 # Colligative Properties : Relative Lowering Of Vapour Pressure

Let us first discuss the meaning of colligative properties. According to the general definition, those properties of a solution that depend on the number of solute molecules, irrespective of their nature, with respect to the total number of molecules present in the solution are called colligative properties.

For a solution, relative lowering of vapour pressure, depression of freezing point, elevation in boiling point and osmotic pressure are colligative properties that find great application in our day to day lives.

## Relative Lowering of Vapour Pressure

Vapour pressure is the pressure exerted by the vapours over the liquid under the equilibrium conditions at a given temperature. Now let us take an example of a pure liquid, the surface of the liquid is occupied by the molecules of the liquid. Suppose a non-volatile solute is now added to this pure liquid. Since the solute molecules are non-volatile, the vapour above the solution consists of only solvent (pure liquid) molecules. After adding the solute, the vapour pressure of the solution is found to be lower than that of the pure liquid at a given temperature. This lowering in vapour pressure is due to the fact that after the solute was added to the pure liquid (solvent), the liquid surface now had molecules of both, the pure liquid and the solute. The number of solvent molecules escaping into vapour phase gets reduced and as a result the pressure exerted by the vapour phase is also reduced. This is known as relative lowering of vapour pressure. This decrease in vapour pressure depends on the amount of non-volatile solute added in the solution irrespective of its nature and hence it is one of the colligative properties.

### Mathematical Representation

We will now see and understand how this lowering in vapour pressure is determined mathematically.

Let us assume a binary solution in which the mole fraction of the solvent be x1 and that of the solute be x2, p1 be the vapour pressure of the solvent and p1o be the vapour pressure of the solvent in pure state.

According to Raoult’s Law:

p1=x1p1o…………………………..(1)

The decrease in vapour pressure of the solvent (∆p1) is given by:

=> ∆p1=p1o-p1

=> ∆p1=p1o-p1ox1                              [using equation (1)]

=> ∆p1=p1o (1-x1)

Since we have assumed the solution to be binary solution, x2=1-x1

=> ∆p1=p1ox2

=> x2= ∆p1/p1o

The above equation gives the relative lowering in vapour pressure which is equal to the mole fraction of the solute.