   Chapter 13, Problem 89IL

Chapter
Section
Textbook Problem

A solution of 5.00 g of acetic acid in 100. g of benzene freezes at 3.37 °C. A solution of 5.00 g of acetic acid in 100. g of water freezes at −1.49 °C. Find the molar mass of acetic acid from each of these experiments. What can you conclude about the state of the acetic acid molecules dissolved in each of these solvents? Recall the discussion of hydrogen bonding in Section 11.3, and propose a structure for the species in benzene solution.

Interpretation Introduction

Interpretation: The molar mass of acetic acid in benzene and in water is to be determined. The state of acetic acid in both solutions is to be explained and the structure of acetic acid in benzene is to be drawn.

Concept introduction:

Colligative properties: Properties of solutions which having influence on the concentration of the solute in it. Colligative properties are,

• Decrease in the vapor pressure
• Increase in the boiling point
• Decline in the freezing point
• Osmotic pressure

Change in freezing point is calculated by using the equation,

ΔTfp=Kfpmsolute

where,

Kfp is the molal freezing point depression constant.

The number of moles of any substance can be determined using the equation

Numberofmole=GivenmassofthesubstanceMolarmass

Explanation

The molar mass of acetic acid in benzene and in water is calculated.

Given,

Freezingpointofbenzene=5.5oCFreezingpointofsolution=3.37oCΔT=2.130C

Mass of acetic acid in benzene is 5.0g

Mass of benzene is 100g=0.100kg

Molal freezing point depression constant of benzene is 5.120C/m

Freezingpointofwater=0oCFreezingpointofsolution=1.49oCΔT=1.49oC

Mass of acetic acid in water is 5.0g

Mass of water is 100g=0.100kg

Molal freezing point depression constant of water is 1.860C/m

Change in freezing point is calculated by using the equation,

ΔTbp=Kbpmsolute

Hence,

The concentration acetic acid in benzene is calculated by,

Concentration,msolute=ΔTbpKbp=(2.130C)(5.120C/m)=0.416m

The amount of acetic acid in benzene is,

(0.416m1kg)(0.100kg)=0.0416mol

The number of moles of any substance can be determined using the equation

Numberofmole=GivenmassofthesubstanceMolarmass

Therefore,

The molar mass of acetic acid in benzene is,

Molarmass=GivenmassofthesubstanceNumberofmole=5

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