   # Consider separate 1.0−L gaseous samples of He, N 2 , and O 2 , all at STP and all acting ideally. Rank the gases in order of increasing average kinetic energy and in order of increasing 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 149CWP
Textbook Problem
41 views

## Consider separate 1.0−L gaseous samples of He, N2, and O2, all at STP and all acting ideally. Rank the gases in order of increasing average kinetic energy and in order of increasing average velocity.

Interpretation Introduction

Interpretation: The given gases samples should be ranked in order of increasing 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,

μave=(8RTπM)1/2 (1)

R=8.314JKmolM=Molarmassinkg

### Explanation of Solution

Explanation

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

All the gases have the same average kinetic energy

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

Average kinetic energy is temperature dependent. Since all the given gases at STP, all the gases have 273K temperate. So all the gases have the same average kinetic energy

• To rank: the given gas samples in order of increasing average velocity

O2(32.00g/mol)<N2(28.02g/mol)<He(4.003g/mol)slowestfastest

The average velocity can be determined,

μave=(8RTπM)1/2

From the equation it is clear that the average velocity of gas molecules is inversely proportional to the mass of gas molecule

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