Question

(a) Write a chemical equation that illustrates the autoionization of water. (b) Write the expression for the ion-product constant for water, \(K_{\mathrm{t} u}\). 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?

Short answer

(a) The autoionization of water is represented by the chemical equation: \[2H_2O(l) \rightleftharpoons H_3O^+(aq) + OH^-(aq)\] (b) The ion-product constant for water, \(K_{tu}\), is given by: \[K_{tu} = [H_3O^+][OH^-]\] \([H_2 O]\) is absent from this expression because its concentration is considered constant. (c) A solution is basic when the concentration of hydroxide ions (\(OH^-\)) is greater than the concentration of hydronium ions (\(H_3 O^+\)), meaning the solution has a pH greater than 7.

Step-by-step solution

(a) Autoionization of Water

In the autoionization of water, water molecules react with each other to produce hydronium ions (H3O+) and hydroxide ions (OH-). The chemical equation for the autoionization of water is as follows: \[2H_2O(l) \rightleftharpoons H_3O^+(aq) + OH^-(aq)\]

(b) Ion-product Constant for Water

The ion-product constant for water (\(K_{tu}\)) is the equilibrium constant for the autoionization reaction. The expression for the ion-product constant for water can be represented as: \[K_{tu} = [H_3O^+][OH^-]\] The concentration of the water molecule, \([H_2 O]\), is not included in this expression because water is the solvent and its concentration is considered constant throughout the reaction.

(c) Basic Solution

A solution is described as basic when the concentration of hydroxide ions (\(OH^-\)) in the solution is greater than the concentration of hydronium ions (\(H_3 O^+\)). In other words, a basic solution has a pH greater than 7.

Key concepts

Ion-product constant

The ion-product constant for water, often represented as \(K_w\), is a crucial element in understanding the behavior of water and aqueous solutions. It is defined in the context of the equilibrium that exists in the autoionization of water, where water molecules react with each other to form hydronium (\(H_3O^+\)) and hydroxide (\(OH^-\)) ions. The equilibrium constant for this reaction is expressed as:

\[K_w = [H_3O^+][OH^-]\].

Here are a few key points to note:

• \(K_w\) is temperature-dependent; at 25°C, \(K_w\) is approximately \(1.0 \times 10^{-14}\).
• The reason \([H_2O]\) does not appear in this expression is because it is the solvent, meaning its concentration is extremely large and changes negligibly, thus considered constant.
• \(K_w\) combines the concentration products of both \(H_3O^+\) and \(OH^-\), painting a picture of a balanced chemical system at equilibrium.

Understanding \(K_w\) is fundamental when predicting how acids and bases will behave when dissolved in water.

Hydronium and hydroxide ions

In aqueous solutions, hydronium (\(H_3O^+\)) and hydroxide (\(OH^-\)) ions are the principal players in determining the solution's acidity or basicity. During the autoionization of water, two water molecules exchange protons:

\[2H_2O(l) \rightleftharpoons H_3O^+(aq) + OH^-(aq)\].

Here’s how they function:

• Hydronium ions (\(H_3O^+\)): These ions form when a water molecule accepts an extra hydrogen ion. They characterize acidic solutions, which have a higher concentration of hydronium ions than hydroxide ions.
• Hydroxide ions (\(OH^-\)): These ions result from the loss of a hydrogen ion from a water molecule. They dominate in basic solutions, where hydroxide ions outnumber hydronium ions.

The delicate balance between \(H_3O^+\) and \(OH^-\) concentrations is what determines if a solution is acidic, neutral, or basic. In a neutral solution, these concentrations are equal, aligning with the ion-product constant \(K_w\).

Basic solutions

A solution is termed "basic" when it features a greater concentration of hydroxide ions (\(OH^-\)) compared to hydronium ions (\(H_3O^+\)). This scenario typically corresponds to a pH value greater than 7.

Here's what you need to know about basic solutions:

• Basic solutions, or alkaline solutions, result from substances like sodium hydroxide (NaOH) dissolving in water, increasing the \(OH^-\) concentration.
• If \([OH^-] > [H_3O^+]\), the solution's pH reflects its basic nature. This relation is rooted in the inverted relationship between these ions within the ion-product constant \(K_w = [H_3O^+][OH^-]\).
• Common indicators of basic solutions include a slippery feel and the ability to turn red litmus paper blue.

Whether in everyday materials such as cleaning agents or biological systems maintaining pH balance, basic solutions play numerous vital roles.