Question

Derive the relation pH + pOH = 14.

Derive the relationship between pH and pOH.

Answer 1

Relationship between pH and pOH:

The ionic product of water is given as:

K_w = [H₃O⁺][OH^–]

Now, K_w = 1 × 10⁻¹⁴ at 298 K

Thus, [H₃O⁺][OH^-] = 1 × 10⁻¹⁴

Taking the logarithm of both the sides, we write

log₁₀[H₃O⁺] + log₁₀[OH^-] = -14

-log₁₀[H₃O⁺] + {-log₁₀[OH^-]} = 14

Now, pH = -log₁₀[H₃O⁺] and pOH = -log₁₀[OH^-]

∴ pH + pOH = 14