Question

State Raoult's law and obtain expression for lowering of vapour pressure when nonvolatile solute is dissolved.

Answer 1

Answer :

Raoult's law : It is defined as the vapor pressure of a solution of a non volatile solute is equal to the mole fraction of pure solvent and multiplied by the vapor pressure of the pure solvent at same temperature.

The expression for lowering of vapor pressure for non volatile solute :

vapor pressure of the solvent in solution = (Mole fraction of the solvent in the solution) × (vapor pressure of the pure solvent)               .............(1)

Now, if the solute is non volatile, it will not contribute to the total vapor pressure of the solution. Thus,

vapor pressure of the solution = vapor pressure of the solvent in the solution       ...............(2)

combining expression (1) and (2), we get

vapor pressure of the solution = (Mole fraction of the solvent in solution) × (vapor pressure of the pure solvent)        .............(3)

or in terms of symbols, we can write

$p_s=x+1\times p^o$

or we can write as,

$\frac{p_s}{p^o}=x_1$            ..............(4)

If the solution contains $n_2$ moles of the solute dissolved in $n_1$ moles of solvent, we have

Mole fraction of the solvent in solution,

$x_1=\frac{n_1}{n_1+n_2}$

Now substituting this value in equation (4), we get

$\frac{p_s}{p^o}= \frac{n_1}{n_1+n_2}$

Now subtracting each side from 1, we get

$1-\frac{p_s}{p^o}= 1-\frac{n_1}{n_1+n_2}$

By rearranging the the terms, we get

$\frac{p^o-p_s}{p^o}= \frac{n_2}{n_1+n_2}$

In this expression,

$\frac{p^o-p_s}{p^o}$ represent the relative lowering of vapor pressure.

$\frac{n_2}{n_1+n_2}$ represent the mole fraction of the solute in the solution.

$p^o-p_s$ represent the lowering of vapor pressure.

Answer 2

According to the Raoult’s law,

“The vapour pressure of a solvent above a solution is equal to the vapour pressure of the pure solvent at the same temperature scaled by the mole fraction of the solvent present will be equal to Psoluton = Csolvent * P0solvent.”

This is usually for the volatile components.