Question

The vapour pressure of a dilute aqueous solution of glucose is 750 mm of Hg at 373 K. Calculate the mole fraction of the solute.
a) 0.013
b) 0.25
c) 0.968
d) 0.75

Answer 1

Hint: Mole fraction of a solute is simply defined as the ratio of the number of moles of the solute divided by the total number of moles present in the solution. Vapour pressure can be defined as the pressure that is formed by the vapor of the liquid over the surface of the liquid.
Complete step by step answer: Vapour pressure is the pressure that is exerted by a gas in equilibrium with a solid or liquid in a closed container at a given temperature is called the vapor pressure. The mole fraction of a solute is given by the following formula:
${ x }_{ 1\quad }=\quad \dfrac { { p }_{ 0 }\quad -\quad { p }_{ s } }{ { p }_{ 0 } }$ ----(1)
where, ${x}_{1}$ = Mole fraction of solute
${p}_{s}$ = Vapour pressure of Glucose
${p}_{0}$= vapour pressure of a pure solvent that is water = 760 mm

This formula is derived from Raoult's law which states that the partial pressure of each component of an ideal mixture of liquids is equal to the vapor pressure of the pure component multiplied by its mole fraction in the mixture.
Now, the value of vapour pressure given in the question is 750 mm. Now, substituting the value in equation --(1)

${ x }_{ 1\quad }=\quad \dfrac { 760-750 }{ 760 }$

$\implies {x}_{1} = 0.013$

Therefore, the mole fraction of the solute is 0.013.

Hence, option (a) is the correct answer.

Note: Temperature does not affect the determination of mole fraction. But it does affect the vapor pressure. As the temperature of a liquid or a solid increases, vapor pressure also increases and vice versa.