For a salt derived exclusively from a weak acid () and a weak base (), which of the following algebr — Ionic Equilibrium Chemistry Question

💡 Solution & Explanation

For a WA-WB salt, both the cation and the anion undergo hydrolysis simultaneously. The overall hydrolysis constant is $K_h = \frac{K_w}{K_a \cdot K_b}$. The degree of hydrolysis is independent of concentration, approximating to $h = \sqrt{K_h}$. The concentration of $[H^+] = K_a \times \frac{h}{1-h} \approx K_a \times h = K_a \times \sqrt{\frac{K_w}{K_a K_b}} = \sqrt{\frac{K_w K_a}{K_b}}$. Taking the negative log yields $pH = \frac{1}{2}(pK_w + pK_a - pK_b) = 7 + \frac{1}{2}(pK_a - pK_b)$.