Question

The vapor pressure of a solvent decreased by 10 mm of Hg when a non-volatile solute was added to the solvent. The mole fraction of the solute in the solution is 0.2. What would be the mole fraction of the solvent if the decrease in vapor pressure is 20 mm of Hg?

(a) 0.1
(b) 0.2
(c) 0.3
(d) 0.4

Answer 1

To find the new mole fraction of the solvent with a 20 mm Hg decrease in vapor pressure, we halve the original solvent mole fraction of 0.8, resulting in a mole fraction of 0.4, which corresponds to option (d).

Step-by-step explanation:

The student's question concerns the colligative properties of solutions, specifically the lowering of vapor pressure due to the presence of a non-volatile solute. According to Raoult's law, the vapor pressure of a solvent in a solution is proportional to the solvent's mole fraction. In the given problem, the decrease of vapor pressure is directly related to the mole fraction of the solute; a larger presence of solute molecules will lead to a greater decrease in vapor pressure.

When the mole fraction of the solute is 0.2, the vapor pressure decreases by 10 mm Hg. Since the relationship between mole fraction and vapor pressure decrease is linear, a 20 mm Hg decrease would correspond to doubling the amount of solute, meaning the solvent mole fraction would be halved. Therefore, if the original solvent mole fraction was 0.8 (since the solute fraction was 0.2), then the new solvent mole fraction would be 0.8 / 2 = 0.4 to achieve a 20 mm Hg decrease.