The value of K_w increases with increasing temperature. Is the autoionization of water endothermic or exothermic?

Verified step by step guidance

1. Understand that the autoionization of water is represented by the equation: \( \text{H}_2\text{O} (l) \rightleftharpoons \text{H}^+ (aq) + \text{OH}^- (aq) \).
2. Recall that \( K_w \) is the equilibrium constant for the autoionization of water, and it is given by \( K_w = [\text{H}^+][\text{OH}^-] \).
3. Recognize that an increase in \( K_w \) with temperature suggests that the equilibrium shifts to the right, favoring the formation of \( \text{H}^+ \) and \( \text{OH}^- \).
4. Apply Le Chatelier's principle, which states that if a system at equilibrium is subjected to a change in temperature, the system will adjust to counteract that change. An increase in temperature favors the endothermic direction.
5. Conclude that since the equilibrium shifts to the right with increasing temperature, the autoionization of water is endothermic.

Key Concepts

Autoionization of Water

The autoionization of water refers to the process where two water molecules react to form a hydronium ion (H3O+) and a hydroxide ion (OH-). This reaction is represented by the equilibrium expression: 2 H2O ⇌ H3O+ + OH-. At 25°C, the ion product constant of water (Kw) is 1.0 x 10^-14, but this value changes with temperature, indicating the dynamic nature of this equilibrium.

Endothermic vs. Exothermic Reactions

Endothermic reactions absorb heat from their surroundings, resulting in a decrease in temperature of the environment, while exothermic reactions release heat, increasing the temperature. The classification of a reaction as endothermic or exothermic is determined by the change in enthalpy (ΔH). If ΔH is positive, the reaction is endothermic; if negative, it is exothermic.

Temperature Dependence of Kw

The value of Kw, the ion product of water, is temperature-dependent. As temperature increases, Kw also increases, indicating that the equilibrium shifts to favor the formation of H3O+ and OH- ions. This shift suggests that the autoionization of water absorbs heat, thus classifying it as an endothermic process, as higher temperatures promote the reaction.