pH of a Weak Acid

Hydrochloric Acid is a strong acid; in aqueous solution all of the HCl molecules present have become ionised.

HCl_(aq) + H₂O_(l) ® H₃O⁺_(aq) + Cl^-_(aq)

Hydrochloric Acid is a monobasic acid, and in a 0.1 mol dm^-3 solution the concentration of H₃O⁺_(aq) is also 0.1 mol dm^-3.

The pH of a 0.1 mol dm^-3 solution of HCl_(aq) can easily be calculated:

pH = -log[H⁺]

\ pH = 1

Ethanoic Acid is a weak acid; in aqueous solution it is in equilibrium with its conjugate base. At any instant in time, only a small proportion of its molecules have become ionised.

CH₃COOH_(aq) + H₂O_(l) = H₃O⁺_(aq) + CH₃COO^-_(aq)

Therefore, in a 0.1 mol dm^-3 solution of CH₃COOH_(aq), the H₃O⁺_(aq) must be much less than 0.1 mol dm^-3.

What is the pH of a 0.1 mol dm^-3 solution of CH₃COOH_(aq) at 298 K?

For this calculation we need to know the acid dissociation constant for ethanoic acid at 298 K.

K_a = [CH₃COO^-_(aq)][H₃O⁺_(aq)] / [CH₃COOH_(aq)] = 1.75 x 10^-5 mol dm^-3

The 'equilibrium table' below sets out the calculation.

In this calculation a 'simplification' can be made, since we have a weak acid with only a small amount of ionisation at equilibrium. This means that the value of y is so small compared with 0.1 that 0.1-y » 0.1.

Substituting the equilibrium concentration values into the equilibrium expression gives

y²/0.1 = 1.75 x 10^-5 mol dm^-3

\ [H₃O⁺_(aq)] = 1.3 x 10^-3 mol dm^-3

\ pH = 2.88