Chapter 21, Problem 73AP

Interpretation Introduction

Interpretation:

The number of marble statues damaged by acid rain is to be calculated and the other undesirable product of acid rain damage is to be determined.

Concept Introduction:

Acid rain is the rain full of acids, which causes environmental pollution. It is very harmful to plants, the soil, insects, bacteria, and also to aquatic life. It results in the corrosion of steel and also has a bad impact on human health.

Global warming is caused by any long-term increase in the temperature of the earth. It is very harmful for the environment and also causes problems to plants and animals.

Answer to Problem 73AP

Solution:

(a)

The total number of statues destroyed by acid rain is $6.2\times {10}^8$.

(b)

The undesirable product is carbon dioxide, which causes global warming.

Explanation of Solution

a) The number of 100 lb marble statues the resulting rain can damage.

Sulfur dioxide released is $50\text{ million tons}$.

20% of sulfur dioxide is converted into sulfuric acid.

The marble statue is of $1000\text{ lb}$.

Acid rain is caused by the emission of sulfur dioxide and nitrogen dioxide in the air. When sulphur dioxide is released into the atmosphere, sulfuric acid is produced. This causes acid rain and damages marble statues.

The reaction which causes acid rain is as follows:

$\begin{array}{l}{\text{2SO}}_2\left(g\right)+{\text{O}}_2\left(g\right)\to 2{\text{SO}}_3\left(g\right);\\ {\text{SO}}_3\left(g\right)+{\text{H}}_2\text{O}\left(l\right)\to {\text{H}}_2{\text{SO}}_4\left(aq\right).\end{array}$

The sulfuric acid produced reacts with the marble that consists of calcium carbonate $\left({\text{CaCO}}_3\right)$ and causes acid rain.

The reaction is as follows:

${\text{H}}_2{\text{SO}}_4\left(aq\right)+{\text{CaCO}}_3\left(s\right)\to {\text{CaSO}}_4\left(s\right)+{\text{H}}_2\text{O}\left(l\right)+{\text{CO}}_2\left(g\right)$.

Conversion of a mass of sulfur dioxide $\left(50\text{ million tons}\right)$ into moles of sulfur dioxide $\left({\text{SO}}_2\right)$ is as follows: $\begin{array}{l}{n}_{{\text{SO}}_2}=\left(50\times {10}^6\cancel{\text{tons}\text{}}{\text{ SO}}_2\right)\left(\frac{2000\cancel{\text{lb}}}{1\cancel{\text{ton}}}\right)\left(\frac{453.6\cancel{\text{g}}}{1\cancel{\text{lb}}}\right)\left(\frac{1\text{ mol }\cancel{{\text{SO}}_2}}{64.07\cancel{\text{g }}\cancel{{\text{SO}}_2}}\right)\\ n_{{\text{SO}}_2}=7.1\times {10}^{11}{\text{ mol SO}}_2\end{array}$

Therefore, the moles in sulfur dioxide are $7.1\times {10}^{11}{\text{ mol SO}}_2$.

Conversion of $20\%$

Sulfur dioxide into moles of sulfuric acid is as follows:

$\begin{array}{l}{n}_{{\text{H}}_2{\text{SO}}_4}=\left(0.20\right)\times \left(7.1\times {10}^{11}\cancel{{\text{mol SO}}_2}\right)\times \frac{1{\text{ mol H}}_2{\text{SO}}_4}{1\cancel{{\text{mol SO}}_2}}\\ n_{{\text{H}}_2{\text{SO}}_4}=1.4\times {10}^{11}{\text{ mol H}}_2{\text{SO}}_4\end{array}$

Therefore, the moles in sulfuric acid are $1.4\times {10}^{11}{\text{ mol H}}_2{\text{SO}}_4$.

The moles in calcium carbonate that destroy $5\%$ of its total mass per statue is calculated as follows:

$\begin{array}{l}{n}_{{\text{CaCO}}_3}=\left(0.05\right)\left(1000\cancel{\text{lb}}\cancel{{\text{CaCO}}_3}\right)\left(\frac{453.6\cancel{\text{g}}}{1\cancel{\text{lb}}}\right)\left(\frac{1{\text{ mol CaCO}}_3}{100.1\cancel{\text{g }}\cancel{{\text{CaCO}}_3}}\right)\\ n_{{\text{CaCO}}_3}=226.6{\text{ mol CaCO}}_3\text{ per statue}\end{array}$

Therefore, the moles in calcium carbonate per statue are $226.6{\text{ mol CaCO}}_3$.

Number of statues destroyed by $1.4\times {10}^{11}\text{ mol }$ of sulfuric acid can be calculated as follows:

$\begin{array}{l}\text{Number of statue}=\left(1.4\times {10}^{11}\cancel{{\text{mol H}}_2{\text{SO}}_4}\right)\left(\frac{1\cancel{{\text{mol CaCO}}_3}}{1\cancel{{\text{mol H}}_2{\text{SO}}_4}}\right)\left(\frac{1\text{ statue}}{226.6\cancel{{\text{mol CaCO}}_3}}\right)\\ \text{Number of statue}=6.2\times {10}^8\text{ statues}\end{array}$

Thus, the number of statues damaged by acid rain is $6.2\times {10}^8$.

b) Other undesirable result of the acid rain damage

Acid rain caused by sulfuric acid in statues produces carbon dioxide as an undesirable product, which supports global warming.

Global warming is mainly caused by the emission of carbon dioxide and chlorofluorocarbons. It has many adverse effects on climate change, human health, and plants.