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, \(K_{w}\) (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) \(\left[\mathrm{H}^{+}\right]<[\mathrm{OH}]\) ?

Step-by-Step Solution

Answer

(a) The autoionization of water is represented by the equation: \[2 H_{2}O \rightleftharpoons H_{3}O^{+} + OH^{-}\] (b) The ion-product constant for water is expressed as: \[K_w = [H^{+}] [OH^{-}]\] (c) For a basic solution, the true statement is (iii) \(\left[\mathrm{H}^{+}\right]<[\mathrm{OH}]\).

Step 1: Part (a): Autoionization of Water

The autoionization of water is represented as the equilibrium reaction between water molecules, where two water molecules form a hydronium ion (H₃O⁺ or H⁺ in simpler notation) and a hydroxide ion (OH⁻). The equation is: \[2 H_{2}O \rightleftharpoons H_{3}O^{+} + OH^{-}\]

Step 2: Part (b): Ion-Product Constant for Water Expression and \(K_w\)

For any chemical equilibrium reaction, we can set up an equilibrium constant (K). In the case of water, we have an ion-product constant, \(K_w\), which is the equilibrium constant for the autoionization of water. The expression for \(K_w\) can be described as: \[K_w = [H^{+}] [OH^{-}]\] It is essential to remember that the concentrations of these ions are in moles per liter (mol/L). At 25°C, the ion-product constant for water is \(K_w = 1.0 \times 10^{-14}\).

Step 3: Part (c): Determining the True Statement for a Basic Solution

A solution is considered basic or alkaline if it has a greater concentration of hydroxide ions (OH⁻) than hydronium ions (H₃O⁺ or H⁺ for simplicity). Let's analyze the given options: (i) \(\left[\mathrm{H}^{+}\right]>\left[\mathrm{OH}^{-}\right]\) - This statement is representative of an acidic solution, where the concentration of H⁺ is greater than OH⁻. (ii) \(\left[\mathrm{H}^{+}\right]=\left[\mathrm{OH}^{-}\right]\) - This statement is representative of a neutral solution, where the concentrations of H⁺ and OH⁻ are equal. (iii) \(\left[\mathrm{H}^{+}\right]<[\mathrm{OH}]\) - This statement is representative of a basic solution, where the concentration of OH⁻ is greater than H⁺. For a basic solution, statement (iii) \(\left[\mathrm{H}^{+}\right]<[\mathrm{OH}]\) is true.

Key Concepts

Chemical Equilibrium

Chemical equilibrium is a dynamic state where the rate of the forward reaction equals the rate of the reverse reaction. This concept is crucial in reactions like the autoionization of water. When water dissociates into hydroxide ions (OH⁻) and hydronium ions (H₃O⁺), an equilibrium is established. This means that the formation of ions occurs at the same rate as their recombination into water molecules.
This balanced dynamic is depicted in the reaction: \[ 2 H_{2}O \rightleftharpoons H_{3}O^{+} + OH^{-} \] Understanding chemical equilibrium helps predict the concentrations of reactants and products in a reversible reaction.

• The equilibrium point does not mean that the reactants and products are equal in concentration but that their concentrations remain constant over time.
• This balance depends on factors like temperature and pressure.

Ion-Product Constant

The ion-product constant of water, denoted as \( K_w \), is a special equilibrium constant for the self-ionization of water. This constant is calculated from the concentrations of H⁺ and OH⁻ ions in the water. At 25°C, the value of \( K_w \) is \[ K_w = [H^{+}] [OH^{-}] = 1.0 \times 10^{-14} \] This tiny value shows that water is not very ionized, pointing to the low concentration of these ions under normal conditions.
Determining \( K_w \) is essential for understanding the nature of aqueous solutions. This constant provides a reference point for deciding whether a solution is acidic or basic, by comparing the concentrations of H⁺ and OH⁻.

• \( K_w \) helps in calculating pH and pOH values, which are measures of acidity and basicity.
• Changes in temperature can affect the \( K_w \) value, indicating a shift in the equilibrium between water, H⁺, and OH⁻ ions.

Basic Solution

A basic solution is one in which the concentration of hydroxide ions (OH⁻) exceeds that of hydrogen ions (H⁺). In simpler terms, there are more OH⁻ ions than H⁺ ions in a basic solution. This can be represented by the inequality: \( [\mathrm{H}^{+}]<[\mathrm{OH}^-] \)
This is derived from the neutral condition in pure water where \( [H^{+}] = [OH^{-}] = 1.0 \times 10^{-7} \). A basic solution presents a higher OH⁻ ion concentration than this neutral level.
To identify a basic solution:

• Check if the pH is greater than 7; this indicates basicity.
• The solution typically has a soapy feel and can turn red litmus paper blue.

Being able to recognize whether a solution is basic is important for many laboratory processes and chemical reactions.

Acidic Solution

An acidic solution has a higher concentration of hydrogen ions (H⁺) compared to hydroxide ions (OH⁻). In the context of the autoionization of water, an acidic solution shifts the equilibrium to produce more H⁺ ions. The inequality representing an acidic solution is:\( [\mathrm{H}^{+}]>[\mathrm{OH}^-] \)
In pure water, the concentrations of H⁺ and OH⁻ are equal, but in an acidic environment, the concentration of H⁺ exceeds \( 1.0 \times 10^{-7} \) mol/L.
To determine if a solution is acidic, consider these points:

• A pH less than 7 indicates an acidic solution.
• Acidic solutions often taste sour and can turn blue litmus paper red.

Understanding whether a solution is acidic aids in various chemical applications, from industrial processes to everyday life.