Final answer:
The pH of a 0.964 M solution of hypochlorous acid (HClO) can be calculated using the equilibrium expression and the K value. The concentration of H3O+ ions can be determined by solving the equilibrium expression and using the K value. Using the formula pH = -log[H3O+], we can calculate the pH of the solution to be approximately 4.73.
Step-by-step explanation:
The pH of a solution can be calculated using the formula: pH = -log[H3O+]. In this case, the concentration of hypochlorous acid (HClO) is given as 0.964 M. The K value for hypochlorous acid is 3.5×10⁻⁸. To calculate the pH, we need to determine the concentration of H3O+ ions. Since HClO is a weak acid, we can assume that it is partially ionized. By using the K value, we can set up an equilibrium expression and solve for the concentration of H3O+ ions.
For the reaction: HClO <=> H+ + ClO-
The initial concentration of HClO is 0.964 M. Let x be the concentration of H+ ions. At equilibrium, the concentration of ClO- ions will also be x. So the equilibrium expression becomes:
K = [H+][ClO-] / [HClO] = (x)(x) / (0.964)
Substituting the values, we get: 3.5×10⁻⁸ = x² / (0.964)
Solving for x, the concentration of H+ ions, we find: x ≈ 1.87×10⁻⁵ M. Since H+ ions are equivalent to H3O+ ions in an aqueous solution, the concentration of H3O+ is approximately 1.87×10⁻⁵ M. Plugging this value into the formula for pH, we can calculate the pH of the solution.
pH = -log(1.87×10⁻⁵) ≈ 4.73