On adding a non volatile solute to a solvent, the vapour pressure of s...
Effect of Non-Volatile Solute on Vapour Pressure of Solvent
When a non-volatile solute is added to a solvent, the vapour pressure of the solvent decreases. The decrease in vapour pressure can be explained using Raoult's law.
Raoult's Law
Raoult's law states that the vapour pressure of a solution is directly proportional to the mole fraction of the solvent in the solution. Mathematically, it can be expressed as:
vapour pressure of solution = mole fraction of solvent x vapour pressure of pure solvent
Explanation
When a non-volatile solute is added to a solvent, the number of solvent molecules at the surface of the solution decreases. This is because the solute molecules occupy some of the space at the surface of the solution. As a result, the rate of evaporation of solvent molecules decreases, leading to a decrease in the vapour pressure of the solvent.
Colligative Property
The decrease in vapour pressure of the solvent is an example of a colligative property. Colligative properties depend only on the number of solute particles in the solution, not on the identity of the solute particles. Other examples of colligative properties include boiling point elevation, freezing point depression, and osmotic pressure.
Vapour Pressure Depression
The decrease in vapour pressure of the solvent can be expressed as:
vapour pressure of solution = mole fraction of solvent x vapour pressure of pure solvent
Since the solute is non-volatile, its contribution to the vapour pressure of the solution is negligible. Therefore, the vapour pressure of the solution is mainly determined by the mole fraction of the solvent. The decrease in vapour pressure can be expressed as:
ΔP = P0 - P
Where ΔP is the vapour pressure depression, P0 is the vapour pressure of the pure solvent, and P is the vapour pressure of the solution.
From Raoult's law, we know that:
P = Xs x P0
Where Xs is the mole fraction of the solvent in the solution. Substituting this expression for P in the equation for ΔP, we get:
ΔP = P0 - Xs x P0 = P0 (1 - Xs)
Therefore, z in the given expression is (1 - Xs).