# What are acid and base dissociation constants?

Sep 7, 2014

They are equilibrium constants for the ionization reactions of acids and bases.

When an acid dissolves in water, it reacts according to the equation

HA + H₂O ⇌ H₃O⁺ + OH⁻

We can write an equilibrium constant expression

${K}_{\text{eq" = "[H₃O⁺][OH⁻]"/"[HA][H₂O]}}$

Since [H₂O] is a constant, we can write

${K}_{\text{eq" × "[H₂O]" = "[H₃O⁺][OH⁻]"/"[HA]}}$

We can define a new constant, the acid dissociation constant, ${K}_{a} = {K}_{\text{eq" × "[H₂O]}}$. So

${K}_{a} = \text{[H₃O⁺][OH⁻]"/"[HA]}$

For a base, we can write the equilibrium reaction as

B + H₂O ⇌ BH⁺ + OH⁻

We can define the base dissociation constant, ${K}_{b} = {K}_{\text{eq" × "[H₂O]}}$. So

${K}_{b} = \text{[BH⁺][OH⁻]"/"[B]}$

Thus, the acid and base dissociation constants are the equilibrium constants without the term for the concentration of water.