Chapter 21, Problem 21.73QP

(a)

Interpretation Introduction

Interpretation: The number of 1000lb marble statues damaged by acid rain for the given condition (a) and undesirable result of acid rain damage should be determined.

Concept introduction:

• Balanced chemical equation of a reaction is written according to law of conservation of mass.
• Equation for Number of moles of a substance, from its given mass is,

$\text{Number of moles}\text{=}\frac{\text{Given}\text{mass}}{\text{Molecular}\text{mass}}$

• Mole ratio or molar ratio is the ratio between the amounts in moles of any two compounds involved in the chemical reaction.
• Pound is a unit of mass used in US customary systems of measurement. It is denoted by lb.

$\text{1}\text{lb}\text{=}\text{0}\text{.45359237}\text{kg}$

• Rock composed of recrystallized carbonate minerals, most commonly calcite or dolomite undergone transformation by heat, pressure and or other natural agencies results the formation of marble. Lime stone is a hard sedimentary rock composed mainly of calcium carbonate.
• Acid rain: It is made up of water droplets that are unusually acidic because of atmospheric pollution, particularly the excessive amounts of sulfur and nitrogen released by cars and industrial processes.
• Global warming is a serious environmental issue, in which there is an increase in the overall temperature of the earth by various factors.
• Greenhouse gases are the gases that trap heat in the atmosphere.

To write: the balanced reaction equation represent the formation of acid rain and the damage that acid rain causes to marble statue.

To explain: the acid rain

Answer to Problem 21.73QP

The number of 1000lb marble statues damaged by acid rain for the given condition is  $\text{6}\text{.2}{\text{×10}}^{\text{8}}\text{statues}$

Explanation of Solution

Acid rain: It is made up of water droplets that are unusually acidic because of atmospheric pollution, particularly the excessive amounts of sulfur and nitrogen released by cars and industrial processes.

Sulfur oxides liberated will react with oxygen in the atmosphere results the formation of sulfur trioxide which is combined with water to form sulfuric acid. Chemical reaction equation for this process can be represented as,

${\text{2SO}}_{\text{2}}{}_{\text{(g)}}\text{+}{\text{O}}_{\text{2}}{}_{\text{(g)}}\to {\text{SO}}_{\text{3}}{}_{\text{(g)}}$

        ${\text{SO}}_{\text{3}}{}_{\text{(g)}}\text{+}{\text{H}}_{\text{2}}{\text{O}}_{\text{(l)}}\to {\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}{}_{\text{(aq)}}$

In the given reaction, Sulfur oxides liberated will react with oxygen in the atmosphere results the formation of sulfur trioxide which is combined with water to form sulfuric acid.

The chemical equation for this reaction is,

${\text{2SO}}_{\text{2}}{}_{\text{(g)}}\text{+}{\text{O}}_{\text{2}}{}_{\text{(g)}}\to {\text{SO}}_{\text{3}}{}_{\text{(g)}}$

${\text{SO}}_{\text{3}}{}_{\text{(g)}}\text{+}{\text{H}}_{\text{2}}{\text{O}}_{\text{(l)}}\to {\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}{}_{\text{(aq)}}$

When ${\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}$ react with the marble to form ${\text{CaSO}}_{\text{4}}$ , ${\text{H}}_{\text{2}}\text{O}\text{and}{\text{CO}}_{\text{2}}$ through this way marble is destroyed. The chemical reaction equation for this process is,

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

Balanced chemical equation of a reaction is written according to law of conservation of mass.

Therefore,

The total number of each atoms in the reactant side should equal to the total number of each atoms in the product side.

So, in order to balance a chemical equation, the coefficients of compounds or atoms are needed to be changed in such a way that total number of each atoms in the reactant side and the total number of each atoms in the product side is to become equal.

Hence,

The above chemical equation is a balanced chemical equation.

Therefore,

The balanced equations for the given reactions are,

${\text{2SO}}_{\text{2}}{}_{\text{(g)}}\text{+}{\text{O}}_{\text{2}}{}_{\text{(g)}}\to {\text{SO}}_{\text{3}}{}_{\text{(g)}}$

${\text{SO}}_{\text{3}}{}_{\text{(g)}}\text{+}{\text{H}}_{\text{2}}{\text{O}}_{\text{(l)}}\to {\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}{}_{\text{(aq)}}$

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

The number of moles of ${\text{SO}}_{\text{2}}$ produced in the given reaction can be calculated as follows,

The mass of ${\text{SO}}_{\text{2}}$ reacts in the reaction is given as $\text{50}\text{million}\text{tons}\text{=}\text{50}\text{×}{\text{10}}^{\text{6}}\text{tons}$.

The 1000 lb of marble should be converted to kg before calculations.

$\text{1}\text{lb}\text{=}\text{0}\text{.45359237}\text{kg}$

$\text{1000}\text{lb}\text{=}\text{0}\text{.45359237×1000}$

          $\text{=}\text{453}\text{.59}\text{kg}$

Number of moles of a substance, from its given mass is,

$\text{Number of moles}\text{=}\frac{\text{Given}\text{mass}}{\text{Molecular}\text{mass}}$

Molecular mass of ${\text{SO}}_{\text{2}}$ is 64.07 mol/g.

