Question

The vapour pressure of a solution of a non-volatile solute B in a solvent A is 95% of the vapor pressure of the solvent at the same temperature. If the molecular weight of the solvent is 0.3 times the molecular weight of the solute, what is the ratio of the weight of solvent to solute?
A. 0.15
B. 5.7
C. 0.2
D. None of these

Answer 1

Hint: This question can be solved by the mathematical expression of Raoult's law where the vapour pressure of the substance is equal to the mole fraction of the substance present in the solution multiplied with the vapour pressure of the substance in pure form.

Complete step by step answer:
Given,
The vapour pressure of a solution of a non-volatile solute B is 95%
The ratio of molecular weight of solvent with the solute is 0.3 times.
Let assume the vapour pressure of solvent be 100 as the vapour pressure of solution is 95.
The Raoult's law states that the vapour pressure of the substance at a given temperature is equal to the mole fraction of the substance present in the solution multiplied with the vapour pressure of the substance in pure form.
The formula for calculating the Raoult's law is shown below.
\[\dfrac{{{P^0} - {P_s}}}{{{P_s}}} = \dfrac{w}{m} \times \dfrac{M}{W}\]
Where,
\[{P^0}\] is the vapour pressure of solvent.
\[{P_s}\] is the vapour pressure of pure solution.
M is the molecular weight of solvent
m is the molecular weight of solute
W is the mass of solvent
w is the mass of solute
Substitute the values in the above equation.
\[\Rightarrow \dfrac{{100 - 95}}{{95}} = \dfrac{w}{W} \times 0.3\]
\[\Rightarrow \dfrac{W}{w} = 0.3 \times \dfrac{{95}}{5}\]
\[\Rightarrow \dfrac{W}{w} = 5.7\]
The ratio of weight of solvent to weight of solute is 5.7.
Therefore, the correct option is B.

Note:
Make sure to assume the vapour pressure of the solvent from the given percentage of vapour pressure of solution. The mole fraction is calculated as the number of moles of solute divided by total number of moles of solution where number of moles is calculated by dividing weight by molecular weight.