Molar Solubility

Molar solubility is the number of moles of solute that dissolve in a solvent before it reaches saturation. It is more often stated as the number of moles of solute that dissolve in a liter of solution. Therefore, it is most often measured in moles/liter and denoted as 'M'. Once the specific number of moles of the solvent are dissolved, the solution is said to be saturated, that is the solute will no more dissolve in the solvent, and this is molar solubility.

To understand this better, you could try a small experiment at home. Try dissolving sugar spoon after spoon in a glass of water, you will observe that as the amount of sugar dissolved starts increasing, the process of dissolving gets slow and there is a point when the sugar will just accumulate and not dissolve no matter how much you try to stir the solution. This is when the water is saturated with sugar. There are various other terms associated that are necessary to calculate and understand it.

Solubility Equilibrium
It is the chemical equilibrium between a solid state and dissolved state of a compound at the point of saturation. This equilibrium greatly depends on temperature. In simple words , it is a dynamic equilibrium in which a particular number of molecules migrate between the solid and dissolved states, at a point dissolution and precipitation become equal and this is when actual equilibrium is reached. This brings us to solubility product constant, Ksp that is used to describe saturated solutions of low solubility. These are mostly ionic compounds. The molar solubility equation will be given as,

M_xA_y → xM^y(aq)+ + yA^x-(aq)

The equilibrium constant for this will be,

K_c = [M^y+]^x[A^x]^y/[MA]

Solubility product will be given as,

Ksp = Kc x [MA]

Calculating Molar Solubility from Ksp
Calculating this value is not as easy as calculating molarity of a substance. Let us learn this with an example. For PbCl₂, Ksp for which is 1.6 x 10^-6.

Solution
PbCl₂ → Pb²⁺ + 2Cl^-

Ksp = [Pb²⁺][Cl^-]²

If [Pb²⁺] = x then, [Cl] = 2x

Hence,

(x)(2x)² = 1.6 x 10^-6

4x³= 1.6 x 10^-6

x = 7.4 x 10^-3 = Molar Solubility (M) of PbCl₂

From the example above, a general formula can be given by S₀,

S₀ = ^x+y√Ksp/x^xy^y

Points to Remember
Calculating molar solubility can get a bit tricky if you are not aware of the small nuances in the phenomenon.

• Always remember to balance the chemical equation for the dissociation. There must be equal number of moles on the reactant and product side.
• To determine M, you must always know the solubility product constant Ksp of the compound.
• Concentrations of the ions will always be square roots of the Ksp.
• The concentration of each ion will be equivalent to the amount of product dissolved.
• When a solvent is heated, the energy available in the system increases, due to which the amount of product that dissociates increases. Remember that dissolution can be an exothermic or an endothermic reaction as well.
• If the temperature of a saturated solution decreases, the value of M will also decrease, that is the solute will begin to precipitate.
• When temperature decreases, the concentration of a solution before precipitation is greater than M, this solution then becomes supersaturated.

Using this formula you can calculate the value of any ionic compound. This value is something every chemist or student of chemistry must know very well, as making solutions is almost an everyday business in this field.