= Solubility product
{title2=$K_{\mathrm{sp}}$}
= Solubility product constant
{synonym}
The <solubility product> is the <equilibrium constant> for dissolution of a specified <solid> into its dissolved <ions>. For a pure bulk AB <solid> at the chosen <temperature>, <pressure> and <standard states>,
$$
\mathrm{AB}(s)\rightleftharpoons\mathrm A^+(aq)+\mathrm B^-(aq),\qquad K_{\mathrm{sp}}=a_{\mathrm A}a_{\mathrm B}.
$$
The pure bulk <solid>'s <thermodynamic activity> is one in this convention. Coexisting <solid> and <chemical solution> at <chemical equilibrium> give this equality. If all available <solid> dissolves, the final <chemical solution> may instead be undersaturated; do not impose equality merely because a salt was initially added.<Chemistry 2e by Paul Flowers and others/15.1 Precipitation and Dissolution>[Chemistry 2e, §15.1, The Solubility Product: saturated solution with excess solid and dissolution equilibrium]{ref}
Using the <thermodynamic activity> definition $a_i=\gamma_i c_i/c^\circ$, with <activity coefficients> $\gamma_i$ and reference <molar concentration> $c^\circ$, gives the independent conversion
$$
K_{\mathrm{sp}}=\gamma_{\mathrm A}\gamma_{\mathrm B}\frac{c_{\mathrm A}c_{\mathrm B}}{(c^\circ)^2},\qquad K_{\mathrm{sp},c}=\frac{K_{\mathrm{sp}}(c^\circ)^2}{\gamma_{\mathrm A}\gamma_{\mathrm B}}.
$$
Thus $K_{\mathrm{sp}}$ is <dimensionless>, while the conditional concentration form $K_{\mathrm{sp},c}$ has units $\mathrm M^2$ for this one-to-one model. Treating $K_{\mathrm{sp},c}$ as constant requires a justified fixed or approximately fixed <activity coefficient> product. Changing <ionic strength> can change that product even at fixed <temperature>; changing <temperature> can change the <equilibrium constant> itself. Specify the <solid> <thermodynamic phase> too: different <crystal polymorphs> need not have the same <solubility product>.
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