K_a(CH₃CH₂CO₂H) = 1.3 × 10^–5

Calculate the pH of 0.10

CH₃CH₂CO₂H.

K_a =	[CH₃CH₂CO₂^–][H₃O⁺]
	[CH₃CH₂CO₂H]

The link between known and unknown is the K_a expression.
Remember that the conjugate base of the acid dissolved has one fewer hydrogens and is one unit more negative.

CH₃CH₂CO₂H + H₂O→ H₃O⁺ + CH₃CH₂CO₂^–

To calculate [H₃O⁺] given K_a need to establish [CH₃CH₂CO₂H] and [CH₃CH₂CO₂^–].
[CH₃CH₂CO₂^–] is formed in the reaction to reach equilibrium.

K_a = 1.3 × 10^–5 =	[CH₃CH₂CO₂^–][H₃O⁺]
	0.10

K_a shows that CH₃CH₂CO₂H is a weak acid.
Weak acids react with water to < 2%.
[acid] ≈ initial concentration acid

1.3 × 10^–5 =	[H₃O⁺]²
	0.10

In the reaction above, one CH₃CO₂^– is formed for each H₃O⁺.
Thus in this solution [H₃O⁺] = [CH₃CO₂^–]:

[H₃O⁺] = 1.14 × 10^–3

pH = 2.94

pH = -log[H₃O⁺]

As would be predicted the pH of the solution is less than 7.
pK_a(CH₃CH₂CO₂H) = –log (1.3 × 10^–5) = 4.89
The pH of a solution prepared by dissolving the acid of the pair only is also less than pK_a.