Question

State and prove Raoult's law for non-volatile solute in volatile solvent. Also give any two limitations of Raoult's law.

Answer 1

The vapour pressure of a solution of a non-volatile solute is equal to the vapour pressure of the pure solvent at that temperature multiplied by its mole fraction.

In equation form:

$p_T=p_B^0.{\chi }_B$

In this equation, $p_B^0$ is the vapour pressure of the pure solvent at a particular temperature, $p_T$ is the total pressure of the solution, ${\chi }_B$ is the mole fraction of the solvent.

For a solution of a volatile solute (A) and solvent (B) total pressure is sum of the partial pressure of the two as:

$p_T=p_A^0.{\chi }_A+p_B^0.{\chi }_B$

As ${\chi }_A++{\chi }_B=1$ or ${\chi }_A=1-{\chi }_B$

or $p_T=p_A^0.(1-{\chi }_B)+p_B^0.{\chi }_B$

$p_T=p_A^0+(p_B^0-p_A^0).{\chi }_B$

For non-volatile solute $p_A^0=0$

thus $p_T=p_B^0.{\chi }_B$

Limitations of Raoult's law:

1. Intermolecular forces between the solvent and solute components shoul be similar to those betweenindividual molecules

A_A=B-B=A-B

2. The gaseous phase are assumed to behave ideal where ideal gas law can be applied.