Ionic Product of Water (Kw) and pH Scale: Complete Guide with Examples

The Ionic Product of Water and pH Scale

Understanding the ionic product of water and the pH scale is essential for grasping acid-base chemistry. Let’s explore these fundamental concepts that form the basis of solution chemistry.

The Ionic Product of Water (Kw)

Definition: The ionic product of water is the product of the concentration of hydrogen ions and hydroxide ions from the self-ionization of water at a given temperature.

Pure Water Behavior

Pure water behaves as both an acid and a base—it is amphoteric or amphiprotic. Water molecules ionize according to the equilibrium:

H₂O(l) ⇌ H₃O⁺(aq) + OH⁻(aq)

Or simply:

H₂O ⇌ H⁺(aq) + OH⁻(aq)

Equilibrium Constant Expression

Applying the equilibrium law:

Kc = [H₃O⁺][OH⁻] / [H₂O]²

Since the concentration of water in its pure state is constant (≈ 55.5 mol/dm³):

Kc[H₂O]² = constant = Kw

Therefore:

Kw = [H⁺][OH⁻]

Value of Kw at Different Temperatures

At 25°C (298K):

• [H⁺] = [OH⁻] = 1×10⁻⁷ mol/dm³
• Kw = (1×10⁻⁷) × (1×10⁻⁷) = 1×10⁻¹⁴ mol²/dm⁶

Important Note: Kw increases with temperature. This means pure water becomes more acidic at higher temperatures.

The pH Scale

Definition: pH is defined as the negative logarithm to the base 10 of the hydrogen ion concentration.

pH = -log₁₀[H⁺] = log(1/[H⁺])

pH Calculations

For Pure Water at 25°C:

Since [H⁺] = [OH⁻] and [H⁺] = 1×10⁻⁷ mol/dm³:

pH = -log(1×10⁻⁷) = 7

Therefore, at 25°C:

• pH = 7 → neutral solution
• pH < 7 → acidic solution ([H⁺] > [OH⁻])
• pH > 7 → alkaline solution ([H⁺] < [OH⁻])

The pOH Scale

Similarly, we can define pOH:

pOH = -log₁₀[OH⁻]

Relationship Between pH and pOH:

Since Kw = [H⁺][OH⁻] = 1×10⁻¹⁴

Taking logarithms:

log(Kw) = log[H⁺] + log[OH⁻]

-14 = -log[H⁺] - log[OH⁻]

-14 = -pH - pOH

pH + pOH = 14

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