Solubility

1. Relevant Principle: This question relates to the colligative property of vapor pressure lowering, which is described by Raoult's Law for ideal solutions with a non-volatile solute.
2. Raoult's Law Statement: Raoult's Law states that the partial vapor pressure of a solvent above a solution ( ) is equal to the vapor pressure of the pure solvent ( ) multiplied by the mole fraction of the solvent in the solution ( ).
3. Applying to Given Symbols:
   • The vapor pressure of the solution ( ) is the partial vapor pressure of the solvent above the solution (assuming a non-volatile solute).
   • The vapor pressure of the pure solvent is given as .
   • The mole fraction of the solvent in the solution is given as .
   • The mole fraction of the solute is given as . (Note: ) is equal to the vapor pressure of the pure solvent ( ) multiplied by the mole fraction of the solvent ( ) in the solution.
   • Mathematical Expression: According to Raoult's Law: or equivalently
   • Definitions from the Question:
     • = Vapor pressure of the pure solvent
     • = Vapor pressure of the solution (effectively, the partial vapor pressure of the solvent above the solution)
     • = Mole fraction of the solvent
     • = Mole fraction of the solute
   • Compare with Options: We need to find the option that matches the formula .
     • (a) : Incorrect.
     • (b) : Correct. This directly matches Raoult's Law.
     • (c) : Incorrect.
     • (d) : Incorrect. Uses the mole fraction of the solute instead of the solvent.

The correct option is (b) .