Question

Indicate each of the following for the ionization of pure water: (a) the molecular collision equation (b) the molar hydrogen ion concentration at \(25^{\circ} \mathrm{C}\) (c) the molar hydroxide ion concentration at \(25^{\circ} \mathrm{C}\)

Short answer

(a) \(\text{H}_2\text{O} \rightleftharpoons \text{H}^+ + \text{OH}^-\) (b) \([\text{H}^+ ] = 1.0 \times 10^{-7}\ \text{mol/L}\) (c) \([\text{OH}^-] = 1.0 \times 10^{-7}\ \text{mol/L}\)

Step-by-step solution

Write the Molecular Collision Equation

In pure water, water molecules can collide and undergo ionization to form hydronium (\(\text{H}_3\text{O}^+\)) and hydroxide ions (\(\text{OH}^-\)). This process can be represented by the following equilibrium equation: \[ \text{H}_2\text{O} + \text{H}_2\text{O} \rightleftharpoons \text{H}_3\text{O}^+ + \text{OH}^- \] For simplicity, it's often written as: \[ \text{H}_2\text{O} \rightleftharpoons \text{H}^+ + \text{OH}^- \] This shows that water can undergo autoionization to form hydrogen ions and hydroxide ions, maintaining a balance in pure water.

Calculate Molar Hydrogen Ion Concentration

At \(25^{\circ} \text{C}\), the concentration of hydrogen ions in pure water is known to be determined by the ion product of water, \(K_w\), which is equal to \(1.0 \times 10^{-14}\) at this temperature. In pure water, \([\text{H}^+ ] = [\text{OH}^-]\). Therefore, \([\text{H}^+ ] = \sqrt{1.0 \times 10^{-14}} = 1.0 \times 10^{-7}\ \text{mol/L}\).

Determine Molar Hydroxide Ion Concentration

Using the equilibrium in Step 1 and the relation \([\text{H}^+ ] = [\text{OH}^- ]\) in neutral water, the molar hydroxide ion concentration is also \(1.0 \times 10^{-7}\ \text{mol/L}\) at \(25^{\circ} \text{C}\).

Key concepts

Molecular Collision Equation

The ionization of water is a fascinating natural process where water molecules interact intensely. It all begins with something called the molecular collision equation. Imagine water molecules bumping into each other like in a microscopic dance party. During these collisions, they have the potential to break apart into two different ions. In this instance, two water molecules collide, and the result is the formation of hydronium (\( \text{H}_3\text{O}^+ \) ) and hydroxide (\( \text{OH}^- \) ) ions.

To keep it simple, chemists often represent this process as: \[ \text{H}_2\text{O} \rightleftharpoons \text{H}^+ + \text{OH}^- \] This implies that water has a built-in ability to create hydrogen ions and hydroxide ions all by itself. This balance is crucial, as the number of each of these ions determine the acidic or basic nature of the water.

Hydrogen Ion Concentration

At room temperature, specifically at \(25^{\circ} \text{C}\) , the concentration of hydrogen ions in pure water is a carefully balanced affair. This concentration is determined through something known as the ion product of water, \( K_w \) . At this temperature, \( K_w \) is equal to \( 1.0 \times 10^{-14} \) , and plays a vital role in keeping the water neutral.

In pure water, the concentration of hydrogen ions \([\text{H}^+ ]\) is equal to the concentration of hydroxide ions because they are produced in equal amounts during the ionization process. Hence, \([\text{H}^+ ] = [\text{OH}^- ]\) . Using the equation \( [\text{H}^+ ] = \sqrt{1.0 \times 10^{-14}} \), we find that the molar hydrogen ion concentration is \( 1.0 \times 10^{-7} \ \text{mol/L} \). This delicate balance demonstrates the autoionization capacity of water, highlighting its fascinating neutral nature at this common temperature.

Hydroxide Ion Concentration

The story of hydroxide ion concentration is intricately connected to that of hydrogen ions. In pure water, and under neutral conditions at\(25^{\circ} \text{C} \), the number of hydroxide ions \([\text{OH}^-]\) equals the number of hydrogen ions. This concept is foundational to understanding the neutrality of water.

Using the equilibrium equation provided in the molecular collision context, we know that the concentration of \(\text{OH}^-\) ions matches thedetermined concentration of \(\text{H}^+\) ions for water. Given from the self-ionization process,\([\text{H}^+ ] = [\text{OH}^- ]\), this makes the \(\text{OH}^-\) ion concentration also \(1.0 \times 10^{-7} \ \text{mol/L} \). This reflects the balance achieved, making water a neutral entity unless influenced by other substances.

Ion Product of Water

The concept of the ion product of water is a cornerstone in understanding the chemistry of water. Represented by the symbol\(K_w\)\,it refers to the equilibrium constant for the self-ionization of water. It encompasses the product of the hydrogen ion concentration and the hydroxide ion concentration in water.

The formula is simple yet profound: \[ K_w = [\text{H}^+] \, [\text{OH}^-] \]
The constant\(K_w\)at\(25^{\circ} \text{C} \)is\(1.0 \times 10^{-14}\).This means that in a neutral environment, such as pure water, the product of the molar concentrations of hydronium and hydroxide ions is always this constant value.

• The self-ionization of water is essential for processes that define the acidity or basicity of solutions.
• Any deviation in these concentrations, induced by other substances, results in either acidic or basic solutions.

The constancy of\(K_w\)ensures predictability, a characteristic that is crucial in reactions involving aqueous solutions.