Chemistry
Chemistry
4th Edition
ISBN: 9780078021527
Author: Julia Burdge
Publisher: McGraw-Hill Education
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Concept explainers

Question
Chapter 10, Problem 66QP
Interpretation Introduction

Interpretation:

The partial pressures of the gasespresent in the given mixture of gases are to be calculated.

Concept introduction:

The mole fraction of an individual gas for the combination of gases is the ratio of the moles of the individual gas to the total number of moles of the mixture.

χi=nintotal

Here, χi is the mole fraction, ni is the mole fraction of the individual gas, and ntotal is the total number of moles.

Also, the mole fraction of an individual gas for the combination of gases can be calculated from the ratio of the partial pressure of the individual gas with the total pressure of the combination.

χi=PiPtotal

Here, χi is the mole fraction, Pi is the partial pressure of the individual gas, and Ptotal is the total pressure.

Expert Solution & Answer
Check Mark

Answer to Problem 66QP

Solution: The partial pressure for CH4 is 0.54 atm, for C2H6 is 0.44 atm, and for C3H8 is 0.51 atm.

Explanation of Solution

Given information:

Number of moles of CH4 nCH4=0.31 mol

Number of moles of C2H6 nC2H6=0.25 mol

Number of moles of C3H8 nC3H8=0.29 mol

Total pressure PT=1.50 atm

From Dalton’s law for the combination of gases, the total number of moles can be calculated as

ntotal=ni=nCH4+nC2H6+nC3H8

Substitute 0.31 mol for nCH4, 0.25 mol for nC2H6, and 0.29 mol for nC3H8 in the above equation as follows:

ntotal=0.31 mol+0.25 mol+0.29 mol=0.85 mol

Calculate the mole fraction of CH4 as follows:

χCH4=nCH4ntotal

Substitute 0.31 mol for nCH4 and 0.85 mol for ntotal in the above equation as follows:

χCH4=0.31 mol0.85 mol=0.36

Thus, the mole fraction of CH4 is 0.36.

Calculate the partial pressure for CH4 as follows:

PCH4=χCH4×Ptotal

Substitute 0.36 for χCH4 and 1.50 atm for Ptotal in the above equation as follows:

PCH4=0.36×1.50 atm=0.54 atm

Thus, for CH4, the partial pressure is 0.54 atm.

Calculate the mole fraction of C2H6 as follows:

χC2H6=nC2H6ntotal

Substitute 0.25 mol for nC2H6 and 0.85 mol for ntotal in the above equation as follows:

χC2H6=0.25 mol0.85 mol=0.29

Thus, the mole fraction of C2H6 is 0.29.

Calculate the partial pressure for C2H6 as follows:

PC2H6=χC2H6×Ptotal

Substitute 0.29 for χC2H6 and 1.50 atm for Ptotal in the above equation as follows:

PC2H6=0.29×1.50 atm=0.44 atm

Thus, for C2H6, the partial pressure is 0.44 atm.

Calculate the mole fraction of C3H8 as follows:

χC3H8=nC3H8ntotal

Substitute 0.29 mol for nC3H8 and 0.85 mol for ntotal in the above equation as follows:

χC3H8=0.29 mol0.85 mol=0.34

Thus, the mole fraction of C3H8 is 0.34.

Calculate the partial pressure for C3H8 as follows:

PC3H8=χC3H8×Ptotal

Substitute 0.34 for χC3H8 and 1.50 atm for Ptotal in the above equation as follows:

PC3H8=0.34×1.50 atm=0.51 atm

Thus, for C3H8, the partial pressure is 0.51 atm.

Conclusion

Thepartial pressure for CH4 is 0.54 atm, for C2H6 is 0.44 atm, and for C3H8 is 0.51 atm.

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Chapter 10 Solutions

Chemistry

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