Question

State Raoult’s law.
The vapour pressure of pure benzene at a certain temperature is 0.850bar. a non-volatile, non-electrolyte solid weighing 0.5g when added to 39.0g of benzene (molar mass 78g/mol). Vapour pressure of the solution, then is 0.845 bar. What is the molar mass of the substance?

Answer 1

Hint: When the solvent is a liquid then liquids solutions are formed and solute can be a gas, a liquid, or a solid. Liquid solutions or solids in liquid may contain one or more volatile components. Raoult’s law discussed the properties of binary solutions only which contain two components named as liquids in liquids and solids in liquids.

Complete step by step solution:
The quantitative relationship between mole fraction and vapour pressure of each component in the solution given by Raoult’s law which states that for a solution of volatile liquids, the partial vapour pressure of each component of the solution is directly proportional to its mole fraction present in solution.
For non-volatile solute, the Raoult’s law states that the relative lowering of the vapour pressure of a solution containing a non-volatile solute is equal to the mole fraction of the solute in the solution.
According to Raoult’s law,
$\dfrac{{{p}^{o}}-{{p}_{s}}}{{{p}^{0}}}=\dfrac{{{n}_{A}}}{{{n}_{A}}+{{n}_{B}}}$ ----- (1)
${{p}^{o}}$ = vapour pressure of pure benzene = 0.850 bar
${{p}_{s}}$ = vapour pressure of the solution = 0.845 bar
Let x be the molar mass of the solids substance which is a non-volatile, non-electrolyte solid added to pure benzene.
No of moles of solid substance, ${{n}_{A}}$ = weight of solid substance/molar mass of solid substance = $\dfrac{0.5}{x}$
No of moles of pure benzene, ${{n}_{B}}$ = (weight of pure benzene)/(molar mass of pure benzene) = $\dfrac{39.0g}{78g/mol}=0.5moles$
 Substitute the above values in equation (1),
$\dfrac{0.850-0.845}{0.850}=\dfrac{(\dfrac{0.5}{x})}{(\dfrac{0.5}{x})+0.5}$
$\dfrac{0.5}{0.5+x}=\dfrac{1}{1+x}$
$\Rightarrow x=\dfrac{0.850}{0.005}-1=169 g/mol$
Hence, the molar mass of solid substance = 169g/mol

Note: Raoult’s law is quite similar to ideal gas laws and this law assumes that the intermolecular forces which exist between different molecules. The exception of this law is only for solutions and also applied for non-ideal solutions.