Is lowering of vapour pressure also a colligative property?

since mathematically p*a - pa/p*a=xa
=>p*a-pa=p*aXa => p*a-pa~xa

Yes, lowering of vapor pressure is a colligative property. Colligative properties depend on the number of solute particles present in a solution, rather than the nature or identity of the solute.

To understand why lowering of vapor pressure is a colligative property, we need to explore the concept of vapor pressure. Vapor pressure is the pressure exerted by the vapor phase in equilibrium with the liquid phase at a given temperature. When a non-volatile solute is added to a solvent, it reduces the number of solvent molecules able to escape into the vapor phase, thus decreasing the vapor pressure of the solution.

Raoult's law is one way to mathematically describe the relationship between the vapor pressure of the solvent in the pure state (p*a), the vapor pressure of the solvent in the solution (pa), and the mole fraction of the solvent (xa). According to Raoult's law, the vapor pressure of a solvent in a solution is equal to the mole fraction of the solvent multiplied by its vapor pressure in the pure state.

The equation you provided, p*a - pa = p*aXa, is an expression of Raoult's law, where p*a is the vapor pressure of the pure solvent, pa is the vapor pressure of the solvent in the solution, and xa is the mole fraction of the solvent.

The term p*a - pa represents the lowering of the vapor pressure caused by the addition of the solute. As you mentioned, xa represents the mole fraction, which is the ratio of the number of moles of the solvent to the total number of moles in the solution.

By using this equation, you can calculate the lowering of vapor pressure caused by the addition of a non-volatile solute. This lowering of vapor pressure, known as vapor pressure depression, is a colligative property because it depends only on the concentration of solute particles and not on their specific nature or identity.