A 0.10 M solution of a weak acid HA has a pH of 4.00. What is the acid dissociation constant, Ka, for HA?
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Correct answer
B. 1.0 × 10^-7
Principle or equation
For a weak acid HA, the concentration of H+ is equal to the square root of (Ka × initial concentration) when the degree of dissociation is small. The pH gives [H+] directly.
Why this answer is correct
Given pH = 4.00, [H+] = 10^-4 M. For a weak acid, [H+] ≈ √(Ka × C0). Rearranging: Ka ≈ [H+]^2 / C0 = (10^-4)^2 / 0.10 = 10^-8 / 0.10 = 1.0 × 10^-7.
Example
If a 0.20 M weak acid has pH 3.00, [H+] = 10^-3, Ka = (10^-3)^2 / 0.20 = 5.0 × 10^-6.
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