Self-Ionization of Water and the Ion Product Constant ($K_w$)

Self-Ionization of Water

Definition and Process

Water can react with itself in a process called self-ionization, where hydronium ions and hydroxide ions are produced. This process is fundamental in understanding the behavior of acids and bases in aqueous solutions.

• Amphoteric Nature of Water: Water is amphoteric, meaning it can act as both an acid (proton donor) and a base (proton acceptor).

• Self-Ionization Reaction:

$\mathrm{H_2O~(l) + H_2O~(l) \rightleftharpoons H_3O^+~(aq) + OH^-~(aq)}$

• This reaction is often simplified as:

$\mathrm{H_2O~(l) \rightleftharpoons H^+~(aq) + OH^-~(aq)}$

Ion Product Constant for Water ($K_w$)

The equilibrium constant for the self-ionization of water is called the ion product constant ($K_w$). It is defined as:

$K_w = [H^+][OH^-]$

• At 25°C, $K_w$ is a constant value, but it is temperature dependent.

• As temperature increases, $K_w$ also increases.

Temperature Dependence of $K_w$

The value of $K_w$ changes with temperature, as shown in the table below:

Temperature (°C)	$K_w$
0	1.14 × 10-15
25	1.00 × 10-14
50	2.93 × 10-14
75	5.476 × 10-14
100	5.13 × 10-13

Purpose: This table shows how the ion product constant for water increases as temperature rises.

Calculating Ion Concentrations

For a neutral solution at a given temperature, the concentrations of hydronium ions ($[H_3O^+]$) and hydroxide ions ($[OH^-]$) are equal. To find their concentrations:

• Use the equation $K_w = [H^+][OH^-]$

• For neutral water: $[H^+] = [OH^-] = \sqrt{K_w}$

Example: At 25°C, $K_w = 1.00 \times 10^{-14}$

$[H^+] = [OH^-] = \sqrt{1.00 \times 10^{-14}} = 1.00 \times 10^{-7}~\mathrm{M}$

At 50°C, $K_w = 2.93 \times 10^{-14}$

$[H^+] = [OH^-] = \sqrt{2.93 \times 10^{-14}} \approx 1.71 \times 10^{-7}~\mathrm{M}$

Key Terms

• Self-ionization: The process by which water molecules produce hydronium and hydroxide ions.

• Amphoteric: A substance that can act as both an acid and a base.

• Ion product constant ($K_w$): The equilibrium constant for the self-ionization of water.

Summary Table: $K_w$ Values at Different Temperatures

Temperature (°C)	$K_w$
0	1.14 × 10-15
25	1.00 × 10-14
50	2.93 × 10-14
75	5.476 × 10-14
100	5.13 × 10-13

Additional info: The concept of $K_w$ is essential for understanding pH, acid-base equilibria, and the behavior of aqueous solutions in GOB Chemistry.