Problem 30 - 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: \(2\,\mathrm{H_2 O} \rightleftharpoons \mathrm{H_3 O^+} + \mathrm{OH^-}\). (b) The ion-product constant for water, \(K_w\), is given by: \(K_w = [\mathrm{H_3 O^+}][\mathrm{OH^-}]\). The concentration of water, \(\left[\mathrm{H}_{2} \mathrm{O}\right]\), is absent from this expression because it remains virtually constant during autoionization, and its change is negligible compared to the concentrations of hydronium and hydroxide ions. (c) A solution is described as basic if it has a pH greater than 7, meaning it has a higher concentration of hydroxide ions (\(\mathrm{OH^-}\)) than hydronium ions (\(\mathrm{H_3 O^+}\)). Basic solutions have the ability to neutralize acidic solutions.

Step 1: (a) Chemical equation for autoionization of water

The autoionization of water is the process by which two water molecules react to produce one hydronium ion (\(\mathrm{H_3 O^+}\)) and one hydroxide ion (\(\mathrm{OH^-}\)). The chemical equation for this process is: \[2\,\mathrm{H_2 O} \rightleftharpoons \mathrm{H_3 O^+} + \mathrm{OH^-}\]

Step 2: (b) Expression for ion-product constant for water, \(K_w\)

The ion-product constant for water, \(K_w\), is the equilibrium constant for the autoionization reaction. It is given by the product of the concentrations of the hydronium and hydroxide ions at equilibrium, i.e., \[K_w = [\mathrm{H_3 O^+}][\mathrm{OH^-}]\] The concentration of water, \(\left[\mathrm{H}_{2} \mathrm{O}\right]\), is not included in the expression for \(K_w\) because it remains virtually constant during the autoionization process. Due to its high concentration (around 55.5 M), the change in the concentration of water is negligible compared to the concentrations of hydronium and hydroxide ions produced during autoionization.

Step 3: (c) Basic solution

A solution is described as basic, or alkaline, if it has a pH greater than 7. In other words, a basic solution has a higher concentration of hydroxide ions (\(\mathrm{OH^-}\)) than hydronium ions (\(\mathrm{H_3 O^+}\)). In these solutions, the hydroxide ions react with hydronium ions to form water, reducing the acidity of the solution. The more basic a solution is, the higher its pH, and the greater its capacity to neutralize acidic solutions.