Chemistry
Chemistry
4th Edition
ISBN: 9780393919370
Author: Thomas R. Gilbert
Publisher: NORTON
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Chapter 6, Problem 6.168AP
Interpretation Introduction

Interpretation: Uranus is given to have a total atmospheric pressure of 130kPa where the following gases are present: 83%H2 , 15%He , and 2%CH4 by volume. The partial pressure of each gas in Uranus atmosphere is to be calculated.

Concept introduction: The mole fraction is defined as the ratio of the number of moles of each individual gas by the total numbers of moles which represent the entire component. The Dalton’s law of partial pressures state that “the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the gases in the mixtures”.

To determine: The partial pressure of each gas in Uranus atmosphere.

Expert Solution & Answer
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Answer to Problem 6.168AP

Solution

The partial pressure of H2 is 118.82kPa_ , the partial pressure of He is 10.79kPa_ , the partial pressure of CH4 is 0.26kPa_ .

Explanation of Solution

Explanation

The composition of gas mixtures are given in terms of their volumes, which is in mass percentage. First the mass percentage is converted into mole fraction of each component.

The mole fraction is defined as the ratio of the number of moles of each individual gas by the total numbers of moles which represent the entire component.

Amountofsample=83gofH2+15gofHe+2gofCH4=100g

The molar mass of each gas is calculated by the formula,

Massofgass=Amountofgas×1molofgassMolecularmassofgas

For hydrogen, the molecular mass of hydrogen molecule is 2.01588g/mol .

Substitute the given values in above expression,

Massofgass=Amountofgas×1molofgassMolecularmassofgasMassofH2=83gofH2×1molofH22.0159gofH2=41.17molesofH2

For helium, the molecular mass of helium is 4.0026g/mol .

Substitute the given values in above expression,

Massofgass=Amountofgas×1molofgassMolecularmassofgasMassofHe=15gofHe×1molofHe4.0026gofHe=3.748molesofHe

For methane, the molecular mass of methane is 16.0425g/mol .

Substitute the given values in above expression,

Massofgass=Amountofgas×1molofgassMolecularmassofgasMassofCH4=2gofCH4×1molofCH42.0159gofCH4=0.1247molesofCH4

Totalnumberofmoles=MolesofH2+MolesofHe+MolesofCH4=41.17mol+3.74mol+0.12mol=45.03mol

The mole fraction of hydrogen gas is calculated by the formula,

χH2=MolesofH2Totalnumbersofmoles

Substitute the given values in the above expression,

χH2=MolesofH2Totalnumbersofmoles=41.17mol45.03mol=0.914

The mole fraction of helium gas is calculated by the formula,

χHe=MolesofHeTotalnumbersofmoles

Substitute the given values in the above expression,

χHe=MolesofHeTotalnumbersofmoles=3.74mol45.03mol=0.083

Similarly the mole fraction of CH4 is calculated by the formula,

χCH4=MolesofCH4Totalnumberofmoles

Substitute the given values in the above expression,

χCH4=MolesofCH4Totalnumberofmoles=0.12mol45.03mol=0.002

According to Dalton’s law of pressure, partial pressure is the product of the mole fraction and the total atmospheric pressure.

The partial pressure of given gases is calculated by the formula,

Px=χxPTotal

Where,

  • Px is the partial pressure of x=PH2,PHe,PCH4 .
  • χx is the mole fraction of χH2 , χHe , χCH4 .
  • PTotal is the total atmospheric pressure 130kPa .

Substitute the given values in the above expression,

PH2=0.914×130kPa=118.82kPa_

PHe=0.083×130kPa=10.79kPa_

PCH4=0.002×130kPa=0.26kPa_

Therefore, the partial pressure of H2 is 118.82kPa_ , the partial pressure of He is 10.79kPa_ , the partial pressure of CH4 is 0.26kPa_ .

Conclusion

The partial pressure of H2 is 118.82kPa_ , the partial pressure of He is 10.79kPa_ , the partial pressure of CH4 is 0.26kPa_

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Chapter 6 Solutions

Chemistry

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