Question

Write the equilibrium expression for the autoionization of water and an equation relating \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\) in solution at \(25^{\circ} \mathrm{C}\).

Short answer

\( K_w = [\text{H}_3\text{O}^+][\text{OH}^-] = 1.0 \times 10^{-14} \) at \( 25^{\circ} \text{C} \).

Step-by-step solution

Understanding Autoionization of Water

Autoionization of water is a process where water molecules donate and accept protons from each other. The equation for this process is \( 2\text{H}_2\text{O}(l) \rightleftharpoons \text{H}_3\text{O}^+(aq) + \text{OH}^-(aq) \).

Writing the Equilibrium Expression

For the equilibrium reaction, the equilibrium expression is \( K_w = [\text{H}_3\text{O}^+][\text{OH}^-] \). This is known as the water dissociation constant.

Autoionization Constant at Standard Conditions

At \( 25^{\circ} \text{C} \), the value of \( K_w \) is \( 1.0 \times 10^{-14} \). Therefore, the equation \( [\text{H}_3\text{O}^+][\text{OH}^-] = 1.0 \times 10^{-14} \) holds true at this temperature.

Key concepts

Equilibrium Expression

The equilibrium expression is a mathematical equation that describes the balance of reactions and products in a chemical equilibrium. This concept is essential in understanding the autoionization of water. Here, water molecules dissociate into ions in a dynamic equilibrium. In the case of water, the equation is:\[ 2\text{H}_2\text{O}(l) \rightleftharpoons \text{H}_3\text{O}^+(aq) + \text{OH}^-(aq) \] For this reaction, the equilibrium expression is:\[ K_w = [\text{H}_3\text{O}^+][\text{OH}^-] \] The equilibrium constant for water's ionization, \( K_w \), represents how far the dissociation reaction proceeds to the right under given conditions.
It quantifies concentrations of hydronium ions and hydroxide ions when the reaction is at equilibrium.

Water Dissociation Constant

The water dissociation constant, often referred to as \( K_w \), is a fundamental concept when discussing the ionization of water. This constant gives us insights into the extent to which water naturally breaks down into hydronium and hydroxide ions at a particular temperature.At the standard temperature of \( 25^{\circ} \text{C} \), the value of \( K_w \) is \( 1.0 \times 10^{-14} \). This means at this temperature, the product of the concentrations of \( \text{H}_3\text{O}^+ \) and \( \text{OH}^- \) ions in pure water is always equal to \( 1.0 \times 10^{-14} \).This constant value is crucial for calculating ion concentrations in aqueous solutions and helps us understand the nature of acidic or basic solutions.

• \( K_w \) at \( 25^{\circ} \text{C} \) = \( 1.0 \times 10^{-14} \)
• Indicates equilibrium between hydronium and hydroxide ions
• Basis for pH and pOH calculations

Hydronium Ion Concentration

The hydronium ion concentration, denoted as \([\text{H}_3\text{O}^+]\), represents the amount of hydronium ions in a solution. It is a critical factor in determining the acidity of a solution. Higher concentrations of hydronium ions mean a more acidic solution. In pure water at equilibrium, the concentration of hydronium ions is the same as that of hydroxide ions due to the nature of the reaction:\[ [\text{H}_3\text{O}^+][\text{OH}^-] = K_w \]When acidity increases, \([\text{H}_3\text{O}^+]\) goes up, leading to a decrease in \([\text{OH}^-]\) according to the \( K_w \) constant. The hydronium ion concentration is directly used to calculate the pH of the solution through the relation:\[ \text{pH} = -\log[\text{H}_3\text{O}^+] \]Thus, knowing the hydronium ion concentration is essential to understanding the solution's acidic characteristics.

Hydroxide Ion Concentration

Hydroxide ion concentration \([\text{OH}^-]\) is the measure of hydroxide ions present in a solution. It reflects the basic nature of a solution. When the equilibrium for water is considered, \([\text{OH}^-]\) reflects the solution's tendency towards basicity.In a neutral solution like pure water, when \( 25^{\circ} \text{C} \) alkali is maintained, \([\text{OH}^-]\) is equal to \([\text{H}_3\text{O}^+]\) based on the equilibrium:\[ [\text{H}_3\text{O}^+][\text{OH}^-] = K_w \]For alkaline solutions, hydroxide ion concentration surpasses hydronium ion concentration, reducing the acidity. Just like hydronium ions influence acid properties, hydroxide ions give insight into the basicity.Additionally,Hydroxide ion concentration is pivotal in determining pOH:\[ \text{pOH} = -\log[\text{OH}^-] \]Understanding \([\text{OH}^-]\) helps in grasping the complete nature of the solution's pH balance.