Question

Explain Raoult's law for solutions containing non-volatile solute in volatile solvent. Derive mathematical expression for this law.

Hint:

Raoult's law helps explain colligative properties like boiling point elevation and freezing point depression.

Answer 1

Step 1: Statement of Raoult’s Law: Raoult’s law states that the partial vapor pressure of a solvent in a solution is directly proportional to its mole fraction. \[ P_A = X_A P_A^0 \] where \( P_A \) is the partial vapor pressure of the solvent, \( X_A \) is its mole fraction, and \( P_A^0 \) is the vapor pressure of the pure solvent. 

Step 2: Mathematical Derivation: For a solution containing a non-volatile solute: \[ X_A + X_B = 1 \] \[ X_A = 1 - X_B \] Substituting in Raoult’s law: \[ P_A = (1 - X_B) P_A^0 \] 

Step 3: Relative Lowering of Vapor Pressure:} \[ \frac{P_A^0 - P_A}{P_A^0} = X_B \] Thus, the relative lowering of vapor pressure is equal to the mole fraction of the solute.