# What is the Ksp equation?

Aug 11, 2017

Depends upon the ionization ratio of the salt in solution

#### Explanation:

Ksp is the Solubility Product Constant for a salt and is a relative measure of solubility 'IF' the ionization ratios of the salts being compared are the same. For example solubility AgCl vs solubility of AgBr can be compared via the Ksp values. That is, the larger Ksp value is the more soluble. However, the Ksp values can NOT be used for comparing solubility of say $A g C l$ and $F e {F}_{2}$ because the two have different ionization ratios. The Ksp expressions and the resulting solubility equations for the two salts are:

For a 1:1 ionization ratio:
$K s p \left(A g C l\right) = \left[A {g}^{+}\right] \left[C {l}^{-}\right]$ => Solubility* = $\sqrt{K s p}$

For a 1:2 ionization ratio:
$K s p \left(F e {F}_{2}\right) = \left[F {e}^{+} 2\right] {\left[{F}^{-}\right]}^{2}$ => Solubility = $\sqrt[3]{\frac{K s p}{4}}$

Other ionization ratios for salts are ...
For a 1:3 ionization ratio:
$K s p \left(A {B}_{3}\right) = \left[{A}^{+ 3}\right] {\left[{B}^{-}\right]}^{3}$ => Solubility = $\sqrt[4]{\frac{K s p}{27}}$

For a 1:4 ionization ratio:
$K s p \left(A {B}_{4}\right) = \left[{A}^{+ 4}\right] {\left[{B}^{-}\right]}^{4}$ => Solubility = $\sqrt[5]{\frac{K s p}{256}}$

For a 2:3 ionization ratio:
$K s p \left({A}_{3} {B}_{2}\right) = {\left[{A}^{+ 3}\right]}^{3} {\left[{B}^{- 2}\right]}^{2}$ => Solubility = $\sqrt[5]{\frac{K s p}{107}}$

*The solubility calculations are expressed in 'Molar' concentrations.