Chapter 17, Problem 105AE

Interpretation Introduction

Interpretation:

The mole fraction of pentane in the solution phase of a pentane-hexane mixture needs to be deduced given that its mole fraction in the vapor phase in 0.15.

Concept Introduction:

Raoult's Law states that the vapour pressure (P_solvent) of a solvent above a solution is directly proportional to its mole fraction in the solution phase (X_solvent), i.e.

  ${\text{P}}_{\text{solvent}}{\text{= X}}_{\text{sovent}}{\text{× P}}_{\text{solvent}}^{\text{0}}\text{ -----(1)}$

Here,

  ${\text{P}}_{\text{solvent}}^{\text{0}}$ is the vapor pressure of the pure solvent.

For a system with more than one solvent, the above equation gives the total pressure of the solution:

  ${\text{P}}_{\text{total}}{\text{= X}}_{\text{solvent(1)}}{\text{P}}_{\text{solvent(1) }}^{\text{0}}{\text{+ X}}_{\text{solvent(2)}}{\text{P}}_{\text{solvent(2) }}^{\text{0}}\text{ + }\mathrm{....}\text{ ------(2)}$

The mole fraction of a solvent in the vapour phase (Y_solvent), is given by the ratio of its vapour pressure(P_solvent), to the total pressure (P_total), i.e.

  ${\text{Y}}_{\text{solvent}}\text{ = }\frac{{\text{P}}_{\text{solvent}}}{{\text{P}}_{\text{total}}}\text{ -----(3)}$