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 dm3 or 1 kg) of a solvent at a particular temperature. For example, the solubility of AgCl in 100 ml of water at 25oC 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 25oC. 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 Ksp = solubility product of AgCl and is 1.8×10-10 at 25oC, [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 AxBy is
Question
Calculate the Ksp for PbCl2, given that its solubility is 0.0108 g/ml at 20oC.
Answer
Solubility of Pb2+ with respect to Cl– =
Solubility of Cl– with respect to Pb2+ =
Just as Ka and Kb are only useful for comparing weak acids and weak bases respectively, Ksp is only useful for comparing sparing soluble salts, as highly soluble salts have a higher probability of forming ion pairs. An 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 Ksp. 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.
Furthermore, just as Kw is constant at a particular temperature regardless of the source of H3O+ and OH–, Ksp for a solid remains constant at a particular temperature regardless of the source of the dissolved ions. For example, the presence of 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 Ksp dependent on the volume of the solution?
Answer
No. is a thermodynamic equilibrium constant that is governed by the formula
Hence, Ksp is only dependent on temperature. If we dilute a solution of PbCl2 that is in equilibrium with solid PbCl2, the increase in volume of the solution shifts the position of the equilibrium according to Le Chatelier’s principle to produce more aqueous Pb2+ and Cl– such that the saturation concentrations (mole per volume) of Pb2+ and Cl– remains unchanged when the new equilibrium is attained.
Another way to look at it is that Ksp 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, Ksp is independent of the volume of solvent.