Chemistry
Chemistry
4th Edition
ISBN: 9780078021527
Author: Julia Burdge
Publisher: McGraw-Hill Education
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Question
Chapter 21, Problem 21QP
Interpretation Introduction

Interpretation:

The number of ozone molecules in the stratosphere and their mass in kg are to becalculated.

Concept introduction:

Stratosphere is the second layer of the Earth’s atmosphere and contains oxygen, ozone,and nitrogen gases.

Ozone is an allotrope of oxygen, containing three oxygen atoms. Ozone is formed in the stratosphere.

Expert Solution & Answer
Check Mark

Answer to Problem 21QP

Solution: The number of ozone molecule is 4.0×1037 and the mass of O3 is 3.2×1012 kg

Explanation of Solution

Given information: The quantity of ozone in the stratosphere is equivalent to a 3.0 mm thick layer of ozone on Earth at STP, the radius of Earth is 6371 km and the surface area of a sphere is 4πr2.

The number of ozone molecules in the stratosphere can be calculated with the help of volume.

Area of Earth surface=4πr2

=4×3.14×(6371×103m)2

=5.098×1014m2

The volume of ozone layer is given by the following expression:

V=4πr2h

Here, r is the radius of the sphere (6.371×103 m) and h is the height of the sphere (3.0 mm = 3.0×103 m)

Now substitute the values in the above equation as shown below:

V=4π(6.371×103 m)2(3.0×103 m)V=(5.098×1014m2)(3.0×103 m)V=1.5×1012m3×1000 L103 m3=1.5×1015L

V=1.5×1015 L

Therefore, the volume of thesphereis 1.5×1015 L.

The number of moles of ozone (O3) is calculated as follows:

Moles of O3= volume of sphere × one mole of gas

At standard temperature and pressure (STP), one mole of gas occupies 22.41 L

By substituting the values in the above equation:

Moles of O3 = (1.5×1015 L)(1 mol22.41 L)

Moles of O3 =6.7×1013 mol O3

Therefore, the number of moles of O3 is 6.7×1013 mole.

The molecule of ozone (O3) is calculated as follows:

A molecule of O3=moles of ozone × Avogadro number

By substituting the values in the above equation:

Molecule of O3= (6.7×1013 mol O3)6.022×1023 molecule1 mol

Molecule of O3= 4.0×1037 molecules

Therefore, the number ofozonemolecules is 4.0×1037.

The mass of ozone (O3) is calculated as follows:

Mass of O3= moles of ozone × molar mass of ozone

Mass of O3= (6.7×1013 mol O3)×48.00 g O31 mol O3×1 kg1000 g

Mass of O3= 3.2×1012 kg

Conclusion

The number of ozone molecules in the stratosphere and their mass in kg are 4.0×1037 molecules and 3.2×1012 kg,respectively.

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Chapter 21 Solutions

Chemistry

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