Calculate the fraction of association

Question

Calculate the fraction of association of a 0.30 F benzoic acid solution. Ka for

Benzoic acid (C6H5COOH) is 6.28 x 10^-5 .

Answer 1

Let benzoic acid be represented as HA

HA <==> H⁺ + A^-

Ka = [H⁺][A^-] / [HA]

6.28x10^-5 = (x)(x) / (0.30 - x)

x² = 1.88x10^-5 - 6.28x10^-5x (if we ignore the 6.28x10^-5x, we can simplify the calculation - see below)

x² = 1.88x10^-5

x = 4.34x10^-3 M = [H⁺] = [A^-] NOTE: since this value is small (~1.4% of 0.3 M) our assumption to ignore it in the above calculation is valid).

% ionization = 4.34x10-3 M / 0.30 M (x100%) = 1.45%

% associated = 100 % - 1.45% = 98.5%

Fraction association = 0.985