What is the pH of a 0.530 M solution of hypochlorus acid? Ka = 2.9 × 10^-8

Question

Quizplus · Accepted Answer

Hypochlorous acid (HClO) is a weak acid that dissociates as follows:
HClO(aq) + H2O(l) ⇌ H3O+(aq) + ClO-(aq)
The equilibrium constant expression is:
Ka = [H3O+][ClO-]/[HClO]
We are given that the concentration of HClO is 0.530 M
Let x be the concentration of H3O+.
Then, the concentration of ClO- is also x because the acid dissociates in a 1:1 ratio.
Using the equilibrium constant expression:
Ka = 2.9 × 10^-8 = x^2/(0.530 - x)
Assuming x << 0.530, we can simplify the expression to:
Ka = 2.9 × 10^-8 ≈ x^2/0.530
Solving for x gives:
x = √(Ka × 0.530) ≈ 1.76 × 10^-4 M
The pH is defined as the negative logarithm of the H3O+ concentration:
pH = -log[H3O+] = -log(1.76 × 10^-4) ≈ 3.9
Therefore, the answer is D.

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