   Chapter 10, Problem 37PS

Chapter
Section
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:

AmountofH2=1gAmountofAr=8gV=3LT=27°C=300K

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

In order the partial pressures of H2andAr we need to know the number of moles.

Numberofmoles=massmolarmass

No.ofmolesofH2=1g2g=0.5molNo.ofmolesofAr=8g39.95g=0.2molTotalamountofgas=0.5mol+0.2002mol=0.7mol

Now we have nH2,nArandntotal

Now we can calculate the partial pressures by the equation

pa=naRTV

pH2=0

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