Chapter 21, Problem 79AP

Interpretation Introduction

Interpretation:

The equations for the given processes are to be represented, and the reasonfor greenhouse gas between ${\text{N}}_2{\text{O and CO}}_2$, that is, more effective is to be explained, and the maximum number of moles of ozone that is destroyedper year as per the given conditionsis to be calculated.

Concept introduction:

Greenhouse effect is a process in which heat is trapped by the atmospheric gases near the surface of the earth.

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

The number of moles in the reaction is represented by the expression as:

$\text{Moles}=\frac{\text{Given mass}}{\text{Molar mass}}$

Answer to Problem 79AP

Solution:

(a)

The reaction between the ${\text{N}}_2\text{O}$ and the oxygen atoms is as follows:

$\begin{array}{c}\underset{\_}{\begin{array}{l}{\text{ N}}_2\text{O }+\text{ O }\underset{}{\overset{}{\rightleftarrows }}2\text{NO}\\ \text{ 2NO }+2{\text{O}}_3\underset{}{\overset{}{\rightleftarrows }}{\text{ 2NO}}_2+2{\text{O}}_2\end{array}}\\ {\text{Overall: N}}_2\text{O }+\text{ O }+{\text{ 2O}}_3\underset{}{\overset{}{\rightleftarrows }}2{\text{NO}}_2+2{\text{O}}_2\end{array}$

(b)

${\text{N}}_2\text{O}$ is a more effective greenhouse gas than ${\text{CO}}_2$.

(c)

$3.0\times {10}^{10}\text{ mol}$.

Explanation of Solution

a) Equations of that representing the reaction between ${\text{N}}_2\text{O}$ and oxygen atoms to produce NO, which is further oxidized by ${\text{O}}_3$ to form ${\text{NO}}_2$.

The reaction between the ${\text{N}}_2\text{O}$ and the oxygen atoms and then between NO and ${\text{O}}_3$ is as follows:

$\begin{array}{c}\underset{\_}{\begin{array}{l}{\text{ N}}_2\text{O }+\text{ O }\underset{}{\overset{}{\rightleftarrows }}2\text{NO}\\ \text{ 2NO }+2{\text{O}}_3\underset{}{\overset{}{\rightleftarrows }}{\text{ 2NO}}_2+2{\text{O}}_2\end{array}}\\ {\text{Overall: N}}_2\text{O }+\text{ O }+{\text{ 2O}}_3\underset{}{\overset{}{\rightleftarrows }}2{\text{NO}}_2+2{\text{O}}_2\end{array}$

b) ${\text{N}}_2\text{O}$ is a more effective greenhouse gas than carbon dioxide to be explained.

${\text{N}}_2\text{O}$ is a more effective greenhouse gas than carbon dioxide. In carbon dioxide, the dipole moment is equal and opposite so, they cancel each other. Hence, the net dipole for carbon dioxide is zero, whereas ${\text{N}}_2\text{O}$ is linear and has more dipole moment than ${\text{CO}}_2$. Therefore, ${\text{N}}_2\text{O}$ is a more effective greenhouse gas.

c) The maximum number of moles of ${\text{O}}_3$ that can be destroyed as a result of the given process per year.

Amount of adipic acid used every year is $2.2\times {10}^9\text{ kg}$.

$1$ mole of adipic acid gives $1$ mole of ${\text{N}}_2\text{O}$.

The number of moles of adipic acid is calculated as follows:

$\text{Moles}=\frac{\text{given mass}}{\text{Molar mass}}$

Substitute the values in the above equation:

$\begin{array}{l}\text{Moles}=\left(2.2\times {10}^9\cancel{\text{kg}}\cancel{\text{adipic acid}}\right)\left(\frac{1000\cancel{\text{g}}}{1\cancel{\text{kg}}}\right)\left(\frac{1\text{ mol adipic acid}}{146.1\cancel{\text{g}}\cancel{\text{adipic acid}}}\right)\\ \text{Moles}=1.5\times {10}^{10}\text{ mol adipic acid}\end{array}$

Thus, the moles of adipic acid is $1.5\times {10}^{10}\text{ mol}$.

As given, $1$ mole of adipic acid gives $1$ mole of ${\text{N}}_2\text{O}$ produced. Thus,

$1.5\times {10}^{10}\text{ mol adipic acid}=1.5\times {10}^{10}{\text{ mol N}}_2\text{O}$

The overall balanced equation is as follows:

${\text{N}}_2\text{O }+\text{ O }+{\text{ 2O}}_3\underset{}{\overset{}{\rightleftarrows }}2{\text{NO}}_2+2{\text{O}}_2$

From this reaction, one mole of ${\text{N}}_2\text{O}$ will react with $2$ moles of ${\text{O}}_3$. Therefore, the number of moles of ${\text{O}}_3$ are as follows:

$\begin{array}{l}1.5\times {10}^{10}\text{ mol adipic acid}=1.5\times {10}^{10}{\text{ mol N}}_2\text{O }=2\left(1.5\times {10}^{10}{\text{ mol O}}_3\right)\\ 1.5\times {10}^{10}\text{ mol adipic acid}=1.5\times {10}^{10}{\text{ mol N}}_2\text{O }=3.0\times {10}^{10}{\text{ mol O}}_3\end{array}$

Thus, the number of moles of ${\text{O}}_3$ is $3.0\times {10}^{10}\text{ mol}$.