Chemistry: The Molecular Nature of Matter and Change - Standalone book
Chemistry: The Molecular Nature of Matter and Change - Standalone book
7th Edition
ISBN: 9780073511177
Author: Martin Silberberg Dr., Patricia Amateis Professor
Publisher: McGraw-Hill Education
Question
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Chapter 13, Problem 13.74P
Interpretation Introduction

Interpretation:

The molality, molarity and mole fraction of NH3 is to be determined.

Concept introduction:

Molality is the measure of the concentration of solute in the solution. It is the amount of solute that is dissolved in one kilogram of the solvent. It is represented by m and its unit is moles per kilograms. The solute is the substance that is present in a smaller amount and solvent is the substance that is present in a larger amount.

The formula to calculate the molality of the solution is as follows:

Molality=amount(mol)ofsolutemass(kg)ofsolvent (1)

Molarity is defined as the number of moles of solute that are dissolved in one litre of solution. It is represented by M and its unit is mol/L.

The formula to calculate the molarity of the solution is as follows:

Molarity=amount(mol)ofsolutevolume (L)ofsolution (2)

The mole fraction is defined as the ratio of the number of moles of solute to the total number of moles in the mixture. It is represented by X.

The formula to calculate the mole fraction is as follows:

Molefraction(X)=amount(mol)ofsoluteamount(mol)ofsolute+amount(mol)ofsolvent (3)

Expert Solution & Answer
Check Mark

Answer to Problem 13.74P

The molality, molarity and mole fraction of the given solution of NH3 is 5.11m, 4.53M and 0.0843.

Explanation of Solution

The formula to calculate the molality of the aqueous solution of NH3 is as follows:

Molality=amount(mol)ofNH3mass(kg)ofH2O (4)

The formula to calculate the moles of a compound is as follows:

Moles of compound=(given massmolar mass of compound) (5)

The formula to calculate the moles of NH3 is as follows:

MolesofNH3=given mass molar mass ofNH3(mass%ofNH3100%ofsolution) (6)

Substitute 100g for the given mass, 8% for the mass percent of NH3 and 17.03g/mol for the molar mass of NH3 in equation (6).

AmountofNH3=(100gsolution)(8%NH3100%solution)(1molNH317.03gNH3)=0.469759mol

The formula to calculate the mass of H2O is as follows:

MassofH2O=(Massofsolution-MassofNH3) (7)

Substitute 100g for the mass of solution and 8g for the mass of NH3 in equation (7).

MassofH2O=(100g-8g)(1kg103g)=0.092kg

Substitute 0.469759mol for the amount of NH3 and 0.092kg for the mass of H2O in equation (4).

MolalityofNH3=(0.469759mol)(0.092kg)=5.106076m=5.11m

The formula to calculate the molarity of the aqueous solution of NH3 is as follows:

MolarityofNH3=amount(mol)ofNH3volume (L)ofsolution (8)

The formula to calculate the volume of the solution is as follows:

Volumeofsolution=Mass of solutionDensity of solution (9)

Substitute 100g for the mass of solution and 0.9651g/mL for the density of the solution in equation (9).

Volumeofsolution=(100gsolution)(1mL0.9651gsolution)(103L1mL)=0.103616 L

Substitute 0.469759mol for the amount of NH3 and 0.103616 L for the volume of solution in equation (8).

MolarityofNH3=0.469759mol0.103616 L=4.53365M=4.53M

The formula to calculate the mole fraction of NH3 is as follows:

MolefractionofNH3=amount(mol)ofNH3amount(mol)ofNH3+amount(mol)ofH2O (10)

Substitute 92g for the given mass and 18.02g/mol for the molar mass in equation (5).

AmountofH2O=(92g)(1molH2O18.02gH2O)=5.1054mol

Substitute 0.469759mol for the amount of NH3 and 5.1054mol for the amount of H2O in equation (10).

MolefractionofNH3=0.469759mol(0.469759mol)+(5.1054mol)=1.80723×103mol5.57516mol=0.084259=0.0843

Conclusion

The molality, molarity and mole fraction of the given solution of NH3 is 5.11m, 4.53M and 0.0843.

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Chapter 13 Solutions

Chemistry: The Molecular Nature of Matter and Change - Standalone book

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