## Acidity of Solutions of Strong Acids

James Richard Fromm

A strong acid, by definition, is an acid that is completely ionized in aqueous solution, that is, an acid which produces one or more protons for every acid molecule originally present. In the case of hydrochloric acid, the ionization equilibrium reaction is

HCl + H2O H3O+ + Cl-, so

[H3O+] = [Cl-]

which is equal to the original acid concentration.

Example. To calculate the pH of 0.001 molar aqueous HCl solution, use [H3O+] = 0.001. Then log[H3O+] = -3.00 and the pH is 3.00.

As in any equilibrium calculation, a(H3O+) is the real chemical activity of hydrogen ion in solution at equilibrium. Is there any other source of protons other than the acid itself? The autoionization of water could give 1 x 10-7 molar H3O+ (and also 1 x 10-7 molar OH-). But this additional source of protons, which cannot exceed about 10-7 molar, is usually negligibly small. In the presence of any significant concentration of strong acid, the ionization of water will be repressed by the strong acid in accordance with Le Chatelier's Principle. When the molar concentration of strong acid is 0.001, the concentration of hydroxide ion is only 1 x 10-11 mol/liter and the concentration of H3O+ produced by water ionization has the negligible value of 1 x 10-11mol/L also. Therefore, in an aqueous solution of a strong acid, acidity is essentially determined by the concentration of strong acid alone.

Only when the concentration of strong acid present is very low does the autoionization of water become a comparable or dominant contributor to the solution pH.

Example. At an added [H3O+] of 1 x 10-8 mol/L, [H3O+] = [H3O+](added) + [H3O+](ionization). Then

[H3O+] = 1 x 10-8 + 1 x 10-7 = 1.1 x 10-7

The pH will be about 6.96 after addition of the acid, a negligible change from 7.00 obtained in water without the acid. The assumption that [H3O+] is actually equal to 10-8 mol/L would give an altogether unrealistic pH of 8. Addition of a strong acid cannot make any solution more basic!