Calculate the exact degree of dissociation () of a solution of () in the presence of . Assume the ge — Ionic Equilibrium Chemistry Question
Question
Calculate the exact degree of dissociation ($\alpha$) of a $0.1 \text{ M }$ solution of $CH_3COOH$ ($K_a = 1.8 \times 10^{-5}$) in the presence of $0.01 \text{ M } HCl$. Assume the $H^+$ generated from the weak acid is entirely negligible compared to that from $HCl$. If your answer is $x \times 10^{-3}$, enter the exact numerical value of $x$.
💡 Solution & Explanation
Let the degree of dissociation be $\alpha$. Then $[CH_3COO^-] = C\alpha$ and $[H^+] \approx 0.01 \text{ M}$ (from the strong acid $HCl$). The equilibrium expression is $K_a = \frac{[CH_3COO^-][H^+]}{[CH_3COOH]} \approx \frac{C\alpha \times 0.01}{C(1-\alpha)}$. Assuming $\alpha \ll 1$, this simplifies to $K_a = \alpha \times 0.01$. Thus, $\alpha = \frac{1.8 \times 10^{-5}}{0.01} = 1.8 \times 10^{-3}$. Therefore, $x = 1.8$.