At 50 °C, the ion-product constant for H2O has the value Kw = 5.48 * 10-14. (a) What is the pH of pure water at 50 °C? (b) Based on the change in Kw with temperature, predict whether ΔH is positive, negative, or zero for the autoionization reaction of water: 2 H2O1l2 Δ H3O+1aq2 + OH-1aq2

검증된 단계별 안내

Calculate the concentration of H3O+ and OH- ions in pure water at 50 °C using the ion-product constant (Kw). Since the water is pure, the concentrations of H3O+ and OH- are equal. Therefore, [H3O+] = [OH-] = \(\sqrt{Kw}\).

Use the concentration of H3O+ to find the pH of the water. pH is calculated using the formula pH = -\(\log\)[H3O+].

Understand the autoionization reaction of water: 2 H2O(l) ⇌ H3O+(aq) + OH-(aq). This reaction is endothermic, absorbing heat to proceed, which shifts the equilibrium towards the products when temperature increases.

Analyze the change in Kw with temperature. As temperature increases, Kw also increases, indicating more products (H3O+ and OH-) are formed.

Conclude the sign of ΔH for the autoionization of water. Since increasing temperature increases the ion-product constant, and the reaction shifts towards more product formation, ΔH is positive.

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주요 개념

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Ion-Product Constant of Water (Kw)

The ion-product constant of water (Kw) is the equilibrium constant for the autoionization of water, represented by the equation 2 H2O ⇌ H3O+ + OH-. At any given temperature, Kw is the product of the concentrations of hydronium ions [H3O+] and hydroxide ions [OH-]. For pure water, these concentrations are equal, allowing us to calculate the pH based on the value of Kw.

pH Scale

The pH scale is a logarithmic scale used to measure the acidity or basicity of a solution. It is defined as pH = -log[H3O+], where [H3O+] is the concentration of hydronium ions in moles per liter. In pure water, the pH is typically 7 at 25 °C, but this value changes with temperature due to variations in Kw, affecting the concentrations of H3O+ and OH-.

Temperature Dependence of Kw

The value of Kw changes with temperature, generally increasing as temperature rises. This is indicative of the endothermic nature of the autoionization reaction of water. If Kw increases with temperature, it suggests that the reaction absorbs heat, leading to a positive ΔH. Understanding this relationship helps predict how pH and ion concentrations will shift with temperature changes.