Ionic Product of Water

The ionic product of water (K_w) is the equilibrium constant associated with the self-ionization of water. In this process, one water molecule acts as an acid and another water molecule acts as a base.

Water therefore undergoes a reversible acid-base reaction:

Self-ionization of water:
2H₂O(l) ⇌ H₃O⁺(aq) + OH⁻(aq)

The hydrogen ion (H⁺) is commonly used as a shorthand notation for H₃O⁺ in aqueous solutions.

Equilibrium Expression

For the self-ionization of water, the equilibrium constant can be written as:

K = \(\dfrac{[H_3O^+][OH^-]}{[H_2O]^2}\)

Since the concentration (more precisely, the activity) of liquid water is essentially constant, it is incorporated into the equilibrium constant. Therefore:

K_w = [H₃O⁺][OH⁻]

The quantity K_w is called the ionic product of water.

Value of K_w at 25°C

In pure water at 25°C, the concentrations of hydronium ions and hydroxide ions are equal:

[H₃O⁺] = [OH⁻] = 1.0 × 10⁻⁷ mol L⁻¹

Therefore:

K_w = [H₃O⁺][OH⁻]

K_w = (1.0 × 10⁻⁷)(1.0 × 10⁻⁷)

K_w = 1.0 × 10⁻¹⁴

Thus, at 25°C:

pK_w = 14.00

Since:

pH = −log[H₃O⁺]
pOH = −log[OH⁻]

For pure water at 25°C:

pH = pOH = 7.00

Important: The value pH = 7 represents neutral water specifically at 25°C. The value of K_w, and therefore the neutral pH, changes with temperature.

Concentration of Water

The approximate number of moles of water present in 1 litre of pure water is:

Number of moles of H₂O = \(\dfrac{1000}{18}\) ≈ 55.5 mol

Therefore, the approximate molar concentration of pure liquid water is:

[H₂O] ≈ 55.5 mol L⁻¹

Number of Water Molecules in 1 Litre

The number of water molecules present in 1 litre of water is approximately:

Number of H₂O molecules = 55.5 × N_A

where N_A is Avogadro's constant (approximately 6.022 × 10²³ mol⁻¹).

Concentration of H₃O⁺ and OH⁻ Ions

In pure water at 25°C:

[H₃O⁺] = 1.0 × 10⁻⁷ mol L⁻¹
[OH⁻] = 1.0 × 10⁻⁷ mol L⁻¹

Hence, the product of the concentrations of hydronium and hydroxide ions remains equal to the ionic product of water at a given temperature:

K_w = [H₃O⁺][OH⁻]