relative lowering of vapour pressure

First, let us define what colligative qualities are and what they mean. According to the broad definition, colligative qualities are those properties of a solution that are dependent on the number of solute molecules present in the solution, regardless of their nature, in relation to the total number of molecules present in the solution.

The colligative qualities of a solution include a relative decrease in vapour pressure, a decrease in freezing point, an increase in boiling temperature, and an increase in osmotic pressure, all of which have practical applications in our daily lives.

Relative Lowering of Vapour Pressure

A measurement of the pressure exerted by vapours over a liquid under equilibrium conditions at a certain temperature is known as the vapour pressure. As an illustration, consider the surface of a pure liquid, which is occupied by the molecules that make up that liquid’s composition. Assume that a non-volatile solute is now introduced to the pure liquid in the previous step. The only molecules in the vapour above the solution are those of the solvent (pure liquid) molecules, because the solute molecules are nonvolatile. After the solute is added, it is discovered that the vapour pressure of the solution is lower than the vapour pressure of the pure liquid at a given temperature.

Due to the fact that when the solute was added to the pure liquid (solvent), the liquid surface contained molecules of both the pure fluid and the solute, the vapour pressure was reduced as a result of this. As a result, the number of solvent molecules that escape into the vapour phase decreases, and as a result, the pressure exerted by the vapour phase diminishes. Relative decrease in vapour pressure is the term used to describe this phenomenon. This decrease in vapour pressure is proportional to the amount of nonvolatile solute that is added to the solution, regardless of its type, and is thus considered to be one of the colligative features of the solution.

Mathematical Representation of above:

We will now look at and understand how the mathematical calculation for this decrease in vapour pressure is done.

Take, for example, a binary solution in which the mole fraction of the solvent is x1 and that of the solute is x2, p1 is the vapour pressure of the solvent in its pure form, and p1o is the vapour pressure of the solvent in its undiluted condition.

In accordance with 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 relative decrease in vapour pressure, which is equal to the mole fraction of the solute, can be calculated using the equation above.

Partial vapour pressure

The partial vapour pressure of a component in a mixture is equal to the vapour pressure of the pure component at that temperature multiplied by its mole fraction in the mixture.

Conclusion: –

Dissolving a non-volatile solute in a pure solvent causes the vapour pressure of the solvent to progressively decrease as a result of the relative decrease in vapour pressure caused by the solute. If p is the vapour pressure of a solvent and ps is the vapour pressure of a solution, then the decrease of vapour pressure can be represented as (p – ps). The term “relative decrease of vapour pressure” refers to the lowering of vapour pressure in comparison to the vapour pressure of the pure solvent.