# Molar Solubility

Molar solubility is a term we all come across while making solutions in a chemistry lab. Learn more about this term and its various aspects in the following article.
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.

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,

MxAy → xMy(aq)+ + yAx-(aq)

The equilibrium constant for this will be,

Kc = [My+]x[Ax]y/[MA]

Solubility product will be given as,

Ksp = Kc x [MA]

Calculating M 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/xxyy

Points to Remember
Calculating molar solubility can get a bit tricky, if you are not aware of the small nuances of this 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 Ksp of the compound.
• Concentration of the ions will always be square root 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.
Using the formula given above, 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.