Question

Autoionization of Water and pH The value of \(K_{\mathrm{w}}\) increases with increasing temperature. Is the autoionization of water endothermic or exothermic?

Short answer

The autoionization of water is endothermic because the equilibrium constant for water, \(K_{\text{w}}\), increases with increasing temperature, indicating heat absorption.

Step-by-step solution

Understand Autoionization of Water

Autoionization of water refers to the chemical reaction where two water molecules react to produce a hydronium ion (\( \text{H}_3\text{O}^+ \)) and a hydroxide ion (\( \text{OH}^- \)). The reaction is as follows: \(2 \text{H}_2\text{O}(l) \rightleftharpoons \text{H}_3\text{O}^+(aq) + \text{OH}^-(aq)\). The equilibrium constant for this reaction is the ionic product of water, \( K_{\text{w}} \).

Relate Change in Equilibrium Constant to Heat Absorption or Release

Le Chatelier's Principle states that if an external condition is changed, the equilibrium will shift to counteract the change. For temperature, if the equilibrium constant increases as temperature increases, it suggests that the forward reaction absorbs heat since the system is shifting to absorb the additional thermal energy. Therefore, the reaction is endothermic.

Determine the Nature of Autoionization

Because the value of \(K_{\text{w}}\) increases with increasing temperature, it indicates that the autoionization of water absorbs heat (it requires heat to proceed). Hence, the autoionization of water is endothermic.

Key concepts

Understanding pH

The concept of pH is profoundly linked to the understanding of acidity and basicity in aqueous solutions. pH is a measure that expresses the acidity or alkalinity of a solution on a logarithmic scale. On the pH scale, which ranges from 0 to 14, a pH value of 7 indicates a neutral solution, such as pure water. Values below 7 signal acidic conditions, while values above 7 denote basic or alkaline conditions.

The pH is calculated using the formula: \( pH = -\text{log}[H_3O^+] \), where \( [H_3O^+] \) represents the concentration of hydronium ions in the solution. The autoionization of water, which forms hydronium and hydroxide ions, directly affects the pH of water. Understanding pH is essential in many fields, from biochemistry to environmental science, as it affects chemical solubility, biological function, and the behavior of pollutants.

Endothermic and Exothermic Reactions

Chemical reactions can be classified based on thermal energy exchange with their surroundings: endothermic and exothermic reactions are two pivotal types. Endothermic reactions absorb heat from the environment, resulting in a cooling effect. On the contrary, exothermic reactions release heat, leading to a warming effect.

When considering autoionization, the increase in the equilibrium constant \(K_{w}\) with temperature indicates that the process absorbs heat from its surroundings, making it an endothermic reaction. This heat absorption is necessary for the reaction to proceed and is a critical consideration in chemical thermodynamics, affecting reaction rates and equilibrium.

Ionic Product of Water

The ionic product of water, denoted by \(K_{w}\), is an essential concept in acid-base chemistry. It represents the equilibrium constant for the autoionization of water, which can be expressed with the equation: \(K_{w} = [H_3O^+][OH^-]\), where \([H_3O^+]\) and \([OH^-]\) are the molar concentrations of the hydronium and hydroxide ions, respectively. At 25°C, the value of \(K_{w}\) is approximately \(1.0 \times 10^{-14}\).

The stability of \(K_{w}\) across different temperatures is fundamental to understanding pH variations and the behavior of aqueous solutions. As temperature rises, \(K_{w}\) increases, suggesting an imbalance that leads to a higher concentration of hydronium and hydroxide ions, each affecting the pH.

Le Chatelier's Principle

Le Chatelier's Principle is a cornerstone in chemical equilibrium. It describes how the equilibrium position shifts when a change in concentration, pressure, volume, or temperature occurs. According to this principle, the system will adjust to partially counteract the change imposed on it.

In the context of the autoionization of water, an increase in temperature results in a higher value of \(K_{w}\), indicating a shift in equilibrium towards the products of the reaction (hydronium and hydroxide ions). This shift is the system's response to maintain equilibrium, a vivid demonstration of Le Chatelier's Principle. This principle helps us predict how alterations in external conditions will affect the position of equilibrium in chemical processes, playing a crucial role in everything from industrial synthesis to biological systems.