Question

Why is the conjugate base of a strong acid weak?

Answer 1

The product of `K_a` and `K_b` for any conjugate acid/base pair is always equal to `K_w`, the self-ionization constant for water (approximately `1 x 10^(-14)`).

Therefore, larger values of `K_a` necessarily mean that `K_b` must be smaller (i.e., the conjugate base of a strong acid must be a weak base.

Proof:
For any acid, `HA` and its conjugate base, `A^-` at equilibrium

`HA + H_2O → H_3O^+ + A^-`
`K_a = ([H_3O^+][A^-])/([HA])`

For the base reaction:
`A^(-) + H_2O → OH^(-) + HA`
`K_b = ([OH^-][HA])/([A^-])`

`K_a · K_b = [H_3O^+][OH^-] = K_w`