   # The partial pressure of CH 4 ( g ) is 0.175 atm and that of O 2 ( g ) is 0.250 atm in a mixture of the two gases. a. What is the mole fraction of each gas in the mixture? b. If the mixture occupies a volume of 10.5 L at 65°C, calculate the total number of moles of gas in the mixture. c. Calculate the number of grams of each gas in the mixture. ### Chemistry

9th Edition
Steven S. Zumdahl
Publisher: Cengage Learning
ISBN: 9781133611097

#### Solutions

Chapter
Section ### Chemistry

9th Edition
Steven S. Zumdahl
Publisher: Cengage Learning
ISBN: 9781133611097
Chapter 5, Problem 89E
Textbook Problem
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## The partial pressure of CH4(g) is 0.175 atm and that of O2(g) is 0.250 atm in a mixture of the two gases.a. What is the mole fraction of each gas in the mixture?b. If the mixture occupies a volume of 10.5 L at 65°C, calculate the total number of moles of gas in the mixture.c. Calculate the number of grams of each gas in the mixture.

a)

Interpretation Introduction

Interpretation: The total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture is needed to be determined if the partial pressure of CH4 is 0.175atm and O2 is 0.250atm .

Concept introduction:

• Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.

Partial pressure of a gas in terms of its mole fraction and total pressure is,

 PA=χA×PTOTAL

• A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture.

• The number of moles of molecule can be find out by using its mole fraction,
• numbersof moles ofmolecule A(nA)=moleculefractionofA,(χA×total number of moles

• Number of grams of a substance from its number of moles is,

Number of moles×Molecularmass in grams=Numberofgrams

• Total number of moles of gases in the mixture of gases can be determined by using ideal gas equation.

According to ideal gas equation,

Total numberofmoles=Total pressure×VolumeR×Temperature

To determine: the total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture.

### Explanation of Solution

To find: the mole fractions of CH4 and O2 in the given mixture if the partial pressure of CH4 is 0.175atm and O2 is 0.250atm .

Mole fraction of CH4 is 0.412 .

Mole fraction of O2 is 0.588 .

The partial pressure of CH4 is given as 0.175atm

The partial pressure of O2 is given as 0.250atm .

Therefore, the total pressure of the mixture is,

0.175atm+0.250atm=0.425atm

Equation for finding mole fraction from partial pressure and total pressure is,

χA=PAPTOTAL

Therefore

b)

Interpretation Introduction

Interpretation: The total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture is needed to be determined if the partial pressure of CH4 is 0.175atm and O2 is 0.250atm .

Concept introduction:

• Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.

Partial pressure of a gas in terms of its mole fraction and total pressure is,

PA=χA×PTOTAL

• A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture.

• The number of moles of molecule can be find out by using its mole fraction,
• numbersof moles ofmolecule A(nA)=moleculefractionofA,(χA×total number of moles

• Number of grams of a substance from its number of moles is,

Number of moles×Molecularmass in grams=Numberofgrams

• Total number of moles of gases in the mixture of gases can be determined by using ideal gas equation.

According to ideal gas equation,

Total numberofmoles=Total pressure×VolumeR×Temperature

To determine: the total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture.

c)

Interpretation Introduction

Interpretation: The total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture is needed to be determined if the partial pressure of CH4 is 0.175atm and O2 is 0.250atm .

Concept introduction:

• Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.

Partial pressure of a gas in terms of its mole fraction and total pressure is,

` PA=χA×PTOTAL

• A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture.

• The number of moles of molecule can be find out by using its mole fraction,
• numbersof moles ofmolecule A(nA)=moleculefractionofA,(χA×total number of moles

• Number of grams of a substance from its number of moles is,

Number of moles×Molecularmass in grams=Numberofgrams

• Total number of moles of gases in the mixture of gases can be determined by using ideal gas equation.

According to ideal gas equation,

Total numberofmoles=Total pressure×VolumeR×Temperature

To determine: the total number of moles in the mixture, the mole fractions and the number of grams of each gas in the given mixture.

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