Chapter 10.6, Problem 10.11CYU

### 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

# Calculate the rms speeds of helium atoms and N2 molecules at 298 K.

Interpretation Introduction

Interpretation:

The rms speed of helium atoms and nitrogen molecules at the given temperature has to be calculated.

Concept Introduction:

Speed of the gas molecules are related to temperature.

Equation which describes this relation is:

rms(rootmeansquare)(u)2=3RTM

M-Molar mass

R-Universal gas constant

T-Temperature

Explanation

The rms speed of helium atom and nitrogen molecules at the given temperature can be calculated as

Given

â€‚Â Tâ€‰â€‰â€‰â€‰â€‰=â€‰298â€‰KRâ€‰â€‰â€‰â€‰â€‰=â€‰8.314â€‰J/K.molMHeâ€‰â€‰â€‰â€‰=â€‰4â€‰Ã—10-3â€‰kg/molMN2â€‰â€‰â€‰â€‰â€‰=â€‰28Ã—10-3â€‰kg/mol

â€‚Â rmsâ€‰(rootâ€‰meanâ€‰square)â€‰(u)2â€‰â€‰â€‰=â€‰â€‰3RTM

â€‚Â rmsHeâ€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰=â€‰3â€‰(8.314â€‰J/K.mol)(298â€‰K)4â€‰Ã—â€‰10-3â€‰kg/molâ€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰=â€‰1.85Ã—106â€‰Jâ€‰/kg1â€‰Jâ€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰=â€‰1â€‰kg.m2/s2rmsâ€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰=â€‰1.85Ã—106â€‰â€‰kg.m2/kg.s2â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰=â€‰1

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