How many grams of sucrose must be added to 320g of water to lower the vapor pressure by 1.3mm Hg at ${{25}^{0}}C$? (Given: The vapor pressure of water at ${{25}^{0}}C$ is 23.8mm Hg and molar mass of sucrose is 324.3g/mol) Options:
(A) 21.5 g
(B) 140 g
(C) 363.36 g
(D) 160.12 g

Hint: Sucrose is a non-volatile solute. When a non-volatile solute is added the vapor pressure of the solution is changed. The vapor pressure of the solution is lower than the vapor pressure of pure solvent. The formula for relative lowering of vapor pressure is given below:
$\dfrac{{{P}^{0}}_{A}\text{ - }{{P}_{A}}}{{{P}_{A}}}\text{ = }{{x}_{solute}}$
Where,
${{P}^{0}}_{A}$ is the vapor pressure of pure solvent,
\[{{P}_{A}}\] is the vapor pressure of solution,
${{x}_{solute}}$is the mole fraction of solute.

Complete answer:
Colligative properties are the properties of solutions that depend on the ratio of the number of solute particles to the number of solvent molecules in a solution, and not on the nature of the chemical species present.
The number ratio can be related to the various units for concentration of a solution, for example, molarity, molality, normality etc.

The colligative properties are:
Relative lowering of vapor pressure Elevation of boiling point Depression of freezing point Osmotic pressure
When a non-volatile solute is dissolved in a liquid solvent, the vapor pressure of the solution becomes lower than the vapor pressure of the pure liquid solvent. The relative lowering of vapor pressure is defined as the ratio between lowering of vapor pressure and the vapor pressure of pure liquid solvent.
$\dfrac{{{P}^{0}}_{A}\text{ - }{{P}_{A}}}{{{P}_{A}}}\text{ = }{{x}_{solute}}$
It is given to us that vapor pressure of pure solvent is 23.8 mm of Hg and vapor pressure of solution is 22.3 mm of Hg. We need to find the number of moles of sucrose added.
Moles of water = $\dfrac{320}{18}\text{ = 17}\text{.7}$
\[\dfrac{1.5}{23.8}\text{ = }\dfrac{n}{17.7}\]
n = 1.115
The mass of sucrose needed:
n = $\dfrac{\text{mass of solute}}{\text{molar mass of solute}}$
mass of solute = 1.115 x 324.3 = 363.36 g

Therefore, the correct answer is option (C).

Note:
Van't Hoff factor is the ratio between the actual concentration of particles produced when the substance is dissolved and the concentration of a substance as per its mass. The value of the Van't Hoff factor is greater than 1 for dissociation of ionic compounds. The factor is used when the solute undergoes dissociation or association in the solvent.