Question

The vapour pressure of benzene at a certain temperature is 640 mm Hg. A non-volatile non-electrolyte solid weighing 2.175 g is added to 39.0 g of benzene? The vapour pressure of the solution is 600 mm Hg. What is the molecular weight of the solid substance?

• A. $6.96\text{g}$
• B. $65.3\text{g}$
• C. $63.8\text{g}$
• D. None of these

Answer 1

The correct option is B $65.3\text{g}$

According to Raoult's law
$\frac{P^0-P_S}{P^0}=\frac{n}{n+N}$
Let, $m$ be the molecular mass of the solid substance.
$n=2.175/m$ (molar mass of solid substance = m)
$N=\frac{39}{78}=0.5$ (molar mass of benzene = $78\text{g/mol}$)
On substituting the values in above equation
$\frac{640-600}{640}=\frac{\frac{2.175}{m}}{\frac{2.175}{m}+0.5}=\frac{2.175}{2.175}+0.5m$
$m=\frac{2.175\times 16-2.175}{0.5}=65.25\text{g}$