The solubility product of a chemical compound is the equilibrium constant of the compound in its solid state dissolving in an aqueous solution.

The **solubility** of a solute is the maximum amount of the solute in grammes that can dissolve in a 100 ml (or sometimes 1 dm^{3} or 1 kg) of a solvent at a particular temperature. For example, the solubility of *AgCl* in 100 ml of water at 25^{o}C is about 1.92×10^{-4} g or 1.34×10^{-5} moles.

To illustrate the concept of solubility product, let’s begin by adding 1.0×10^{-5} moles of solid *AgCl* in 100 ml of water at 25^{o}C. The solid completely dissolves in water to give 1.0×10^{-5} moles of *Ag ^{+}* and 1.0×10

^{-5}moles of

*Cl*ions. When the amount of solid added reaches 1.34×10

^{–}^{-5}moles, the solid continues to dissolve completely to give 1.34×10

^{-5}moles of

*Ag*and 1.34×10

^{+}^{-5}moles of

*Cl*ions in the solution, the maximum amount of

^{– }*Ag*and

^{+}*Cl*ions in 100ml of water. We call such a solution, a

^{–}**saturated solution**. When we add more than 1.34×10

^{-5}moles of

*AgCl*in 100ml of water, the concentration of

*Ag*and

^{+}*Cl*ions remain at 1.34×10

^{–}^{-5}mol ml

^{-1 }each, and an equilibrium is established between the undissolved solid

*AgCl*and the

*Ag*and

^{+}*Cl*ions such that the rate of solid dissociating into the ions is equal to that of the ions forming the solid.

^{–}Since the concentration of solid silver chloride is assumed to be the same as that of its pure state, the equilibrium constant is:

with *K_{sp }*= solubility product of

*AgCl*and is 1.8×10

^{-10 }at 25

^{o}C, [

*Ag*] = maximum amount of

^{+}*Ag*in 100 ml of water and [

^{+}*Cl*] = maximum amount of

^{–}*Cl*in 100 ml of water.

^{–}The solubility product of *AgCl* is therefore the mathematical product of the solubility of *Ag ^{+ }*(with respect to

*Cl*) and the solubility of

^{–}*Cl*(with respect to

^{– }*Ag*) raised to the power of their respective stoichiometric coefficients in 100 ml of solvent at a particular temperature. In general, the

^{+}**solubility product**of

*A*

_{x}*B*is

_{y }

###### Question

Calculate the *K_{sp}* for

*PbCl*, given that its solubility is 0.0108 g/ml at 20

_{2}*C.*

^{o}###### Answer

Solubility of *Pb ^{2+}* with respect to

*Cl*=

^{– }Solubility of *Cl ^{–}* with respect to

*Pb*=

^{2+ }

Just as *K_{a}* and

*K*are only useful for comparing weak acids and weak bases respectively,

_{b}*K*is only useful for comparing sparing soluble salts, as highly soluble salts have a higher probability of forming ion pairs. An

_{sp}**ion pair**consists of a cation and an anion that are electrostatically attracted to each other rather than individually being surrounded by solvent molecules. This changes their physical properties, e.g. mobility and distorts the measurement of the concentration of ions in the solution by ionic or conductivity methods and hence compromises on the accuracy of the value of

*K*. In general, the higher the solubility of a solid is, the greater the concentration of ions in the solvent, which results in a higher probability of forming ion pairs.

_{sp}Furthermore, just as *K_{w}* is constant at a particular temperature regardless of the source of

*H*

_{3}*O*

*and*

^{+}*OH*

*,*

^{–}*K*for a solid remains constant at a particular temperature regardless of the source of the dissolved ions. For example, the presence of

_{sp }*NaCl*in a saturated solution of

*AgCl*causes the latter to precipitate, as

*Cl*

*is common to both species. The decrease in the solubility of a dissolved compound in the presence of an ion in common with the dissolved compound is called the*

^{–}**.**

*common ion effect*

###### Question

Is *K_{sp}* dependent on the volume of the solution?

###### Answer

No. is a thermodynamic equilibrium constant that is governed by the formula

Hence, *K_{sp }*is only dependent on temperature. If we dilute a solution of

*PbCl*that is in equilibrium with solid

_{2}*PbCl*, the increase in volume of the solution shifts the position of the equilibrium according to Le Chatelier’s principle to produce more aqueous

_{2}*Pb*and

^{2+}*Cl*such that the saturation concentrations (mole per volume) of

^{–}*Pb*and

^{2+}*Cl*remains unchanged when the new equilibrium is attained.

^{–}Another way to look at it is that *K_{sp }* is the mathematical product of the solubility of the ions of a compound, raised to the power of their respective stoichiometric coefficients in a particular volume of solvent at a particular temperature. Since solubility is an intensive property,

*K*is independent of the volume of solvent.

_{sp }