   Chapter 11, Problem 107AE

Chapter
Section
Textbook Problem

# The freezing point of an aqueous solution is − 2.79°C.a. Determine the boiling point of this solution.b. Determine the vapor pressure (in mm Hg) of this solution at 25°C (the vapor pressure of pure water at 25°C is 23.76 mm Hg).c. Explain any assumptions you make in solving parts a and b.

Interpretation Introduction

Interpretation: The boiling point and vapor pressure of the given aqueous solutions are should be calculated.

Concept introduction:

• Elevation of boiling point:

The boiling point of the solution is increases when the solute is dissolved in the solvent is called Elevation of boiling point. it is one of the colligative Properties thus,

ΔT=iKbmsolute......(1)ΔT is boiling-point elevationKbismolal boiling-point elevation constantmis molality of the soluteiisthevan't Hoff factor

• Depression in freezing point:

The freezing point the solution is decreases when the solute is dissolved in the solvent is called depression in freezing point. it is one of the colligative Properties thus,

ΔT=iKfmsolute......(2)ΔT is boiling-point elevationKfismolal freezing-point depression constantmis molality of the soluteiisthevan't Hoff factor

• Raoult's law:

The mole fraction of a solute is related to the vapor pressure of the solution thus,

Psolution=P°solventXsolvent......(3)Pisvapor pressureof the solutionsolventpressureof the solventXsolvent mole fraction ofsolvent

Explanation

Record the given data,

Freezing point of an aqueous solution =- 2.79°C

To calculate molality of the aqueous solution:

Molal boiling-point elevation constantof water =0.51°C/molMolal freezing-point elevation constantof water=1.86°C/mol

m=ΔTfKf=2.79°C1.86°C/molal=1.50molal

• The given values are plugging in to equation 1 and do some rearrangement to give molality of the aqueous solution.
• The molality of the aqueous solution is 1.50molal .

To calculate the boiling point of aqueous solution.

ΔT=Kbm=0.51°C/molal×1.50molal=0.77°C=100+0.77°C=100.077°C

• The calculated molality of the aqueous solution and molal boiling point elevation constant are plugging in to equation 1and do some rearrangement to give boiling point of the aqueous solution.
• The boiling point of aqueous solution is 100.077°C .

Record the given data,

Vapor pressure of pure water at 25°C=23.76 mm Hg

To calculate the vapor pressure of the given aqueous solution.

χwater=molwatermolofsolutionAssuming1

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