Calculate the pH of 0.20

CH₃CH₂NH₂ using pK_a(CH₃CH₂NH₃⁺) = 10.67.

K_a =	[CH₃CH₂NH₂][H₃O⁺]	= 2.1 × 10^–11
	[CH₃CH₂NH₃⁺]

CH₃CH₂NH₂ + H₂O

CH₃CH₂NH₃⁺ + OH^–

K_a =	0.2 [H₃O⁺]	= 2.1 × 10^–11
	[CH₃CH₂NH₃⁺]

K_a for the conjugate acid relates H₃O⁺, [base] and [acid] in aqueous solution

CH₃CH₂NH₂ is weak base (pK_a = 10.67).
The extent of its reaction with water is small.
Thus [base] = initial c(base) = 0.2.

The reaction is the only source of [CH₃CH₂NH₃⁺].
Thus [CH₃CH₂NH₃⁺] = [OH^–].

[CH₃CH₂NH₃⁺] = K_w/[H₃O⁺]

As in any aqueous solution K_w = [H₃O⁺][OH^–],

[CH₃CH₂NH₂][H₃O⁺]	=	0.20 × [H₃O⁺]	= 0.20 × [H₃O⁺] ×	[H₃O⁺]	=	0.20 × [H₃O⁺]²	= 2.4 × 10^–11
[CH₃CH₂NH₃⁺]		10^–14 /[H₃O⁺]		10^–14		10^–14

[H₃O+] = 1 × 10^–12

therefore pH = 12.0.