Problem 28 - Chemistry: The Central Science in SI Units, Global Edition

Question

(a) Write a chemical equation that illustrates the autoionization of water. (b) Write the expression for the ionproduct constant for water, \(K_{w} .(\mathbf{c})\) If a solution is described as basic, which of the following is true: (i) \(\left[\mathrm{H}^{+}\right]>\left[\mathrm{OH}^{-}\right]\), (ii) \(\left[\mathrm{H}^{+}\right]=\left[\mathrm{OH}^{-}\right],\) or (iii) \(\left[\mathrm{H}^{+}\right]<\left[\mathrm{OH}^{-}\right] ?\)

Step-by-Step Solution

Answer

(a) The chemical equation for the autoionization of water is: \[ H_2O \rightleftharpoons H^+ + OH^- \] (b) The expression for the ion product constant for water, \(K_w\), is: \[ K_w = [H^+][OH^-] \] (c) For a basic solution, the following condition is true: (iii) \([H^+] < [OH^-]\).

Step 1: A chemical equation representing autoionization of water

Autoionization of water involves the self-ionization of water molecules into hydronium ions (H+) or protons and hydroxide ions (OH-). The chemical equation can be written as follows: \[ 2H_2O \rightleftharpoons H_3O^+ + OH^- \] Or we can more simply write: \[ H_2O \rightleftharpoons H^+ + OH^- \] In both cases, it depicts the autoionization of water. #b) Writing the expression for the ion product constant for water#

Step 2: Ion product constant expression

The ion product constant for water, denoted as \(K_w\), is the equilibrium constant for the autoionization of water. It is the product of the equilibrium concentrations of H+ ions and OH- ions in water. The expression can be written as: \[ K_w = [H^+][OH^-] \] #c) Identifying the true condition for a basic solution#

Step 3: True condition for a basic solution

A basic solution is characterized by a higher concentration of hydroxide ions (OH-) compared to hydronium ions (H+). Hence, we compare the given options (i), (ii), and (iii) to determine which condition is true for a basic solution: (i) \([H^+] > [OH^-]\): This is true for an acidic solution, not basic. (ii) \([H^+] = [OH^-]\): This is true for a neutral solution, not basic. (iii) \([H^+] < [OH^-]\): This is true for a basic solution, as it indicates the concentration of hydroxide ions is greater than the concentration of hydronium ions. Therefore, option (iii) \([H^+] < [OH^-]\) is true for a basic solution.

Key Concepts

Ion Product Constant

The ion product constant of water, symbolized as \(K_w\), is a pivotal concept in understanding chemical equilibrium in aqueous solutions. It signifies the equilibrium constant for the autoionization of water, which is essentially the self-ionization process.
Here, water naturally forms ions by dissociating into hydronium ions \((H^+)\) and hydroxide ions \( (OH^-) \). The chemical representation of this is a dynamic equilibrium, meaning the forward and reverse reactions occur simultaneously:

• Balanced Equation: \( H_2O \rightleftharpoons H^+ + OH^- \)

The ion product constant is derived from the concentrations of these ions when water is in equilibrium. This can be mathematically expressed as:
- \[ K_w = [H^+][OH^-] \]
In pure water at 25°C, \(K_w\) is constantly around \(1.0 \times 10^{-14}\) \((mol^2/dm^6)\). This value demonstrates that even in neutral solutions, water maintains a consistent level of ionization, crucial for predicting reactions in chemistry.

Basic Solution

A basic or alkaline solution is defined by its distinct concentration of ions. In such solutions, the concentration of hydroxide ions \((OH^-)\) surpasses that of hydronium ions \((H^+)\). This imbalance leads to a solution's basic nature and is a core concept in acid-base chemistry.
To ascertain if a solution is basic, analyze the relationship of \([H^+]\) vs. \([OH^-]\):

• If \([H^+] < [OH^-]\), the solution is basic.
• In contrast, if \([H^+] > [OH^-]\), it is acidic.
• When \([H^+] = [OH^-]\), neutrality is achieved.

Essentially, the presence of more \(OH^-\) ions shifts the pH above the neutral value of 7, characteristically marking basic solutions. Understanding this relationship helps explain how solutions like household ammonia or baking soda demonstrate basic properties.

Chemical Equilibrium

Chemical equilibrium serves as the foundation for interpreting the interactions in autoionization and other chemical reactions. It is a state at which the rates of the forward and reverse reactions are equal, maintaining a stable concentration of reactants and products over time.
In the context of water's autoionization:

• The equation can be represented as \( H_2O \rightleftharpoons H^+ + OH^- \).
• At equilibrium, both the creation and recombination of ions occur at an equal rate.

Chemical equilibrium is influenced by several factors, including temperature, concentration, and pressure in other contexts, but for aqueous solutions like water, \(K_w\) plays a pivotal role. Equilibrium is central to predicting the behavior of chemical systems, enabling the calculation of concentrations and understanding the nature of solutions, whether they are acidic, neutral, or basic.