Question

The vapour pressure of a dilute aqueous solution of glucose is 750 mm of Hg at 373K. Calculate the mole fraction of the solute.
A.0.013
B.0.25
C.0968
D.0.75

Answer 1

Mole Fraction can be understood as a quantity which represents the ration of the number of molecules of a given solute present in the solution, to the total number of molecules present in the entire solution. In a way, it represents the molecular concentration of a solute in the solution.

Complete Step-by-Step Answer:
Before we move forward with the solution of the given question, let us first understand some important concepts.
If ‘n’ represents the number of moles of solute and ‘m’ represent the number of moles of solvent, then:
Mole fraction of solute $= \dfrac{n}{{n + m}}$
Now in a situation where only the vapour pressures are given, we can use Raoult’s Law. Raoult’s Law states that the vapour pressure of a given solution is equivalent to the product of the vapour pressure of the pure solvent and the mole fraction of the solvent present. If ${P_0}$ is the original vapour pressure and ${P_s}$ is the lowered vapor pressure of the solution, and the mole fraction of the solvent is represented by ${\chi _{solvent}}$ , then,
${P_s} = {\chi _{solvent}}{P_0}$
Now, we know that the sum of mole fractions of all constituents of a given solution is 1, then the mole fraction of the solute can be calculated as:
Mole fraction of solute $= \dfrac{{{P_0} - {P_s}}}{{{P_0}}}$
Where ${P_0}$ is the original vapour pressure and ${P_s}$ is the lowered vapor pressure of the solution
Hence, the mole fraction of the given solute can be calculated as:
Mole fraction of solute $= \dfrac{{{P_0} - {P_s}}}{{{P_0}}}$
Mole fraction of solute $= \dfrac{{760 - 750}}{{760}}$
Here, ${P_0}$ = 760 because the vapour pressure of pure water (in this case the solvent) is 760 mm of Hg
Mole fraction of solute = 0.013
Hence, Option A is the correct option

Note: Raoult's Law only works for ideal solutions. "An ideal solution shows thermodynamic mixing characteristics identical to those of ideal gas mixtures [except] ideal solutions have intermolecular interactions equal to those of the pure components."