Question

Define Raoult's law. Establish an expression for calculating molar mass of solute on the basis of this law.

Hint:

Raoult's law is used to calculate molar mass and study colligative properties.

Answer 1

 Raoult's Law: The relative lowering of vapour pressure is proportional to the mole fraction of the solute: \[ \frac{P^0 - P}{P^0} = x_2 = \frac{n_2}{n_1 + n_2}, \] where \( P^0 \) is the vapour pressure of the pure solvent, \( P \) is the vapour pressure of the solution, \( n_1 \) and \( n_2 \) are moles of solvent and solute. 

Expression for Molar Mass: For dilute solutions, \( n_2 \ll n_1 \), so: \[ \frac{P^0 - P}{P^0} = \frac{w_2}{M_2} \cdot \frac{M_1}{w_1}. \] Rearranging: \[ M_2 = \frac{w_2 M_1}{w_1 \cdot \frac{P^0 - P}{P^0}}. \]