The difference between a strong acid and a weak acid is that a strong acid completely ionizes in solution while a weak acid only does so partially. The pH scale directly corresponds to the amount of ionized hydrogen in a solution. For weak acids, the pH depends on the concentration of the solution. If you know the pH and the type of acid, you can derive the initial concentration and the percentage of ionization. This type of calculation is fundamental to learning to work with acids and bases.
Calculate the hydrogen-ion concentration with the formula [H+] = 1/(10^pH), where [H+] is the concentration of hydrogen ions. This formula is derived from the definition of pH: pH = -log[H+]. For example, if the pH of a solution of benzoic acid is 2.51, [H+] = 1/(10^2.51) = 3.09 x 10^-3 moles/liter.
Look up the acid's dissociation constant (Ka) on a table of weak acids (see Resource). From the table, the dissociation constant for benzoic acid is Ka = 6.46 x 10^-5.
Calculate the initial concentration of the acid. By definition, the dissociation constant is Ka = [H+][A-]/[HA], where [HA] is the initial concentration, and [A-] is the concentration of the acid's anions, which are negatively charged ions. At equilibrium, [HA] will decrease by an amount equal to [H+], and [H+] is also equal to [A-]. Therefore, you can rewrite the expression as Ka = [H+]²/([HA] - [H+]). Solve for [HA] to derive the formula [HA] = [H+]²/Ka + [H+]. For example: [HA] = (3.09 x 10^-3)²/(6.46 x 10^-5) + (3.09 x 10^-3) = 0.151 moles/liter.
Find the percentage of ionization with the formula I = 100_[H+]/[HA]. For example, I = 100_(3.09 x 10^-3)/0.151 = 2.05 percent.