   # Consider separate 1.0−L gaseous samples of H 2 , Xe, Cl 2 , and O 2 all at STP. a. Rank the gases in order of increasing average kinetic energy. b. Rank the gases in order of increasing average velocity. c. How can separate 1.0−L samples of O 2 and H 2 each have the same average velocity? ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 8, Problem 110E
Textbook Problem
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## Consider separate 1.0−L gaseous samples of H2, Xe, Cl2, and O2 all at STP.a. Rank the gases in order of increasing average kinetic energy.b. Rank the gases in order of increasing average velocity.c. How can separate 1.0−L samples of O2 and H2 each have the same average velocity?

Interpretation Introduction

Interpretation: The given four gases should be ranked in order of increasing their average kinetic energy and average velocity.

Concept introduction:

• Kinetic molecular theory explains the properties of ideal gas. From the postulates of kinetic molecular theory it is clear that kinetic energy of gas particle is directly proportional to the Kelvin temperature of the gas.

Average kinetic energy of gas can be determined as,  KEavg=(3/2)RT

• The average  velocity can be determined,

Cave=(8RTπM)1/2 (1)

R=8.314JKmolM=Molarmassinkg

### Explanation of Solution

Explanation

• To rank: the given gases in order of their increasing average kinetic energy

All the gases have same average kinetic energy

From the postulates of kinetic molecular theory it is clear that kinetic energy of gas particle is directly proportional to the Kelvin temperature of the gas. Here in the case of four gases all are in STP (standard temperature and pressure) condition. That is all the gases have 273 k temperature. At the same temperature, the average kinetic energy is same for all gases.

• To rank: the given gases in order of their increasing average velocity.

Increasing order of average velocity of three gases is,

Xe<Cl2<O2<H2

The average velocity can be determined,

Cave=(8RTπM)1/2

From the equation it is clear that the average velocity of gas molecules is inversely proportional to the mass of gas molecules. So at constant temperature, the lighter gas molecule H2 has fastest average velocity and heavier Xe has slowest average velocity from the rest of other gas molecules.

• To explain: How can separate the samples of O2 and H2 each have the same average velocity

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