Question

The Vapour pressure of water at 20 C is 17.54mm. when 20g of a non-ionic substance is dissolved in 100g of water, the vapour pressure is lowered by 0.30mm. What is the molecular weight of the substances?
A.150.2
B.206.89
C.315.2
D.100.8

Answer 1

Hint: So the question is based on Raoult’s law. According to Raoult’s law the vapor pressure of the given substance or the component is equal to the mole fraction of the same component present in the solution which is multiplied by the vapor pressure of the component in pure state. It is used to determine the estimated quantity of each component in liquid or solid mixture to the total pressure exerted by the system.

Complete step by step answer:
Given, vapour pressure of pure water, \[{{P}_{o}}\] , is 17.54 mm. Therefore, the vapour pressure of the solution will be vapour pressure of pure water subtracted by the amount of vapour pressure lowered which is,
17.54-0.30 = 17.24.
The weight of the non-ionic substance is 20g and that of water is 100g. The molecular weight of water is 18g/mol. According to relative lowering of vapour pressure formula, the lowering in vapour pressure divided by vapour pressure of solution is equal to mole fraction of solute.
\[{{P}_{o}}\] = 17.54mm
$\therefore$ \[{{P}_{s}}\] = 17.54 - 0.30 = 17.24mm
Also, we have,
w(amount of solute) = 20g
W(amount of water) = 100g
Molecular weight of water = 18
Molecular weight of substance = ?
Thus use the following equation to derive the molecular weight of the substance
\[\dfrac{{{P}_{o}}-{{P}_{s}}}{{{P}_{s}}}\] \[=\dfrac{w\times M}{mW}\]
\[\dfrac{17.58-17.24}{17.24}=\dfrac{20\times 18}{m\times 100}\]
M=206.88
Hence option B is the correct one.

Additional Information:
In chemistry, colligative properties are those 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 assumption that solution properties are independent of nature of solute particles is exact only for ideal solutions, and is approximate for dilute real solutions. In other words, colligative properties are a set of solution properties that can be reasonably approximated by the assumption that the solution is ideal.

Note:
Henry law is the law which is applied to only sufficient dilute solutions, whereas Raoult law is applicable for those substances which are in liquid phase. Raoult law is applicable to the solutions which are having non volatile solutions. Raoult law is not applicable to the solutes which get dissociated or associated in solutions.