Summary equal amounts

When the concentrations of the acid and base of the conjugate pair are equal (irrespective of whether they are both large or both small), at equilibrium

[H₃O⁺] equals K_a.
pH equals pK_a

because, as shown, the concentrations cancel irrespective of whether both concentrations are large or both are small.

K_a = [H₃O⁺] ×	[conjugate base]
	[acid]

K_a = [H₃O⁺] ×	[conjugate base]
	[acid]

This is also shown in the graph of the change in pH as NaOH is added to an ethanoic acid solution. At 12.5

added NaOH, the concentrations of the CH₃CO₂H and CH₃CO₂^– are equal, and pH equals 4.76 which is pK_a(CH₃CO₂H).

titration curve ethanoic acid with sodium hydroxide	CH₃CO₂^–
	CH₃CO₂H/ CH₃CO₂^–
	CH₃CO₂H

Measuring a curve like the one shown above is a common method for determining, by experiment, the pK_a of a weak acid-base conjugate pair.