= Base dissociation constant
{title2=$K_b$}
For the <conjugate base> $\mathrm A^-$ accepting a <proton> from <water>,
$$
\mathrm A^-+\mathrm H_2\mathrm O\rightleftharpoons\mathrm{HA}+\mathrm{OH}^-,\qquad
K_b=\frac{a_{\mathrm{HA}}a_{\mathrm{OH}^-}}{a_{\mathrm A^-}}.
$$
This <base dissociation constant> uses the same <water> <thermodynamic activity> approximation and <standard state> conventions as the <acid dissociation constant>. Multiplying the two relations cancels the partner <thermodynamic activities>:
$$
K_aK_b=a_{\mathrm H^+}a_{\mathrm{OH}^-}=K_w,\qquad
\mathrm pK_a+\mathrm pK_b=\mathrm pK_w,\qquad
\mathrm pK_b=-\log_{10}K_b,\quad \mathrm pK_w=-\log_{10}K_w.
$$
Here $K_w$ is the aqueous ion product associated with <self-ionization of water>. At fixed <temperature>, a larger <acid dissociation constant> gives a smaller <base dissociation constant> for its own <conjugate base>; this reciprocal rule compares matching <conjugate acid-base pairs>. A <weak acid> does not necessarily have a <conjugate base> that reacts almost completely with <water>. For example, stipulated $K_a=10^{-5}$ and $K_w=10^{-14}$ give $K_b=10^{-9}$.<Chemistry 2e by Paul Flowers and others/14.3 Relative Strengths of Acids and Bases>[§14.3, Relative Strengths of Conjugate Acid-Base Pairs, cancellation giving Ka Kb = Kw]{ref}
The value of $K_w$ changes with <temperature>; $10^{-14}$ is the familiar approximate value near $25\,{}^\circ\mathrm C$, not a universal constant. If <water> is retained explicitly in both full <equilibrium constants>, their product instead equals $a_{\mathrm H_3\mathrm O^+}a_{\mathrm{OH}^-}/a_{\mathrm H_2\mathrm O}^2$, the full <equilibrium constant> for $2\mathrm H_2\mathrm O\rightleftharpoons\mathrm H_3\mathrm O^++\mathrm{OH}^-$. The <acid dissociation constant>, <base dissociation constant> and <self-ionization of water> convention must agree.
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