Chapter 21, Problem 21.21QP

Interpretation Introduction

Interpretation: The number of ozone molecules present and the mass of ozone molecules should be determined.

Concept Introduction:

Atmosphere: The atmosphere is defined as air that is layer of gases which surrounds the earth due to gravity of earth.

The earth atmosphere consists of layers such as thermosphere, mesosphere, stratosphere and troposphere depending on the temperature and its composition.

Stratosphere:

It is found below the mesosphere layer in which the concentration of ozone and other gases are high. The increasing temperature for this layer with respect to increasing height is due to the presence of high concentration of ozone and other gases in it.

The increased temperature is due to the response of UV radiation from sun and hence ozone is formed due to this reaction and the use of ozone is that it prevents the UV radiation from the sun which is actually harmful.

Balanced Equation: A chemical reaction is considered as balanced equation if all the number of atoms, the charge and the mass of elements on both reactant and the product side are equal in the reaction.

Moles: It is the number of particles present in the given specific substance. The formula used to identify the moles present in given mass of a compound is as follows,

$\text{x}\text{moles}\text{=}\frac{\text{Given}\text{mass}\text{of}\text{the}\text{sample}}{\text{Molecular}\text{mass}\text{of}\text{the}\text{sample}}$

Molar mass: It is the total mass of the substance including all the number and the mass of the elements present in substance.

Answer to Problem 21.21QP

The number of ozone molecules present in the stratosphere is.

The mass of ozone is $3.2\times {10}^{12}\text{kg}$

To determine: The number of ozone molecules and the mass of the molecules present using given data’s.

Explanation of Solution

Determine the total volume.

$\begin{array}{l}\text{Given}\text{data: }\\ \text{Radius = 6}\text{.371}\times {\text{10}}^{\text{6}}\text{m}\\ \text{Thickness, h = 3}\text{.0}\times {\text{10}}^{-3}\text{m}\\ {\text{Volume of sphere = 4πr}}^{\text{2}}\text{h}\\ \text{= 4}\times \frac{22}{7}\times {\left(\text{6}\text{.371}\times {\text{10}}^{\text{6}}\text{m}\right)}^2\left(\text{3}\text{.0}\times {\text{10}}^{-3}\text{m}\right)\\ =1.5\times {\text{10}}^{12}{\text{m}}^{\text{3}}\times \frac{1000\text{L}}{1{\text{m}}^{\text{3}}}\\ =1.5\times {\text{10}}^{15}\text{L}\end{array}$

In order to find the number of molecules one needs to find the moles and to determine the moles present in the stratosphere we need to know the total volume present hence volume is obtained by substituting the given radius and thickness data in volume of sphere formula since earth considered as sphere.

Determine the molecules.

$\begin{array}{l}{\text{Moles of O}}_{\text{3}}\text{ present in given volume}\\ \text{Moles}\text{= }\left(1.5\times {\text{10}}^{15}\text{L}\right)\times \frac{\text{1 mol}}{22.41\text{L}}\\ =6.7\times {\text{10}}^{13}\text{mol}\\ \text{Number of molecules,}\\ \text{Molecules = }6.7\times {\text{10}}^{13}\text{mol}\times \frac{6.022\times {10}^{23}\text{molecules}}{\text{1 mol}}\\ =4.0\times {\text{10}}^{37}\text{molecules}\\ \end{array}$

First, the moles present is determined by dividing the volume of ozone present with the $22.41\text{L}$ since the gas at standard temperature and pressure condition it occupies that volume yields the value of $6.7\times {\text{10}}^{13}\text{mol}$.

The next step is to find the number of molecules which is accomplished by multiplying the number of moles present with Avogadro’s number ( $6.022\times {10}^{23}\text{molecules}$)

Determine the mass of the ozone molecules.

$\begin{array}{l}{\text{Mass of O}}_{\text{3}}\\ \text{Mass}\text{= }\left(6.7\times {\text{10}}^{13}\text{mol}\right)\times \frac{48\text{g}}{\text{1 mol}}\times {10}^{-3}\\ =3.2\times {\text{10}}^{12}\text{kg}\\ \\ \end{array}$

The mass of ozone molecules present is determined by using the given moles formula where the moles of ozone and the molar mass of ozone are known hence substituting it gives the mass of the ozone which is converted into kilograms by multiplying with ${10}^{-3}$ since $\text{1 kg = 1000 g}$.

Conclusion

Conclusion

The number of molecules and the mass present is determined by using the moles formula.