}\right]\left[{\mathrm{A}}^{-}\right]}{\left[\mathrm{HA}\right]} \\ \left[{\mathrm{H}}^{+}\right]={\mathrm{K}}_{\mathrm{a}}\frac{\left[\mathrm{HA}\right]}{\left[{\mathrm{A}}^{-}\right]}={\mathrm{K}}_{\mathrm{a}}\frac{\mathrm{C}(1-\mathrm{x})}{\mathrm{Cx}}={\mathrm{K}}_{\mathrm{a}}\left(\frac{1-\mathrm{x}}{\mathrm{x}}\right) \\ \log \left[{\mathrm{H}}^{+}\right]={\mathrm{logK}}_{\mathrm{a}}+\log (1-\mathrm{x})-\mathrm{logx} \\ -\log \left[{\mathrm{H}}^{+}\right]=-{\mathrm{logK}}_{\mathrm{a}}-\log (1-\mathrm{x})-(-\mathrm{logx}) \\ \mathrm{pH}={\mathrm{pK}}_{\mathrm{a}}+{\mathrm{p}}_{(1-\mathrm{x})}-{\mathrm{p}}_{\mathrm{x}} \\ \mathrm{pH}-{\mathrm{pK}}_{\mathrm{a}}={\mathrm{p}}_{1-\mathrm{x}}-{\mathrm{p}}_{\mathrm{x}} \end{gathered}$$