# Calculate the vapor pressure at 35°C of a solution made by dissolving 24.8 g of sucrose, C 12 H 22 O 31 , in 70.1 g of water. The vapor pressure of pure water at 35°C is 42.2 mmHg. What is the vapor-pressure lowering of the solution? (Sucrose is nonvolatile.)

### 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 12.67QP
Textbook Problem
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## Calculate the vapor pressure at 35°C of a solution made by dissolving 24.8 g of sucrose, C12H22O31, in 70.1 g of water. The vapor pressure of pure water at 35°C is 42.2 mmHg. What is the vapor-pressure lowering of the solution? (Sucrose is nonvolatile.)

Expert Solution
Interpretation Introduction

Interpretation:

Vapor pressure lowering of the sucrose solution has to be calculated.  Vapor pressure of the solution of 24.8 g naphthalene dissolved in 70.1 g of chloroform 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

Given

24.8 g of sucrose is dissolved in 70.1 g of water. Molar mass of sucrose and water are 342.3 g/mol and 18.02 g/mol respectively. Calculate the number of moles and then mole fraction of sucrose and water as follows –

No. of moles of sucrose mass of sucrosemolar mass of sucrose                                                24.8 g342.3 g/mol = 0.07245 molNo. of moles of water mass of watermolar mass of water                                              70.1 g18.02 g/mol = 3.890 molTotal no.of moles in solution  = 0

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