A 0.20 M solution of a weak acid HA has a pH of 3.00. What is the acid dissociation constant, Ka, for HA?
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Correct answer
A. 5.0 × 10^-6
Principle or equation
For a weak monoprotic acid HA, the acid dissociation constant is Ka = [H+][A-]/[HA]. If the initial concentration is C and the degree of dissociation is small, [H+] ≈ [A-] and [HA] ≈ C - [H+] ≈ C. Thus Ka ≈ [H+]^2 / C.
Why this answer is correct
Given pH = 3.00, [H+] = 10^-3.00 = 1.0 × 10^-3 M. The initial acid concentration C = 0.20 M. Using the approximation Ka ≈ [H+]^2 / C = (1.0 × 10^-3)^2 / 0.20 = (1.0 × 10^-6) / 0.20 = 5.0 × 10^-6. The approximation is valid because [H+] is much smaller than C.
Example
For a 0.10 M weak acid with pH = 4.00, [H+] = 1.0 × 10^-4 M, Ka ≈ (1.0 × 10^-4)^2 / 0.10 = 1.0 × 10^-7.
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