Chemistry: An Atoms-Focused Approach
Chemistry: An Atoms-Focused Approach
14th Edition
ISBN: 9780393600681
Author: Gilbert
Publisher: W. W. Norton & Company
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Chapter 10, Problem 10.120QA
Interpretation Introduction

To calculate:

The root-mean-square speed of CO2 molecules that have an average kinetic energy of 3.2×10-21 J per molecule.

Expert Solution & Answer
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Answer to Problem 10.120QA

Solution:

Root-mean-square speed of CO2 molecules is 3.0 ×102 m/s.

Explanation of Solution

1) Concept:

To calculate the root-mean-square speed of CO2 molecules, we will use the kinetic energy formula. We will convert the molar mass in  kg/mol and kinetic energy in J/mol. From this, we will calculate the root-mean-square speed of CO2 molecules by using the kinetic energy formula.

2) Formula:

KEavg=12mμrms2

 Where, KE is kinetic energy in J/mol, m is the molar mass of CO2 molecules in kg/mol, and μrms is the root-mean-square speed.

3) Given:

i) KEavg = 3.2×10-21 J per molecule.

ii) m of CO2=44.01 gmol

iii) 1 mol=6.022×1023molecule

iv) 1 J=1 kg.m2s2

4) Calculations:

First, calculate the molar mass of CO2 in kg/mol.

MCO2=44.01gmol×1 kg1000 g=0.04401kgmol

Now, convert kinetic energy from

Jmolecule toJmol using Avogadro’s number.

KEavg=3.2×10-21Jmolecule×6.022×1023molecule1 mol× 1 kg.m2s21 J=1927.04kg.m2s2.mol

KEavg= 1927.04kg.m2s2.mol

Calculate the μrms from the KEavg.

μrms=KEavg×2m

Plugging values of kinetic energy and the molar mass, we can get the value of root-mean-square speed of CO2 molecules.

μrms=1927.04kg.m2s2.mol×20.04401 kgmol= 87572.82 m2s2=295.93ms

Root-mean-square speed of CO2 molecules is 3.0 ×102 m/s.

Conclusion:

We calculated the root-mean-square speed by using kinetic energy and the atomic mass of CO2 molecules.

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Chapter 10 Solutions

Chemistry: An Atoms-Focused Approach

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