What is Raoult’s law of lowering of vapour pressure?

Raoult’s law states that the vapor pressure of a solution is directly proportional to the mole fraction of the solvent present in the solution.

This law applies to ideal solutions, which are solutions that follow all of the assumptions of the kinetic molecular theory of gases, such as non-interacting particles, no volume changes upon mixing, and no energy transfer upon mixing.

In simpler terms, when a non-volatile solute (a substance that does not evaporate easily) is added to a solvent, it lowers the vapor pressure of the solvent.

This is because some of the solvent molecules are replaced by the solute molecules at the surface of the solution, making it harder for solvent molecules to escape and form a vapor. As a result, the vapor pressure of the solvent decreases, and the boiling point of the solution increases.

Use of Raoult’s law

Raoult’s law helps us to predict the vapor pressure and boiling point of solutions based on the properties of the pure solvent and solute. It is an important concept in chemistry and is used in many industrial processes, such as the production of pharmaceuticals, fuels, and chemicals.

Mathematical derivation of Raoult’s law of lowering of vapour pressure

Consider a solution containing a solvent and a non-volatile solute. Let the mole fraction of the solvent be x and the mole fraction of the solute be (1 – x).

According to Dalton’s law of partial pressures, the total vapor pressure of the solution is equal to the sum of the partial pressures of the solvent and the solute vapors. Thus,

P_total = P_solvent + P_solute

where P_total is the total vapor pressure of the solution, P_solvent is the partial pressure of the solvent vapor, and P_solute is the partial pressure of the solute vapor.

Now, according to Raoult’s law, the partial pressure of the solvent vapor is directly proportional to its mole fraction in the solution, i.e.,

P_solvent = x * P°_solvent

where P°_solvent is the vapor pressure of the pure solvent.

Similarly, the partial pressure of the solute vapor is directly proportional to its mole fraction in the solution, i.e.,

P_solute = (1 – x) * P°_solute

where P°_solute is the vapor pressure of the pure solute.

Substituting these expressions for P_solvent and P_solute into the equation for P_total, we get:

P_total = x * P°_solvent + (1 – x) * P°_solute

This equation represents Raoult’s law of lowering of vapor pressure. It states that the total vapor pressure of a solution is equal to the sum of the partial pressures of the solvent and the solute vapors, and that the partial pressure of the solvent vapor is proportional to its mole fraction in the solution.

Note that this derivation assumes that the solution is ideal, which means that the solute and solvent particles do not interact with each other and that their volumes are negligible compared to the total volume of the solution. In practice, real solutions may deviate from Raoult’s law due to intermolecular interactions and other factors.