8. pH of a Solution of a Weak Acid

When a weak acid like HOAc (acetic acid) is dissolved in water, only a few HOAc-molecules will donate a proton:

HOAc(aq) + H₂O(l) H₃O⁺(aq) + Ac^-(aq)
or
HOAc(aq) H⁺(aq) + OAc^-(aq)

[H₃O⁺] or [H⁺] and pH of the solution can be calculated from K_a.

Let us calculate the pH of 0.1 mol/L HOAc.

	HOAc	H+	OAc-
Beginning	0.1 mol/L	0 mol/L (*)	0 mol/L
D	- x mol/L	+ x mol/L	+ x mol/L
Equilibrium	(0.1 - x) mol/L	x mol/L	x mol/L

(*) The hydrogen ions delivered by the ionization of water are neglected. The weak acid HOAc (K_a = 1.8 x 10^-5) is much stronger than the weak acid H₂O (K_a = 1.0 x 10^-14).

So we find at equilibrium: [H⁺] = 1.3 x 10^-3 mol/L pH = - log 1.3 x 10^-3 = 2.88.

pH + pOH = 14 pOH = 13.

Summary

pH of a solution of a weak acid HA in water

Calculate the concentrations in the equilibrium state Calculate pH