Chemistry
Chemistry
4th Edition
ISBN: 9780393919370
Author: Thomas R. Gilbert
Publisher: NORTON
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Chapter 6, Problem 6.99QP
Interpretation Introduction

Interpretation: A gas mixture is give to have N2, H2 and CH4 gas. The mole fraction of H2 gas, the pressure of the gas mixture and the partial pressure of each constituent gas are to be calculated.

Concept introduction: The mole fraction of H2 gas is calculated by the formula,

XH2=nH2nH2+nN2+nCH4

The partial pressure of the each constituent of gas is calculated by the ideal gas equation.

PV=nRT

The pressure of the gas mixture is sum of all partial pressure of each constituent of gas and it is calculated by the formula,

Pmixture=PH2+PN2+PCH4

To determine: The mole fraction of H2 gas, the pressure of the gas mixture and the partial pressure of each constituent gas.

Expert Solution & Answer
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Answer to Problem 6.99QP

The mole fraction of H2 gas is 0.20_, the pressure of the gas mixture is 2.44atm_ and the partial pressure of constituent H2 gas is 0.49atm_, the partial pressure of constituent N2 gas is 1.7atm_, the partial pressure of constituent CH4 gas is 0.25atm_.

Explanation of Solution

Given

The number of moles of H2 gas is 0.20mol.

The number of moles of N2 gas is 0.70mol.

The number of moles of CH4 gas is 0.10mol.

The temperature of the gas mixture is (T) is 27°C.

The volume of gas mixture (V) is 10.0L.

The value of universal gas constant (R) is 0.082057LatmK1mol1.

The relation between degree Celsius and Kelvin is,

0°C=0+273.15K

Apply this relation for the conversion of given temperature into Kelvin.

27°C=27+273.15K=300.15K

The mole fraction of H2 gas (XH2) is calculated by the formula,

XH2=nH2nH2+nN2+nCH4 (1)

Where,

  • nH2 is number of moles of H2 gas.
  • nN2 is number of moles of N2 gas.
  • nCH4 is number of moles of CH4 gas.

Substitute the values of nH2, nN2 and nCH4 in equation (1).

XH2=0.20mol0.70mol+0.70mol+0.10molXH2=0.20mol1molXH2=0.20

The partial pressure of H2 gas (PH2) is calculated by the ideal gas equation.

PH2V=nH2RT (2)

Where,

  • V is volume of gas mixture.
  • T is temperature of gas mixture.
  • R is universal gas constant.
  • nH2 is number of moles of H2 gas.

Rearrange the equation (2).

PH2=nH2RTV (3)

Substitute the values of V, T, R and nH2 in equation (3).

PH2=0.20mol×0.082057LatmK1mol1×300.15K10.0L=4.92atmL10.0L=0.49atm

Rewrite the equation (3) for the calculation of partial pressure of N2 gas (PN2).

PN2=nN2RTV (4)

Where,

  • nN2 is number of moles of N2 gas.

Substitute the values of V, T, R and nN2 in equation (4).

PH2=0.70mol×0.082057LatmK1mol1×300.15K10.0L=17.24atmL10.0L=1.7atm

Rewrite the equation (3) for the calculation of partial pressure of CH4 gas (PCH4).

PCH4=nCH4RTV (5)

Where,

  • nCH4 is number of moles of CH4 gas.

Substitute the values of V, T, R and nCH4 in equation (5).

PCH4=0.10mol×0.082057LatmK1mol1×300.15K10.0L=2.5atmL10.0L=0.25atm

The pressure of the gas mixture (Pmixture) is sum of all partial pressure of each constituent of gas and it is calculated by the formula,

Pmixture=PH2+PN2+PCH4 (6)

Where,

  • PH2 is partial pressure of H2 gas.
  • PN2 is partial pressure of N2 gas.
  • PCH4 is partial pressure of CH4 gas.

Substitute the values of PH2, PN2 and PCH4 in equation (6).

Pmixture=0.49atm+1.7atm+0.25atm=2.44atm

Thus, the mole fraction of H2 gas is 0.20_, the pressure of the gas mixture is 2.44atm_ and the partial pressure of constituent H2 gas is 0.49atm_, the partial pressure of constituent N2 gas is 1.7atm_, the partial pressure of constituent CH4 gas is 0.25atm_.

Conclusion

The mole fraction of H2 gas is 0.20_, the pressure of the gas mixture is 2.44atm_ and the partial pressure of constituent H2 gas is 0.49atm_, the partial pressure of constituent N2 gas is 1.7atm_, the partial pressure of constituent CH4 gas is 0.25atm_.

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Chapter 6 Solutions

Chemistry

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