   Chapter 13, Problem 48PS

Chapter
Section
Textbook Problem

To make homemade ice cream, you cool the milk and cream by immersing the container in ice and a concentrated solution of rock salt (NaCl) in water. If you want to have a water-salt solution that freezes at −10. °C, what mass of NaCl must you add to 3.0 kg of water? (Assume the van’t Hoff factor, i, for NaCl is 1.85.)

Interpretation Introduction

Interpretation: The mass of NaCl added has to be determined.

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

Decline in the freezing point is huge when solute is an electrolyte than when solute is nonelectrolyte. Therefore, change in freezing point is calculated by using the equation,

ΔTfp=Kfpmsolutei

where,

Kfp is the molal freezing point depression constant.

i is van’t Hoff factor

van’t Hoff factor, i: it is the ration between change in in freezing point measured and change in in freezing point calculated. It indicates the total number of ions that are produced.

Molality (m): Molality is the number of moles of solute present in one kilogram of solvent.

Molality (m) =Numberofmolesofsolute1kgofsolvent

Explanation

The mass of NaCl added is calculated.

Given,

ΔT=0.100C

i=1.85

Molar mass of NaCl is 58.44g/mol

Mass of water is 3kg

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

Change in freezing point is calculated by using the equation,

ΔTfp=Kfpmsolutei

Hence,

The concentration is calculated by,

Concentration,cmsolute=ΔTfpKbp×i=(0.100C)(1.860C/m)×(1.85)=2

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