Calculate the pH of a 0.40 M solution of hypochlorous acid, for which Ka value is 2.90 x 10^-8

Question

Calculate the pH of a 0.40 M solution of hypochlorous acid, for which Ka value is 2.90 x 10^-8

The answer is: 3.96

please explain the steps used, thank you!

Answer 1

Hypochlorous acid is HClO.

HClO <==> H⁺ + ClO^-

Ka = [H⁺][ClO^-]/[HClO]

2.98x10^-8 = (x)(x)/0.40-x and if we assume x is small compared to 0.40 M, we can ignore it

2.98x10^-8 = x²/0.4

x² = 1.19x10^-8

x = 1.09x10^-4 M = H⁺ (note: this is very small compared to 0.4, so assumption above was valid)

pH = -log [H⁺] = -log 1.09x10^-4

pH = 3.96