At 25°C, a chemist prepares an aqueous solution where the hydrogen ion concentration, [H⁺], is measured to be 1.0 × 10⁻⁶ M and the hydroxide ion concentration, [OH⁻], is 1.0 × 10⁻⁹ M. Given that the ion-product constant for water, Kw, is 1.0 × 10⁻¹⁴ at this temperature, what is the reaction quotient (Q) for the autoionization of water in this solution, and how does it compare to Kw?
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The answer
Correct answer: B. The reaction quotient Q is 1.0 × 10⁻¹⁵, which is less than Kw, indicating the reaction will proceed to the right.
Tested concept: Reaction quotient (Q)
Explanation
The autoionization of water is represented by the equilibrium H₂O(l) ⇌ H⁺(aq) + OH⁻(aq). The reaction quotient, Q, for this reaction is calculated as Q = [H⁺][OH⁻]. Given [H⁺] = 1.0 × 10⁻⁶ M and [OH⁻] = 1.0 × 10⁻⁹ M, Q = (1.0 × 10⁻⁶ M)(1.0 × 10⁻⁹ M) = 1.0 × 10⁻¹⁵. The ion-product constant for water, Kw, is 1.0 × 10⁻¹⁴ at 25°C. Comparing Q to Kw, we find that 1.0 × 10⁻¹⁵ < 1.0 × 10⁻¹⁴, meaning Q < Kw. When Q < K, the reaction will proceed in the forward direction (to the right) to reach equilibrium, producing more products (H⁺ and OH⁻).
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