pH Calculations - Bases

Calculating the pH of bases requires an extra step, as they dissociate with water to make hydroxide ions, OH^-, instead of hydronium ions, H₃O⁺.

WATER DISSOCIATION CONSTANT, K_W

The extra step requires us to have an understanding of the dissociation of water:

H₂O + H₂O ⇌ H₃O⁺ + OH^-

In pure water, the pH = 7.0, so the concentration of hydronium ions is 10^-7 mol L^-1. As the number of moles of hydronium ions is the same as the number of moles of hydroxide ions, the concentration of hydroxide ions is also 10^-7 mol L^-1.

Therefore, the equilibrium constant for this (called K_W) is 10^-7 × 10^-7 = 10^-14. This will become very important shortly.

K_W = [H₃O⁺][OH^-] = 10^-14

Acids increase the concentration of hydronium ions, so shift this equilibrium to the left, reducing the concentration of hydroxide ions, to return the equilibrium constant to 10^-14.

Likewise, bases increase the concentration of hydroxide ions, so shift this equilibrium to the left, reducing the concentration of hydronium ions, to return the equilibrium constant to 10^-14.

CALCULATING HYDRONIUM ION CONCENTRATION

This is the key extra step, and uses the water dissociation constant. This assumes that you know the hydronium ion concentration.

OPTION ONE: Using K_W

1. Rearrange  K_W = [H₃O⁺][OH^-]

[H₃O⁺] = K_W/[OH^-] = 10^-14/[OH^-]

2. Now, you have the hydronium ion concentration, so can calculate pH:

pH = ^-log₁₀[H₃O⁺]

OPTION TWO: Using pOH

1. Calculate pOH:

pOH = ^-log₁₀[OH^-]

2. Use pK_W to find the pH:

pH = pK_W - pOH = 14 - pOH