Ionic product of water

Ionic Product of Water: Definition, Explanation & Mathematical Derivation

Water is a very weak electrolyte and undergoes self-ionization to a small extent. This phenomenon leads to the formation of hydrogen ions (H⁺) and hydroxide ions (OH⁻) in pure water. The product of their concentrations at equilibrium is known as the ionic product of water.

Definition

The ionic product of water, represented as K_w, is the product of the molar concentrations of hydrogen ions [H⁺] and hydroxide ions [OH⁻] in water at a particular temperature.

Mathematically,
K_w = [H⁺][OH⁻]

Self-Ionization of Water

Water molecules react with each other in a reversible reaction as follows:

    H₂O (l) + H₂O (l) ⇌ H₃O⁺ (aq) + OH⁻ (aq)
    or simplified as:
    H₂O (l) ⇌ H⁺ (aq) + OH⁻ (aq)
  

Based on the principles of chemical equilibrium, the expression for the equilibrium constant (K_eq) becomes:

    K = [H⁺][OH⁻] / [H₂O]
  

Since the concentration of water is very large and remains nearly constant, it is combined with K to give a new constant:

    K × [H₂O] = Kw = [H⁺][OH⁻]
  

Value of K_w at 25°C

At 25°C (298 K), the value of ionic product of water is:

    Kw = 1.0 × 10−14 mol²·L−2
  

In pure water, [H⁺] = [OH⁻], so:
[H⁺] = √(K_w) = √(1.0 × 10⁻¹⁴) = 1.0 × 10⁻⁷ mol/L

Thus, the pH is calculated as –log[H⁺] = 7, indicating a neutral solution.

Effect of Temperature

The value of K_w increases with temperature. This means both [H⁺] and [OH⁻] increase as temperature rises, though water remains neutral as long as [H⁺] = [OH⁻].

• K_w is the equilibrium constant for the self-ionization of water.
• At 25°C, K_w = 1.0 × 10⁻¹⁴ mol²·L⁻².
• It helps in calculating pH and understanding acid-base behavior in aqueous solutions.
• K_w is temperature dependent and increases with heat.