Dissociation constant of propionic acid is \(1.32 \times 10^{-5}\). Calculate the degree of dissociation of acid in \(0.05 \mathrm{M}\) solution.

\(\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{COOH}\) (Propionic Acid)
\(
\begin{aligned}
& \mathrm{CH}_3 \mathrm{CH}_2 \mathrm{COOH}_{(\mathrm{aq})} \rightleftharpoons \mathrm{CH}_3 \mathrm{CH}_2 \mathrm{COO}_{(\mathrm{aq})}^{-}+\mathrm{H}_{(\mathrm{aq})}^{+} \\
& \mathrm{t}=0_1 \quad \mathrm{C} \\
& \mathrm{t}=\mathrm{t}_{\mathrm{aq}}, \quad \mathrm{C}-\mathrm{C} \propto \quad \mathrm{C} \propto \quad \mathrm{C} \propto \\
& \mathrm{k}_{\mathrm{a}}=\frac{\mathrm{c} \propto^2}{1-\propto} \quad(1-\propto \simeq 1) \\
&
\end{aligned}
\)
\(\propto=\sqrt{\frac{\mathrm{k}_{\mathrm{a}}}{\mathrm{C}}}=\sqrt{\frac{1.32 \times 10^{-5}}{0.05}}=\sqrt{\frac{132 \times 10^{-1}}{5}}\) \(\times~ 10^{-2} \quad \mathrm{k}_{\mathrm{a}}=\mathrm{c}^2 \)
\( =\sqrt{2.64} \times 10^{-2}=1.61 \times 10^{-2}\)