Problem 28 - Chemistry The Central Science

Question

(a) Write a chemical equation that illustrates the autoionization of water. (b) Write the expression for the ion-product constant for water, \(K_{w}\). Why is \(\left[\mathrm{H}_{2} \mathrm{O}\right]\) absent from this expression? (c) A solution is described as basic. What does this statement mean?

Step-by-Step Solution

Answer

(a) The chemical equation for the autoionization of water is: \(\mathrm{H_2O} + \mathrm{H_2O} \rightleftharpoons \mathrm{H_3O^+} + \mathrm{OH^-}\). (b) The ion-product constant for water, \(K_w\), is given by: \(K_w = [\mathrm{H_3O^+}][\mathrm{OH^-}]\). The concentration of water, \([\mathrm{H_2O}]\), is not included in the expression because it is a liquid. (c) A solution is basic if its pH is greater than 7, meaning the concentration of hydroxide ions (\(\mathrm{OH^-}\)) is greater than the concentration of hydronium ions (\(\mathrm{H_3O^+}\)).

Step 1: (a) Autoionization of Water Chemical Equation

In the autoionization of water, two water molecules react to form a hydronium ion (\(\mathrm{H_3O^+}\)) and a hydroxide ion (\(\mathrm{OH^-}\)). The chemical equation for this process is: \[ \mathrm{H_2O} + \mathrm{H_2O} \rightleftharpoons \mathrm{H_3O^+} + \mathrm{OH^-} \]

Step 2: (b) Ion-Product Constant for Water

The ion-product constant for water (\(K_w\)) is the equilibrium constant for the autoionization of water. This constant helps us understand the relationship between the concentration of hydronium ions, \([\mathrm{H_3O^+}]\), and hydroxide ions, \([\mathrm{OH^-}]\), in water. The expression for \(K_w\) is: \[ K_w = [\mathrm{H_3O^+}][\mathrm{OH^-}] \] Since water is a liquid, its concentration is not included in the equilibrium constant expression.

Step 3: (c) Basic Solution Definition

A solution is described as basic if it has a pH greater than 7. This means that the concentration of hydroxide ions (\(\mathrm{OH^-}\)) in the solution is greater than the concentration of hydronium ions (\(\mathrm{H_3O^+}\)). In a basic solution, \(K_w\) remains unchanged; however, the ratio of hydroxide ions to hydronium ions shifts in favor of hydroxide ions.

Key Concepts

Chemical Equilibrium

Chemical equilibrium is a fundamental concept in chemistry, referring to a state in which reactants and products of a chemical reaction exist at constant levels. This state occurs when the rate of the forward reaction equals the rate of the backward reaction. In the case of the autoionization of water, a constant dynamic equilibrium is established.
The chemical equilibrium for autoionization can be represented by the equation:

• \( \mathrm{2H_2O} \rightleftharpoons \mathrm{H_3O^+} + \mathrm{OH^-} \)

This means that water continuously dissociates into hydronium and hydroxide ions while simultaneously recombining back into water molecules. The concentrations of these species remain constant as long as the system is undisturbed, exemplifying chemical equilibrium.
In equilibrium, small changes in conditions, such as temperature or pressure, can shift the balance, illustrating the dynamic nature of chemical reactions. Understanding this helps in predicting how changes might affect ion concentrations in water.

Ion-Product Constant

The ion-product constant, symbolized as \(K_w\), is a special equilibrium constant that applies to the autoionization of water. It reflects the concentrations of hydronium and hydroxide ions in pure water or aqueous solutions.
The equation representing this relationship is:

• \( K_w = [\mathrm{H_3O^+}][\mathrm{OH^-}] \)

In pure water at 25°C, \(K_w\) is approximately \(1.0 \times 10^{-14}\) mol²/L². This constant value indicates the relationship between ions in water, irrespective of external influences such as the purity of water or presence of solutes.
The reason \([\mathrm{H_2O}]\) is not part of the expression for \(K_w\) is because it is a pure liquid. Pure liquids and solids do not appear in equilibrium constant expressions since their concentrations are constant and negligible compared to the concentrations of gases or solutions.

pH Scale

The pH scale is an essential tool in understanding acidity and basicity of solutions. It represents how acidic or basic a solution is based on the concentration of hydronium ions.
The equation linking pH with the concentration of hydronium ions is:

• \( \text{pH} = -\log[\mathrm{H_3O^+}] \)

A solution is considered acidic if its pH is less than 7, and basic if its pH is greater than 7. A neutral solution, like pure water, has a pH of exactly 7.
In basic solutions, the concentration of hydroxide ions \([\mathrm{OH^-}]\) exceeds that of hydronium ions \([\mathrm{H_3O^+}]\). Despite this shift, the product of these ion concentrations remains constant at the ion-product constant \(K_w\). Knowing the pH can help predict how a solution will interact chemically and the potential impact on chemical reactions involved.