# What is the total vapor pressure at 20°C of a liquid solution containing 0.30 mole fraction benzene, C 6 H 6 , and 0.70 mole fraction toluene, C 6 H 5 CH 3 ? Assume that Raoult’s law holds for each component of the solution. The vapor pressure of pure benzene at 20°C is 75 mmHg; that of toluene at 20°C is 22 mmHg.

### General Chemistry - Standalone boo...

11th Edition
Steven D. Gammon + 7 others
Publisher: Cengage Learning
ISBN: 9781305580343

### General Chemistry - Standalone boo...

11th Edition
Steven D. Gammon + 7 others
Publisher: Cengage Learning
ISBN: 9781305580343

#### Solutions

Chapter
Section
Chapter 12, Problem 12.94QP
Textbook Problem

## What is the total vapor pressure at 20°C of a liquid solution containing 0.30 mole fraction benzene, C6H6, and 0.70 mole fraction toluene, C6H5CH3? Assume that Raoult’s law holds for each component of the solution. The vapor pressure of pure benzene at 20°C is 75 mmHg; that of toluene at 20°C is 22 mmHg.

Expert Solution
Interpretation Introduction

Interpretation:

Total vapor pressure of the solution containing 0.30 mole fraction benzene and 0.70 mole fraction toluene has to be calculated.

Concept Introduction:

Vapor pressure of a substance is known as the pressure exerted by molecules on the vapor phase when they are in equilibrium with their actual phase which can be liquid or solid.

A solution is at least made up of two components.  Mole fraction of a component in the solution correlates to the ratio of number of moles of that component to the total number of moles.  It is expressed as,

Mole fraction = number of moles of a componenttotal number of moles in the solution

A substance is said to be volatile if it vaporizes readily at room temperature itself.  Such substances have high vapor pressure as most of its molecules tend to exist in vapor phase.  A substance is said to be non-volatile if it doesn’t vaporize spontaneously and remains stable.

Vapor pressure of a volatile solvent can be lowered by addition of a non-volatile solute. Raoult’s law deals with the vapor pressure of pure solvents and solution which states –

Partial pressure of solvent is equivalent to the product of vapor pressure of the solvent in its pure state and mole fraction of solvent in the solution.  It is expressed as,

PA = PA° XA

Where,

PA = Partial vapor pressure of solvent in solutionPA° = Vapor pressure of pure solventXA= mole fraction of solvent in the solution

When the solute is non-volatile, the vapor pressure of the whole solution is equal to PA.

The lowering of vapor pressure of the solvent due to the addition of non-volatile solute is expressed as,

ΔP = PA° XB

Where,

XB is the mole fraction of the solute.

### Explanation of Solution

Total vapor pressure of the solution is equivalent to the sum of vapor pressure of ethylene dibromide, ‘PB and propylene dibromide, ‘PT in the solution.

Given that mole fraction of benzene and toluene are 0.30 and 0.70 respectively.  Vapor pressure of benzene and toluene is 75 mmHg and 22 mmHg respectively.

Calculate PB and PT as follows –

PB = P°B(XB) = 75 mmHg×0.30 = 22

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