Chapter 4, Problem 4D.1ST

Interpretation Introduction

Interpretation:

The vapour pressure of benzene has to be determined when the amount of naphthalene is 0.75 mol instead of 1.5 mol.

Concept introduction:

Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.

Partial pressure of a gas in terms of its mole fraction and total pressure is,

`            ${\text{P}}_{\text{A}}\text{=}{\text{χ}}_{\text{A}}\text{×}{\text{P}}_{\text{TOTAL}}$

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.

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

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,

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