   # You have an equimolar mixture of the gases SO 2 and O 2 , along with some He, in a container fitted with a piston. The density of this mixture at STP is 1.924 g/L. Assume ideal behavior and constant temperature and pressure. a. What is the mole fraction of He in the original mixture? b. The SO 2 and O 2 react to completion to form SO 3 . What is the density of the gas mixture after the reaction is complete? ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 8, Problem 154CP
Textbook Problem
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## You have an equimolar mixture of the gases SO2 and O2, along with some He, in a container fitted with a piston. The density of this mixture at STP is 1.924 g/L. Assume ideal behavior and constant temperature and pressure.a. What is the mole fraction of He in the original mixture?b. The SO2 and O2 react to completion to form SO3. What is the density of the gas mixture after the reaction is complete?

a)

Interpretation Introduction

Interpretation: The mole fraction of He in the original mixture containing SO2, O2 and He should be determined, if the density of original mixture is 1.924g/L at constant temperature and pressure.

Concept introduction:

• Equation for density and number of moles are,

Density=MassVolume  and  Number of moles=MassMolarmass

Therefore,

According to ideal gas equation for molar mass in terms of density is,

Molarmass=Density×R×Temperaturepressure

• Mass of a substance from its number of moles is,

Number of moles×Molecularmass in grams=takenMass

• Equation for mole fraction of a molecule in a mixture of three molecules (A, B and C) is,
• moleculefractionofA,(χA=numbersof moles ofmolecule A(nA)total number of moles(nA+nB+nC

• Balanced equation of a reaction is written according to law of conservation of mass.
• Limiting reagent: limiting reagent is a reactant, which consumes completely in the chemical reaction. The quantity of the product depends on this limiting reagent, it can be determined with the help of balanced chemical equation for the reaction.
• Mole ratios between the reactant and products of a reaction are depends upon the coefficients of respective reactant in a balanced chemical equation.
• Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.

To determine: The mole fraction of He in the original mixture containing SO2, O2 and He and the density of gas mixture after completion of given reaction between SO2 and O2

### Explanation of Solution

To find: the total molar mass of given original mixture containing SO2, O2 and He.

The total molar mass of given original mixture containing SO2, O2 and He is 43.13g.

The given data’s of the given original mixture are,

The density of given mixture is given as 1.924g/L.

Temperature = 273.2 K

Pressure =1atm

According to ideal gas equation for molar mass in terms of density is,

Molarmass=Density×R×Temperaturepressure

Therefore, the molar mass of given original mixture is,

Molarmass=1.924g/L×0.08206Latm/Kmol×273.2K1atm=43.13g/mol

To find: the number of moles of SO2, O2 and He in the original mixture.

Assumes the total number of moles in the original mixture is 1 mole.

The number of moles of SO2 in the original mixture is 0.4443mol.

The number of moles of O2 in the original mixture is 0.4443mol.

The number of moles of He in the original mixture is 0.1114mol.

Let’s take the number of moles of SO2 and O2 are x, since the both are equimolar and the number of moles of He is z.

The total number of moles is 1 mole.

Therefore,

nSO2+nO2+nHe=1mol Equation_1

x+x+z=1mol Equation_1

The total molar mass of given original mixture containing SO2, O2 and He is calculated as 43.13g.

The molar mass of SO2, O2 and He are 64g, 32g and 4g respectively

b)

Interpretation Introduction

Interpretation: The density of gas mixture after completion of given reaction between SO2 and O2 should be determined, if the density of original mixture is 1.924g/L at constant temperature and pressure.

Concept introduction:

• Equation for density and number of moles are,

Density=MassVolume  and  Number of moles=MassMolarmass

Therefore,

According to ideal gas equation for molar mass in terms of density is,

Molarmass=Density×R×Temperaturepressure

• Mass of a substance from its number of moles is,

Number of moles×Molecularmass in grams=takenMass

• Equation for mole fraction of a molecule in a mixture of three molecules (A, B and C) is,
• moleculefractionofA,(χA=numbersof moles ofmolecule A(nA)total number of moles(nA+nB+nC

• Balanced equation of a reaction is written according to law of conservation of mass.
• Limiting reagent: limiting reagent is a reactant, which consumes completely in the chemical reaction. The quantity of the product depends on this limiting reagent, it can be determined with the help of balanced chemical equation for the reaction.
• Mole ratios between the reactant and products of a reaction are depends upon the coefficients of respective reactant in a balanced chemical equation.
• Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.

To determine: The density of gas mixture after completion of given reaction between SO2 and O2

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