The strength of a weak acid or base can be quantified by the equilibrium constant of its reaction with water.

For a weak acid

$$\mathrm{HA+H_2O\rightleftharpoons H_3O^+ + A^-},$$

the acid-ionization constant is

$$K_a=\frac{[\mathrm{H_3O^+}][\mathrm{A^-}]}{[\mathrm{HA}]}.$$

A larger $K_a$ means the equilibrium lies farther toward ionized products and the acid is stronger.

For a weak base

$$\mathrm{B+H_2O\rightleftharpoons HB^+ + OH^-},$$

the base-ionization constant is

$$K_b=\frac{[\mathrm{HB^+}][\mathrm{OH^-}]}{[\mathrm B]}.$$

A larger $K_b$ means stronger basic behavior in water.

Because acid-base constants often span many orders of magnitude, logarithmic forms are widely used:

$$pK_a=-\log K_a,$$

$$pK_b=-\log K_b.$$

The logarithm reverses the ordering: smaller $pK_a$ means a stronger acid, while smaller $pK_b$ means a stronger base.

Conjugate pairs are linked

For a conjugate pair $\mathrm{HA/A^-}$,

$$K_a(\mathrm{HA})K_b(\mathrm{A^-})=K_w.$$

At $25,^\circ\mathrm C$, this implies

$$pK_a+pK_b=pK_w\approx14.00.$$

Therefore a strong acid has a weak conjugate base, and a strong base has a weak conjugate acid.

For example, acetic acid has $K_a\approx1.8\times10^{-5}$, so

$$pK_a\approx4.74.$$

Its conjugate base acetate has

$$K_b=\frac{K_w}{K_a}\approx\frac{1.0\times10^{-14}}{1.8\times10^{-5}} \approx5.6\times10^{-10},$$

showing that acetate is a weak base.

$K_a$ and $K_b$ describe equilibrium position at a specified temperature. They are not concentrations and do not say how much acid or base was initially added. The initial concentration and the ionization constant must be combined to predict an actual equilibrium pH.