Background for pH calculations weak acid and weak base

Compare the reasoning used to deduce [acid] and [conjugate base] for solutions prepared by dissolving only one member of the weak acid-base conjugate pair CH₃NH₃⁺/CH₃NH₂.

In both solutions two equilibrium conditions are satisfied:

K_a =	=	[CH₃NH₂][H₃O⁺]	= 2.29 × 10^–11
		[CH₃NH₃⁺]

K_w = [H₃O⁺][OH]^–

If only the acid of the conjugate pair is dissolved in c(acid),
to reach equilibrium:

CH₃NH₃⁺+H₂O

CH₃NH₂ + H₃O⁺

For a weak acid, extent of reaction is small,

THUS [acid] ≈ c(acid) = c(CH₃NH₃⁺) (the initial concentration)

From the equation for the reaction occurring to reach equilibrium:

[ base] = [CH₃NH₂] = [H₃O⁺]

Substitute above to find [H₃O⁺] and then pH.

The pH will be less than 7 and less than pK_a.

If only the base of the pair is dissolved in c(base),
to reach equilibrium

CH₃NH₂ + H₂O

CH₃NH₃⁺+OH^–

For a weak base extent of reaction is small,
THUS [base] ≈ c(base) = c(CH₃NH₂) (the initial concentration)

From the equation for the reaction occurring to reach equilibrium:

[acid] = [CH₃NH₃⁺] = [OH^–] =	10^–14
	[H₃O⁺]

Substitute above to find [H₃O⁺] and then pH.

The pH will be greater than 7 and greater than pK_a.