   Chapter 13, Problem 56GQ

Chapter
Section
Textbook Problem

Making homemade ice cream is one of life’s great pleasures. Fresh milk and cream, sugar, and flavorings are churned in a bucket suspended in an ice-water mixture, the freezing point of which has been lowered by adding salt. One manufacturer of home ice cream freezers recommends adding 2.50 lb (1130 g) of salt (NaCl) to 16.0 lb of ice (7250 g) in a 4-qt freezer. For the solution when this mixture melts, calculate the following: (a) the weight percent of NaCl (b) the mole fraction of NaCl (c) the molality or the solution

(a)

Interpretation Introduction

Interpretation: The weight percentage of NaCl has to be determined.

Concept introduction:

Mole fraction: Amount of that component divided by the total amount of all of the components of the mixture ( nA +  nB +  n...).

Mole fraction of A (χA)= nA nA +  nB +  n...

Weight percent: The mass of one component divided by the total mass of the mixture, multiplied by 100%

weight % A = Mass of A Mass of A + Mass of B + Mass of C + ...×100%

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

Numberofmole=GivenmassofthesubstanceMolarmass

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

Molality (m) =Numberofmolesofsolute1kgofsolvent

Explanation

Given,

Given mass of NaCl is 1130g

Given mass of ice is 7250g=7.25kg

Weight percentage of NaCl is calculated,

Weight percentageofNaClMass of NaCl Mass of NaCl + Mass of ice

(b)

Interpretation Introduction

Interpretation: The mole fraction of NaCl has to be determined.

Concept introduction:

Mole fraction: Amount of that component divided by the total amount of all of the components of the mixture ( nA +  nB +  n...).

Mole fraction of A (χA)= nA nA +  nB +  n...

Weight percent: The mass of one component divided by the total mass of the mixture, multiplied by 100%

weight % A = Mass of A Mass of A + Mass of B + Mass of C + ...×100%

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

Numberofmole=GivenmassofthesubstanceMolarmass

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

Molality (m) =Numberofmolesofsolute1kgofsolvent

(c)

Interpretation Introduction

Interpretation: The molality of the solution of NaCl has to be determined.

Concept introduction:

Mole fraction: Amount of that component divided by the total amount of all of the components of the mixture ( nA +  nB +  n...).

Mole fraction of A (χA)= nA nA +  nB +  n...

Weight percent: The mass of one component divided by the total mass of the mixture, multiplied by 100%

weight % A = Mass of A Mass of A + Mass of B + Mass of C + ...×100%

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

Numberofmole=GivenmassofthesubstanceMolarmass

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

Molality (m) =Numberofmolesofsolute1kgofsolvent

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