Chapter 20, Problem 20.83QP

(a)

Interpretation Introduction

Interpretation:

The number of $5\%$ of $\text{1000lb}$ statues get damaged by acid rain has to be calculated.

Concept introduction:

Acid rain:

Acid rain is a kind of precipitation which is acidic that it has more hydrogen ions.  It affects buildings, plants and animals.  It occurs due to emission of sulfur dioxide and nitrogen oxide which reacts with water to form acid rain.

Molar mass:

• Molar mass of a molecule can be calculated from its molecular formula by taking the sum of atomic masses of all the elements present in it.
• Conversion formula for mass of a molecule into number moles,

$Numberofmoles=\frac{Massingrams}{Molarmass}$

Answer to Problem 20.83QP

The number of $5\%$ of $\text{1000lb}$ statues get damaged by acid rain is $6.2\times 10^{8}statues$

Explanation of Solution

Given,

Every year $50$ million tons of sulphur dioxide are released into atmosphere.

The formation of sulphuric acid due to emission of sulphur dioxide is given as,

$\begin{array}{l}{\text{2SO}}_{\text{2}}{}_{\text{(g)}}\text{+}{\text{O}}_{\text{2}}{}_{\text{(g)}}\underset{}{\overset{}{\to }}{\text{SO}}_{\text{3}}{}_{\text{(g)}}\\ \\ {\text{SO}}_{\text{3}}{}_{\text{(g)}}\text{+}{\text{H}}_{\text{2}}{\text{O}}_{\text{(l)}}\underset{}{\overset{}{\to }}{\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}{}_{\text{(aq)}}\end{array}$

The reaction between acid (sulphuric acid) and statues (calcium carbonate) is given as,

${\text{CaCO}}_{\text{3}}{}_{\text{(s)}}\text{+}{\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}{}_{\text{(aq)}}\underset{}{\overset{}{\to }}{\text{CaSO}}_{\text{4}}{}_{\text{(s)}}\text{+}{\text{H}}_{\text{2}}{\text{O}}_{\text{(l)}}\text{+}{\text{CO}}_{\text{2}}{}_{\text{(g)}}$

The number of moles of sulphur dioxide is calculated to determine the amount of sulphuric acid formed.

$\begin{array}{l}1lb=0.45359237kg\\ \\ 1000lb=0.45359237\times 1000\\ \\ =453.59kg\\ \\ (50\times 10^{6}tonsS{O}_2)\times \frac{2000lb}{1ton}\times \frac{453.6g}{1lb}\times \frac{1molS{O}_2}{64.07gS{O}_2}==7.1\times 10^{11}molS{O}_2\end{array}$

Only $20\text{}\%$ of sulphur dioxide is converted to sulphuric acid.  Therefore, number of sulphuric acid is calculated as,

$(0.20)\times (7.1\times 10^{11}molS{O}_2)\times \frac{1mol{H}_{2}S{O}_4}{1molS{O}_2}=1.4\times 10^{11}mol{H}_{2}S{O}_4$

The number of moles of calcium carbonate destroyed per statue is determined as,

$(0.05)\times (1000lbCaC{O}_3)\times \frac{453.6g}{1lb}\times \frac{1molCaC{O}_3}{100.1gCaC{O}_3}=226.6molCaC{O}_3/statue$

The number of statues destroyed by $20\text{}\%$ of sulphur dioxide is calculated as,

$(1.4\times 10^{11}mol{H}_{2}S{O}_4)\times \frac{1molCaC{O}_3}{1mol{H}_{2}S{O}_4}\times \frac{1statue}{226.6molCaC{O}_3}==6.2\times 10^{8}statues$

(b)

Interpretation Introduction

Interpretation:

The other damage occured by acid rain has to be identified.

Concept introduction:

Acid rain:

Acid rain is a kind of precipitation which is acidic that it has more hydrogen ions.  It affects buildings, plants and animals.  It occurs due to emission of sulfur dioxide and nitrogen oxide which reacts with water to form acid rain.

Explanation of Solution

The formation of sulphuric acid due to emission of sulphur dioxide is given as,

$\begin{array}{l}{\text{2SO}}_{\text{2}}{}_{\text{(g)}}\text{+}{\text{O}}_{\text{2}}{}_{\text{(g)}}\underset{}{\overset{}{\to }}{\text{SO}}_{\text{3}}{}_{\text{(g)}}\\ \\ {\text{SO}}_{\text{3}}{}_{\text{(g)}}\text{+}{\text{H}}_{\text{2}}{\text{O}}_{\text{(l)}}\underset{}{\overset{}{\to }}{\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}{}_{\text{(aq)}}\end{array}$

The reaction between acid (sulphuric acid) and statues (calcium carbonate) is given as,

${\text{CaCO}}_{\text{3}}{}_{\text{(s)}}\text{+}{\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}{}_{\text{(aq)}}\underset{}{\overset{}{\to }}{\text{CaSO}}_{\text{4}}{}_{\text{(s)}}\text{+}{\text{H}}_{\text{2}}{\text{O}}_{\text{(l)}}\text{+}{\text{CO}}_{\text{2}}{}_{\text{(g)}}$

Apart from sulphuric acid destroying calcium carbonate, it forms carbon dioxide.  Carbon dioxide is a greenhouse gas which gets trapped in atmosphere and causes global warming.