   Chapter 13, Problem 58GQ

Chapter
Section
Textbook Problem

A 10.7 m solution of NaOH has a density of 1.33 g/cm3 at 20 °C. Calculate the following: (a) the mole fraction of NaOH (b) the weight percent of NaOH (c) the molarity of the solution

(a)

Interpretation Introduction

Interpretation: The mole fraction of NaOH solution 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

Molarity (M): Molarity is number of moles of the solute present in the one liter of the solution.

Molarity (M) =Numberofmolesofsolute1literofsolution

Density is calculated by the equation,

Density=massvolume

Explanation

Given,

Molar mass of water is 18.02 g/mol

Molality of the solution is 10.7m

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

Numberofmole=GivenmassofthesubstanceMolarmass

Number of moles of water is,

nwater=1000g18.02 g/mol=55

(b)

Interpretation Introduction

Interpretation: The weight percent of NaOH solution 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

Molarity (M): Molarity is number of moles of the solute present in the one liter of the solution.

Molarity (M) =Numberofmolesofsolute1literofsolution

Density is calculated by the equation,

Density=massvolume

(c)

Interpretation Introduction

Interpretation: The molarity of NaOH solution 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

Molarity (M): Molarity is number of moles of the solute present in the one liter of the solution.

Molarity (M) =Numberofmolesofsolute1literofsolution

Density is calculated by the equation,

Density=massvolume

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