Vapour Pressure of solutions - Practice Questions & MCQ

It is the pressure exerted by vapours of a pure liquid over its surface when they are in equilibrium with the liquid at a given temperature.

For example, if we take the case of water, then the equilibrium constant of the following physical process will represent the Vapor Pressure of Water (Also sometimes called as Aqueous Tension)

At equilibrium, the rate of vaporisation = the rate of condensation and the equilibrium constant of the above vapour-liquid equilibrium represent the vapour pressure of the liquid.

It depends upon the nature of the liquid and temperature. Pure liquid has always a vapour pressure greater than its solution.
Vapour pressure of a liquid helps us to have an idea of forces of attraction amongst the molecules of liquid that is, more the force of attraction, lower is the vapour pressure and vice versa.
Vapour pressure of a liquid increase with an increase in temperature due to an increase in kinetic energy of solvent molecules that is, an increase in evaporation however it is independent of the nature of the vessel.

Vapour Pressure of a Solution
When a miscible solute is added to a pure solvent, it results in the formation of a solution. As some molecules of solute will replace the molecules of the solvent from the surface, therefore, escaping tendency of solvent molecules decreases. This causes a lowering of vapour pressure.

• The vapour pressure of a solution is less than that of the pure solvent.
• If the vapour pressure of the solvent is P and that of the solution is P_s then lowering of V.P = P - P_s.
• Vapour pressure of solution decreases as the surface area occupied by solvent molecule decreases and density increases.

Factors governing the vapour pressure:

1. Temperature: As Temperature increases, Kinetic Energy of the molecules in the liquid phase increases and as a result, more number of molecules are able to escape to the gaseous phase and hence the vapour Pressure increases.

The Clausius Clapeyron Equation relates the vapour pressure of the liquid to the temperature and is given as 

Where ΔH is the heat of vaporisation of the liquid and P1 and P2 are the vapour pressure at temperature T₁ and T₂ respectively.

2. Vapour pressure depends on the nature of the liquid. Greater the force of attraction between the liquid molecules, lesser is the vapour pressure

 3. vapour pressure does not depend on the shape or the size of the container and has a fixed value at a particular temperature.
 

Significance of vapour pressure:

• Vapour pressure gives us an idea of intermolecular forces of attraction in the liquid. The greater the force of attraction, lower is the vapour pressure and vice versa.

2. Vapour pressure gives us an idea of the volatility (vapour forming tendency of the liquid). Greater the vapour pressure, greater is the volatility of the liquid.

3. Vapour pressure also gives an idea of the boiling point of the liquid. Greater the vapour pressure, lesser is the boiling point of the liquid.

Raoult’s law:

Let us consider a binary solution obtained upon mixing of two volatile liquids A and B. When the solution is taken in a closed vessel, both the components would evaporate and eventually an equilibrium would be established between vapour phase and the liquid phase. The vapor pressure over this solution would depend on the volatility of each of the liquids as well as the relative amount of the liquids present in solution. French Chemist Raoult gave this quantitative relationship between these parameters.

Statement of Raoult’s law: 

For a solution of volatile liquids, the partial vapour pressure of each component in the solution is directly proportional to its mole fraction in the solution.

Let us represent solvent as "A" and solute as "B". 

Before mixing, vapour pressure of A is  and vapour pressure of B is .

Now, after mixing of solute and solvent, let the partial pressures of solvent A and solute B be  P_A and P_B respectively

Now according to Raoult's law, vapour pressure of liquid A is proportional to the mole fraction of liquid A.

Thus,

Now, to find the value of K_A and K_B, when we have only liquid A, then partial pressure of A is equal to

Thus,   And similarly, it can be shown that .

Thus, we can write:

Now according to Dalton's law of partial pressure, we have:

Total pressure 

Thus, the total pressure exerted by the vapors of the solutions can be represented as

Using these equations, the mole fraction of A and B represented as Y_A and Y_B in the vapor phase can be calculated as given by the equations:

A solution is obtained by mixing a non-volatile solid solute in the liquid solvent.

Let's name the solvent as "A" and solute as "B". Let the vapour pressure of the pure solvent be represented as . Now when the solute is dissolved in the solvent, then the vapour pressure of the solution decreases and is represented as . 

According to Raoult's law, we know:

Now, the sum of mole fraction of solvent and solute is equal to 1.

Thus

On putting the value of XA in equation (i), we get:

Therefore,  

Thus, it can be said that,

The RHS in the above expression gives us the 'Relative lowering of vapour pressure and is equal to the mole fraction of the solute.