Calculate the exact percentage degree of hydrolysis () of a solution of sodium acetate () at . The g — Ionic Equilibrium Chemistry Question
Question
Calculate the exact percentage degree of hydrolysis ($h\%$) of a $0.1 \text{ M}$ solution of sodium acetate ($CH_3COONa$) at $25^\circ C$. The governing mechanism is anionic hydrolysis. Given $K_a(CH_3COOH) = 1.0 \times 10^{-5}$ and $K_w = 1.0 \times 10^{-14}$. If the percentage hydrolysis is $z\%$, enter the exact value of $z \times 1000$.
💡 Solution & Explanation
The anionic hydrolysis mechanism is $CH_3COO^- + H_2O \rightleftharpoons CH_3COOH + OH^-$. The hydrolysis constant is $K_h = \frac{K_w}{K_a} = \frac{10^{-14}}{10^{-5}} = 10^{-9}$. The degree of hydrolysis $h = \sqrt{\frac{K_h}{C}} = \sqrt{\frac{10^{-9}}{0.1}} = \sqrt{10^{-8}} = 10^{-4}$. To find the percentage degree of hydrolysis, multiply by 100: $z = 10^{-4} \times 100 = 10^{-2}\% = 0.01\%$. We need $z \times 1000 = 0.01 \times 1000 = 10$.