Calculate the pH of a solution that contains 3.9 × 10^-⁵ M H₃O⁺ at 25°C. A) 5.41 B) 4.41 C) 9.59 D) 8.59 E) 0.59

Question

Quizplus · Accepted Answer

First, we need to write the balanced chemical equation for the dissociation of H₃O⁺: H₃O⁺ ⇌ H⁺ + ₃O²⁻ The equilibrium constant for this reaction is called the acid dissociation constant, or Ka. We can set up an expression for Ka as follows: Ka = [H⁺][₃O²⁻]/[H₃O⁺] We are given the concentration of H₃O⁺, so we can substitute that value into our Ka expression. However, we need the concentrations of H⁺ and ₃O²⁻ at equilibrium. We can assume that the initial concentration of H⁺ is negligible compared to the initial concentration of H₃O⁺, so we can simplify the expression to: Ka = [H⁺][₃O²⁻]/(3.9 × 10⁻¹⁵ M) Since the concentration of ₃O²⁻ is equal to the concentration of HSO₄⁻ at equilibrium, we can assign x to the concentration of H⁺ and [₃O²⁻] = [H₃O⁺] - x. Plugging in values, we get: 4.86 × 10⁻⁹ = x(3.9 × 10⁻¹⁵)/(3.9 × 10⁻¹⁵ - x) Solving for x using quadratic formula and using approximation, the pH is found to be 4.41. Therefore, the answer is B.

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