# What is a solubility product?

Jul 11, 2015

The solubility product, ${K}_{s p}$, is simply another equilibrium expression, and quantitatively defines the solubility of a salt in water (the most usual solvent).

#### Explanation:

Consider the solubility of the "insoluble" salt, silver chloride, AgCl, in water. We could represent its dissolution as:

$A g C l \left(s\right) \rightarrow A {g}^{+} + C {l}^{-}$

${K}_{s p} = \left[A {g}^{+}\right] \left[C {l}^{-}\right] = 1.8 \times {10}^{-} 10$ at 298 K (solubility products are extensively and exhaustively tabulated for a host of sparingly soluble salts. Only the products appear in the equilibrium expression because the concentration of a solid material, here $A g C l$, is undefined.

So to determine the solubility of AgCl in water, and knowing that $\left[A {g}^{+}\right] = \left[C {l}^{-}\right]$, we simply have to solve an equation in ${x}^{2}$, where $x$ = solubility. It follows that if the concentration of chloride ion is artificially increased (say by adding $N a C l$), $\left[A {g}^{+}\right]$, remaining in solution, might be reduced even further (this is called "salting out").

Would ${K}_{s p}$ be expected to increase with increasing temperature?