Chapter 10, Problem 37PS

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# What is the total pressure in atmospheres of a gas mixture that contains 1.0 g of H2 and 8.0 g of Ar in a 3.0-L container at 27 °C? What are the partial pressures of the two gases;

Interpretation Introduction

Interpretation:

The total pressure of mixture of gases and the partial pressures of given amount of gases has to be given.

Concept Introduction:

• Partial pressure: The pressure of each gas in a mixture of gases is the partial pressure.
• Dalton’s law of partial pressure: The total pressure of gases in a mixture of gases is the sum of the pressure of each gas in the mixture
• Mole fraction: Quantity which defines the number of moles of a substance in a mixture divided by the total number of moles of all substances present.

xa=nantotal

pa=xa×Ptotal

Partial pressure of a gas in the mixture of gases is the product of mole fraction of the gas and the total pressure.

• Ideal gas equation:PV=nRT
Explanation

Given:

â€‚Â Amountâ€‰ofâ€‰H2â€‰â€‰â€‰â€‰â€‰=â€‰â€‰1gAmountâ€‰ofâ€‰Arâ€‰â€‰â€‰â€‰â€‰=â€‰8â€‰gVâ€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰=â€‰3â€‰LTâ€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰=â€‰27Â°Câ€‰â€‰â€‰â€‰=â€‰â€‰300â€‰K

The total pressure and partial pressures of given amount of gases in the mixture can be calculated as

In order the partial pressures of H2â€‰andâ€‰Ar we need to know the number of moles.

â€‚Â Numberâ€‰ofâ€‰molesâ€‰=â€‰massmolarâ€‰mass

â€‚Â No.â€‰ofâ€‰molesâ€‰ofâ€‰H2â€‰=â€‰1â€‰g2â€‰gâ€‰â€‰=â€‰0.5â€‰molNo.â€‰ofâ€‰molesâ€‰ofâ€‰Arâ€‰â€‰=â€‰8â€‰g39.95â€‰gâ€‰â€‰â€‰â€‰â€‰=â€‰0.2â€‰molTotalâ€‰amountâ€‰ofâ€‰gasâ€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰=â€‰0.5â€‰molâ€‰+â€‰0.2002â€‰molâ€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰=â€‰0.7â€‰mol

Now we have nH2â€‰,â€‰nArâ€‰andâ€‰ntotal

Now we can calculate the partial pressures by the equation

â€‚Â paâ€‰â€‰=â€‰â€‰naâ€‰RTV

â€‚Â pH2â€‰â€‰=â€‰â€‰0

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