Solubility product principle and its application

Solubility product is an important concept that is used in explaining phenomena like solubility and precipitation of compounds in analytical chemistry.

Calculation of solubility

Knowing the solubility product of a sparingly soluble salt like AgCl, PbI₂, BaSO₄ etc. the solubility of the salt can be calculated.

Problem

16. What is the solubility of Ag₂CrO₄ in water if the value of solubility product, K_sp = 1.7 x 10^-11(mol / L) ³_.

Solution

Ag₂CrO₄ dissolves in water in accordance with the equilibrium.

If S is the solubility of Ag₂CrO₄ then in a saturated solution,

Then, K_sp (Ag₂CrO₄) = [Ag⁺]² [CrO₄^2-] = (2S)² (S)

1.7 x 10^-11 (mol / L)³ = 4S³

Thus, the solubility of Ag₂CrO₄ in water at 298 K is 1.48 x 10^-4 mol/ L.

Molar mass of Ag₂CrO₄ = (2 x 108 + 52 + 4 x 16) g/mol = 332 g/mol

So, Solubility of Ag₂CrO₄ = 1.48 x 10^{- 4} mol /L

= 1.48 x 10^{- 4} mol / L x 332 g/mol = 0.049 g /L

In predicting the precipitation in reactions

Knowing the solubility product of a salt, it is possible to predict whether on mixing the solution of its ions, a precipitate will be formed or not. For precipitation to occur, its ionic product should exceed solubility product. Therefore, to predict the precipitation reaction, we calculate the ionic product of the ions and find out whether it is greater than K_sp or not. Thus, if

For example in order to precipitate barium sulphate from a solution of barium chloride at a concentration of 0.5 M, the precipitation is done by adding sulphuric acid in small amounts to the solution. Initially no precipitation occurs because the small amount of SO₄^2- is insufficient to make the ionic product, [Ba²⁺] [SO₄^2-] equal to solubility product of barium sulphate. When we have added sufficient amount of sulphuric acid is added so that the ionic product exceeds solubility product, barium sulphate would get precipitated.

Problems

17. The concentration of Ca⁺⁺ in blood is 0.0025M. If an oxalate solution with oxalate ion concentration 1 x 10^-7M is added to it, state whether precipitation occurs or not. Solubility product of calcium oxalate = 2.3 x 10^-9.

Solution

In the resulting solution, [Ca⁺⁺ ] = 0.0025M. [C₂O₄^2-] = 1 x 10^-7 M.

[Ca⁺⁺][C₂O₄^2-] = 0.0025 x 10^-7 = 2.5 x 10^-10

This is less than the solubility product of calcium oxalate. Thus, precipitation of calcium oxalate does not occur.

18. A solution is prepared by mixing equal volumes of 0.01M MgCl₂, and 0.02M MgC₂O₄ at 18°C. Would MgC₂O₄ precipitate out? K_sp of MgC₂O₄ at 18°C = 8.57 x 10^-5.

Solution

When mixed, the total volume gets doubled and hence the effective concentrations of the ions would be half of the initial concentration, i.e., in solution

[Mg²⁺] =(0.01/2)=0.005 mol/L

[C₂O₄^2-] = (0.02/2) = 0.01 mol/L

These ions would react to form sparingly soluble salt MgC₂O₄ in accordance with the reaction,

Then, the ionic product function in the solution is given by,

[Mg²⁺] [C₂O₄^2-] = 0.005 x 0.01 = 5 x 10^-5

the K_sp value for MgC₂O₄ at 18°C is 8.57 x 10^-5. Since, the ionic product function in the solution is less than the K_sp value, precipitation does not take place.

In inorganic qualitative analysis

The concepts of solubility product and common ion effect play an important role in qualitative analysis for the separation of basic radicals (cations) into different groups.

Weak acids and weak bases ionise in water slightly and an equilibrium is established in their solutions. For example, in the ionization of a weak base NH₄OH as:

The ionization constant for the base,

If solid NH₄Cl is added to the solution, the concentration of NH₄⁺ ions increases. According to Le Chatelier's principle, the equilibrium shifts to the left. As a result, the concentration of OH^- is considerably decreased and the weak base NH₄OH becomes even weaker in the presence of its salt.

This is common ion effect and may be defined as the suppression of the degree of dissociation of a weak acid or a weak base by the addition of a strong electrolyte containing a common ion.

Qualitative analysis

The common ion effect is generally employed in qualitative analysis.

The cations of group II (Hg²⁺, Pb²⁺, Bi³⁺, Cu²⁺, As³⁺, Sb³⁺, Sn²⁺) are precipitated as their sulphides (such as CuS, PbS) by passing H₂S gas in the presence hydrochloric acid (Common H⁺ ions).

The cations of group III are precipitated as their hydroxides by NH₄OH in the presence of NH₄Cl.

The cations of group V are precipitated as their carbonates by the addition (NH₄)₂CO₃, in the presence of HCl.

Purification of sodium chloride

Sodium chloride obtained from sea-water or lakes is always impure. It can be purified on the basis of common ion effect as described below:

The saturated solution of impure sodium chloride is prepared by dissolving in minimum quantity of water. HCl gas is then passed through this solution. The following equilibria are set up:

Due to the presence of common chloride ions, the dissociation of sodium chloride is suppressed. This is known as common ion effect. The dissociation of sodium chloride is decreased to such an extent that the ionic product of NaCl exceeds its solubility product and it is thrown down as a precipitate.

Salting out of soap

Soap is a sodium salt of higher fatty acids e.g. sodium stearate, sodium oleate etc. When soap is prepared it floats over spent lye (the residual aqueous solution containing unused alkali, glycerol etc.). A significant amount of soap remains dissolved in this solution. To recover this soap, sodium chloride is added to the boiling soap solution.

The recovered soap separates out due to the common ion effect of Na⁺, in accordance with the reactions.

The increased concentration of Na⁺ in the solution due to the dissociation of NaCl, shifts the equilibrium towards left and thus soap is precipitated. The recovery of a dissolved salt by adding another salt to the solution is termed salting out.

Comparison of solubility product and ionic product

Solubility product	Ionic product
It is the product of the concentration of ions of the electrolyte each raised to the power of their coefficients in the balanced chemical equation in a saturated solution	It is the product of the concentration of ions of the electrolyte each raised to the power of their coefficients in the balanced chemical equation in a solution at any concentration
It is applicable to only saturated solutions	It is applicable to all types of solutions of any concentration
It has a constant value for an electrolyte at a constant temperature	Its value is not constant and varies with change in concentration