Chapter 4, Problem 4E.1E

Interpretation Introduction

Interpretation:

The molar mass of the compound in the given solution has to be determined.

Concept introduction:

Colligative properties: properties of solutions which having influence on the concentration of the solute in it. Colligative properties are,

• Decrease in the vapour pressure
• Increase in the boiling point
• Decline in the freezing point
• Osmotic pressure

Raoult’s law: The vapour pressure of the solvent over the solution ${\text{P}}_{\text{solvent}}$ is proportional to the mole fraction of the solvent. The ideal solution obeys the Raoult’s law.

$\begin{array}{l}{\text{P}}_{solvent}\text{= }{\chi }_{solvent}{\text{P}}_{solvent}^{\circ }\text{,}\\ \text{where,}{\text{P}}_{solvent}\text{is}\text{the}\text{vapor pressure of the solvent over the solution,}\\ {\chi }_{solvent}\text{is mole fraction of solvent in solution, }\\ {\text{P}}_{solvent}^{\circ }\text{ is the vapor pressure of the pure solvent}\text{.}\end{array}$

This equation can also written in the following form too,

$\frac{{\text{P}}_{\text{A}}^{\text{o}}{\text{-P}}_{\text{A}}}{{\text{P}}_{\text{A}}^{\text{o}}}\text{=}\frac{{\text{W}}_{\text{B}}}{{\text{M}}_{\text{B}}}\text{×}\frac{{\text{M}}_{\text{A}}}{{\text{W}}_{\text{A}}}\boxed{\begin{array}{l}\text{where,}\\ {\text{P}}_{\text{A}}^{\text{o}}\text{-}\text{vapour}\text{pressure}\text{of}\text{pure}\text{solvent}\\ {\text{P}}_{\text{A}}\text{-}\text{vapour}\text{pressure}\text{of}\text{solution}\\ {\text{W}}_{\text{B}}\text{-}\text{Mass}\text{of}\text{solute}\\ {\text{W}}_{\text{A}}\text{-}\text{Mass}\text{of}\text{solvent}\\ {\text{M}}_{\text{B}}\text{-}\text{Molar}\text{mass}\text{of}\text{solute}\\ {\text{M}}_{\text{A}}\text{-}\text{Molar}\text{mass}\text{of}\text{sovent}\end{array}}$

A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture. Equation for mole fraction of a molecule in a mixture of three molecules (A, B and C) is,

  $\text{molecule}\text{fraction}\text{of}\text{A,}\text{(}{\text{χ}}_{\text{A}}\text{) }\text{=}\frac{\text{numbers}\text{of moles of}\text{molecule A}{\text{(n}}_{\text{A}}\text{)}}{\text{total number of moles}{\text{(n}}_{\text{A}}{\text{+n}}_{\text{B}}{\text{+n}}_{\text{C}}\text{) }}$