Calculate the pH of a 0.01 M solution of acetic acid (Ka = 1.8×10−5).

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Multiple Choice

Calculate the pH of a 0.01 M solution of acetic acid (Ka = 1.8×10−5).

Explanation:
Weak acids set their pH by their dissociation equilibrium. For acetic acid, Ka = [H+][A−]/[HA]. If the initial concentration is C = 0.01 M and we let x = [H+] = [A−], then [HA] ≈ C − x. The equilibrium equation becomes x^2/(C − x) = Ka. Since Ka is small, only a small fraction of the acid dissociates, so x is much smaller than C and we can approximate C − x ≈ C. This gives x^2 ≈ Ka · C = (1.8×10−5)(0.01) = 1.8×10−7, so x ≈ √(1.8×10−7) ≈ 4.2×10−4 M. The pH is −log10(4.2×10−4) ≈ 3.37. A more exact approach by solving the quadratic x^2 + Ka x − Ka C = 0 yields x ≈ 4.16×10−4, which gives pH ≈ 3.38. In either method, the pH is about 3.37.

Weak acids set their pH by their dissociation equilibrium. For acetic acid, Ka = [H+][A−]/[HA]. If the initial concentration is C = 0.01 M and we let x = [H+] = [A−], then [HA] ≈ C − x. The equilibrium equation becomes x^2/(C − x) = Ka.

Since Ka is small, only a small fraction of the acid dissociates, so x is much smaller than C and we can approximate C − x ≈ C. This gives x^2 ≈ Ka · C = (1.8×10−5)(0.01) = 1.8×10−7, so x ≈ √(1.8×10−7) ≈ 4.2×10−4 M. The pH is −log10(4.2×10−4) ≈ 3.37.

A more exact approach by solving the quadratic x^2 + Ka x − Ka C = 0 yields x ≈ 4.16×10−4, which gives pH ≈ 3.38. In either method, the pH is about 3.37.

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