HL — Ka, Kb, Buffers, and Titration Curves

At Higher Level the strength of a weak acid or base is quantified with a dissociation constant. For a weak acid $HA \rightleftharpoons H^+ + A^-$, the acid dissociation constant is $K_a = \frac{[H^+][A^-]}{[HA]}$. A larger $K_a$ means the equilibrium lies further to the right and the acid is stronger. Because $K_a$ values span many orders of magnitude, we use $pK_a = -\log_{10}K_a$; a smaller $pK_a$ means a stronger acid. Similarly, for a weak base $B + H_2O \rightleftharpoons BH^+ + OH^-$, the base dissociation constant is $K_b = \frac{[BH^+][OH^-]}{[B]}$, and $pK_b = -\log_{10}K_b$. For any conjugate acid-base pair the constants are linked by $K_a \times K_b = K_w$, which at 298 K gives the tidy relationship $pK_a + pK_b = 14.0$.

To calculate the pH of a weak acid, set up the equilibrium