Prove that relative lowering of vapour pressure is a colligative prope

1.	Prove that relative lowering of vapour pressure is a colligative property.
Answer» Solution :The VAPOUR pressure of a solution containing a nonvolatile , non-electrolyte solute is ALWAYS lower than the vapour pressure of the pure solvent . Consider a CLOSED system in which a pure solvent is in equilibrium with its vapour At equilibrium the molar Gibb's free energies of solvent in the liquid and gaseous phase are equal ` (Delta G=0 ) ` When a solute is added to this solvent , the dissolution takes place and its free energy (G) decreases due to increase in entropy .In order to maintain the equilibrium the free energy of the vapour phase must also decrease . At a given temperature ,the only way to lower the free energy of the vapour is to reduce its pressure Thus the vapour pressure of the solution must decrease to maintain the equilibrium. ` (##SUR_CHE_XI_V02_C09_E05_007_S01.png" width="80%"> We know that from the RAOULT's law the relative lowering of the vapour pressure is equal to the mole fraction of the solute From the above equation , it is clear that the relative lowering of vapour pressure depends only on the mole fraction of the solute ` (X_B) ` and is independent of its nature . Therefore , relative lowering of vapour pressure is a colligative property.

Prove that relative lowering of vapour pressure is a colligative property.