Chapter 21, Problem 8QP

Calculate the mass (in kg) of nitrogen, oxygen, and carbon dioxide gases in the atmosphere. Assume that the total mass of air in the atmosphere is $5.25\times {10}^{21}\text{g}\text{.}$

Interpretation Introduction

Interpretation:

The masses of nitrogen, oxygenand carbon dioxide gases in the atmosphere are to becalculated.

Concept introduction:

Nitrogen is a colorless and odorless gas. Itis found in the Earth’s atmosphere as a diatomic gas with thechemical formula ${\text{N}}_2$.

Oxygen is a chemical element found in solid, liquid andgaseous forms. In the Earth’s atmosphere, it is found as adiatomic gas with thechemical formula ${\text{O}}_2$.

Carbon dioxide is an odorless and colorless gas with thechemical formula ${\text{CO}}_2$. It is found in theEarth’s atmosphere as a trace gas.

Answer to Problem 8QP

Solution: The mass of nitrogen $\left({\text{N}}_2\right)$ is $3.96\times {10}^{18}\text{ kg}$, the mass of oxygen $\left({\text{O}}_2\right)$ is $1.22\times {10}^{18}\text{ kg}$ and the mass of carbon dioxide $\left({\text{CO}}_2\right)$ is $2.6\times {10}^{15}\text{ kg}$.

Explanation of Solution

Given information: The total mass of the air in the atmosphere is $5.25\times {10}^{21}\text{ g}$.

The total moles of gases areexpressed as follows:

$n=\text{Total mass of air}\times \text{molar mass of air}$

Substitute the values in the above expression and solve as follows:

$\begin{array}{l}n=\left(5.25\times {10}^{21}\cancel{\text{g}}\times \frac{1\text{ mol}}{29.0\cancel{\text{g}}}\right)\\ n=\text{1}\text{.81}\times {\text{10}}^{20}\text{ mol}\end{array}$

Therefore, the total moles of gases $\left(n\right)$ are $\text{ 1}\text{.81}\times {\text{10}}^{20}\text{ mol}$.

Nitrogen is a colorless and odorless gas. It is found in the Earth’s atmosphere as a diatomic gas.

The mass of nitrogen is expressed as follows:

$\text{Mass of nitrogen} =\text{Composition of air by volume} \times \text{Total moles of gases}\times \text{Molar mass of nitrogen}$

Substitute the values of the molar mass, the composition of air by volume and the total moles of the gases.

$\begin{array}{c}{n}_{N_2}=\left(0.7803\right)\left(1.81\times {10}^{20}\cancel{\text{mol}}\right)\left(\frac{28.02\text{ g}}{1\cancel{\text{mol}}}\right)\\ =3.96\times {10}^{21}\text{ g}\end{array}$

Therefore, the mass of nitrogen $\left({\text{N}}_2\right)$ is $3.96\times {10}^{18}\text{ kg}$.

Oxygen is a chemical element found in solid, liquid or gaseous forms. In theEarth’s atmosphere, it is found as a diatomic gas with the chemical formula ${\text{O}}_2$.

The mass of oxygen is expressed as follows:

$\text{Mass of Oxygen}=\text{Composition of air by volume }\times \text{Total moles of gases}\times \text{Molar mass of Oxygen}$

Substitute the values of the molar mass, the composition of air by volume and the total moles of the gases.

$\begin{array}{c}{n}_{o_2}=\left(0.2099\right)\left(1.81\times {10}^{20}\cancel{\text{mol}}\right)\left(\frac{32.00\text{ g}}{1\cancel{\text{mol}}}\right)\\ =1.22\times {10}^{21}\text{ g}\\ =1.22\times {10}^{18}\text{ kg}\end{array}$

Therefore, the mass of oxygen $\left({\text{O}}_2\right)$ is $1.22\times {10}^{18}\text{ kg}$.

Carbon dioxide is an odorless and colorless gas with the chemical formula ${\text{CO}}_2$. It is found in the Earth’s atmosphere as a trace gas.

The mass of carbon dioxide is expressed as follows:

$\text{Mass of Carbon dioxide}=\left(\begin{array}{c}\text{Composition of air by volume}\times \text{Total moles of gases}\times \\ \text{Molar mass of Carbon dioxide}\end{array}\right)$

Substitute the values of the molar mass, the composition of air by volume, and the total moles of the gases,

$\begin{array}{c}{n}_{C{O}_2}=\left(3.3\times {10}^{-4}\right)\left(1.81\times {10}^{20}\cancel{\text{mol}}\right)\left(\frac{44.01\text{ g}}{1\cancel{\text{mol}}}\right)\\ =2.6\times {10}^{18}\text{ g}\\ =2.6\times {10}^{15}\text{ kg}\end{array}$

Therefore, the mass of carbon dioxide $\left({\text{CO}}_2\right)$ is $2.6\times {10}^{15}\text{ kg}$.

Conclusion

The masses of nitrogen, oxygen, and carbon dioxide gases in the atmosphere are $3.96\times {10}^{18}\text{ kg}$, $1.22\times {10}^{18}\text{ kg}$, and $2.6\times {10}^{15}\text{ kg}$, respectively.