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)?
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.
Write the balanced chemical equation for the autoionization of water: \(2\ H_2O(l) \rightleftharpoons H_3O^+(aq) + OH^-(aq)\).
Express the equilibrium constant \(K_c\) for this reaction using the concentrations of the aqueous species and water: \(K_c = \frac{[H_3O^+][OH^-]}{[H_2O]^2}\).
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: \(K_w = [H_3O^+][OH^-]\).
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.