What is the pH of a 0.0100 M sodium benzoate solution?
K_b (C₇H₅O₂¯) = 1.5 * 10¯¹⁰

Question

What is the pH of a 0.0100 M sodium benzoate solution? K_b (C₇H₅O₂¯) = 1.5 * 10¯¹⁰

Quizplus · Accepted Answer

Sodium benzoate is the sodium salt of benzoic acid. In solution, it dissociates into its component ions, Na+ and C6H5COO-. The benzoate anion can react with water to produce benzoic acid and hydroxide ions:

C6H5COO- + H2O → C6H5COOH + OH-

Therefore, the solution contains both sodium benzoate and benzoic acid. The benzoic acid equilibrium controls the pH of the solution. Benzoic acid is a weak acid with a Ka value of 6.46 × 10-5.

C6H5COOH + H2O ⇌ C6H5COO- + H3O+

The equilibrium constant expression for this reaction is

Ka = [C6H5COO-][H3O+] / [C6H5COOH]

At equilibrium, the concentrations of C6H5COO- and H3O+ are equal because one mole of C6H5COOH produces one mole of each ion.

Ka = [H3O+]

Therefore,

pH = -log[H3O+] = -log(Ka) + log[C6H5COOH] = 4.19 + log(0.0100) = 8.09

Therefore, the pH of the solution is 8.09, and the best choice is C.

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