Which of the following correctly completes the autoionization reaction of water and provides the expressions for its equilibrium constant (K_c) and ion product (K_w)?

• A. H_2O(l) ightleftharpoons H_2(g) + O_2(g); K_c = \frac{[H_2][O_2]}{[H_2O]}; K_w = [H_2][O_2]
• B. 2 H_2O(l) ightleftharpoons H_3O^+(aq) + OH^-(aq); K_c = \frac{[H_3O^+][OH^-]}{[H_2O]^2}; K_w = [H_3O^+][OH^-]
• C. 2 H_2O(l) ightarrow H_2O_2(aq) + H_2(g); K_c = \frac{[H_2O_2][H_2]}{[H_2O]^2}; K_w = [H_2O_2][H_2]
• D. H_2O(l) ightleftharpoons H^+(aq) + OH^-(aq); K_c = \frac{[H^+][OH^-]}{[H_2O]}; K_w = [H^+][OH^-]

Answer: (B)

Verified step by step guidance

1. Identify the correct autoionization reaction of water. The autoionization involves water molecules reacting with each other to form hydronium ions (H_3O^+) and hydroxide ions (OH^-), not gases like H_2 or O_2.
2. Write the balanced chemical equation for the autoionization of water: \$2\ H_2O(l) \rightleftharpoons H_3O^+(aq) + OH^-(aq)$.
3. Express the equilibrium constant \(K_c\) for this reaction using the concentrations of the aqueous species and water: \(K_c = \frac{[H_3O^+][OH^-]}{[H_2O]^2}\).
4. Understand that the ion product constant of water, \(K_w\), is defined as the product of the concentrations of the hydronium and hydroxide ions at equilibrium: \(K_w = [H_3O^+][OH^-]\).
5. Note that because water is a pure liquid, its concentration is often treated as constant and incorporated into the equilibrium constant expression, simplifying \(K_c\) to \(K_w\) in many contexts.