Weak Acid Equilibria

Strong acids like HCl ionize completely: every molecule hands off its proton, so [H+] equals the starting concentration. Weak acids like acetic acid (CH_3COOH) only partially ionize. At any moment, most molecules are still intact, sitting in equilibrium with the small slice that has donated a proton to water. Ka is the equilibrium constant for that reaction, and its size tells you how far the reaction leans toward products. A small Ka, like 1.8 x 10⁻⁵ for acetic acid, means equilibrium sits far to the left: few molecules are ionized, fewer H+ ions are floating around, and the solution stings less than an HCl solution of the same concentration.

To find the pH, set up an ICE table. Start with concentration c of the weak acid and 0 for H+ and the conjugate base. Let x be the amount that ionizes: the acid's concentration becomes c - x, while H+ and conjugate base both become x. Plug into Ka = x² / (c - x). Because Ka is small, x is tiny compared to c, so you approximate c - x as c. That turns the equation into Ka = x² / c, so x = √(Ka times c). That x is [H+], and pH = -log[H+].

This setup is the quiet engine behind everything else in the unit: buffers are just this same equilibrium with extra conjugate base already present, and titration curves are a series of these calculations as acid gets neutralized. Get comfortable with the ICE table here and the rest of the unit reads as variations on it.