Therefore,

The number of moles of ${\text{SO}}_{\text{2}}$ is,

${\text{(50×10}}^{\text{6}}\text{tons}{\text{SO}}_{\text{2}}\text{)}\text{×}\frac{\text{2000}\text{lb}}{\text{1}\text{ton}}\text{×}\frac{\text{453}\text{.6}\text{g}}{\text{1}\text{lb}}\text{×}\frac{\text{1}\text{mol}{\text{SO}}_{\text{2}}}{\text{64}\text{.07}\text{g}{\text{SO}}_{\text{2}}}$ $\text{=}\text{7}\text{.1}{\text{×10}}^{\text{11}}\text{mol}{\text{SO}}_{\text{2}}$

The number of moles of ${\text{SO}}_{\text{2}}$ formed in the reaction is $\text{7}\text{.1}{\text{×10}}^{\text{11}}\text{mol}{\text{SO}}_{\text{2}}$.

From the number of moles of ${\text{SO}}_{\text{2}}$ it is easy to determine the number of moles of ${\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}$ produced in the reaction.

It should be noted that only 20% of ${\text{SO}}_{\text{2}}$ is converted to ${\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}$.

The number of moles of ${\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}$ formed from 20% of ${\text{SO}}_{\text{2}}$ is,

$\text{(0}\text{.20)×(7}{\text{.1×10}}^{\text{11}}\text{mol}{\text{SO}}_{\text{2}}\text{)}\text{×}\frac{\text{1}\text{mol}{\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}}{\text{1}\text{mol}{\text{SO}}_{\text{2}}}\text{=}\text{1}\text{.4}{\text{×10}}^{\text{11}}\text{mol}{\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}$

Therefore the number of moles of ${\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}$ formed from 20% of ${\text{SO}}_{\text{2}}$ is $\text{1}\text{.4}{\text{×10}}^{\text{11}}\text{mol}{\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}$

Rock composed of recrystallized carbonate minerals, most commonly calcite or dolomite undergone transformation by heat, pressure and or other natural agencies results the formation of marble.

${\text{CaCO}}_{\text{3}}$ in marble is destroyed to ${\text{CaSO}}_{\text{4}}$ by the action of ${\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}$ in acid rain.

The reaction equation for this process is,

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

Number of moles of a substance, from its given mass is,

$\text{Number of moles}\text{=}\frac{\text{Given}\text{mass}}{\text{Molecular}\text{mass}}$

Molecular mass of  ${\text{CaCO}}_{\text{3}}$ is 100.1 mol/g

The moles of ${\text{CaCO}}_{\text{3}}$ damaged per statue are:

$\text{(0}\text{.05)×(1000}\text{lb}{\text{CaCO}}_{\text{3}}\text{)}\text{×}\frac{\text{453}\text{.6}\text{g}}{\text{1}\text{lb}}\text{×}\frac{\text{1}\text{mol}{\text{CaCO}}_{\text{3}}}{\text{100}\text{.1}\text{g}{\text{CaCO}}_{\text{3}}}$ $\text{=}\text{226}\text{.6}\text{mol}{\text{CaCO}}_{\text{3}}\text{/statue}$

The number of moles of ${\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}$ produced from 20% of ${\text{SO}}_{\text{2}}$ is $\text{1}\text{.4}{\text{×10}}^{\text{11}}\text{mol}{\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}$. From this value, the number of statues damaged by this amount of sulfuric acid can be calculated as follows,

The number of statues damaged by $\text{1}\text{.4}{\text{×10}}^{\text{11}}\text{mol}{\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}$ is,

$\text{(1}{\text{.4×10}}^{\text{11}}\text{mol}{\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}\text{)×}\frac{\text{1}\text{mol}{\text{CaCO}}_{\text{3}}}{\text{1}\text{mol}{\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}}\text{×}\frac{\text{1}\text{statue}}{\text{226}\text{.6}\text{mol}{\text{CaCO}}_{\text{3}}}$ $\text{=}\text{6}\text{.2}{\text{×10}}^{\text{8}}\text{statues}$

This value shows that any objects/statues made of marble are susceptible to attack by acid rain.

(b)

Interpretation Introduction

Interpretation: The number of 1000lb marble statues damaged by acid rain for the given condition (a) and undesirable result of acid rain damage should be determined.

Concept introduction:

• Balanced chemical equation of a reaction is written according to law of conservation of mass.
• Equation for Number of moles of a substance, from its given mass is,

$\text{Number of moles}\text{=}\frac{\text{Given}\text{mass}}{\text{Molecular}\text{mass}}$

• Mole ratio or molar ratio is the ratio between the amounts in moles of any two compounds involved in the chemical reaction.
• Pound is a unit of mass used in US customary systems of measurement. It is denoted by lb.

$\text{1}\text{lb}\text{=}\text{0}\text{.45359237}\text{kg}$

• Rock composed of recrystallized carbonate minerals, most commonly calcite or dolomite undergone transformation by heat, pressure and or other natural agencies results the formation of marble. Lime stone is a hard sedimentary rock composed mainly of calcium carbonate.
• Acid rain: It is made up of water droplets that are unusually acidic because of atmospheric pollution, particularly the excessive amounts of sulfur and nitrogen released by cars and industrial processes.
• Global warming is a serious environmental issue, in which there is an increase in the overall temperature of the earth by various factors.
• Greenhouse gases are the gases that trap heat in the atmosphere.
• To determine: undesirable result of acid rain damage for the given reaction

Answer to Problem 21.73QP

The ${\text{CO}}_{\text{2}}$ liberated from limestone contributes to global warming.

Explanation of Solution

Explanation

Acid rain: It is made up of water droplets that are unusually acidic because of atmospheric pollution, particularly the excessive amounts of sulfur and nitrogen released by cars and industrial processes.

In the given reaction, Sulfur oxides liberated will react with oxygen in the atmosphere results the formation of sulfur trioxide which is combined with water to form sulfuric acid.

The chemical equation for this reaction is,

${\text{2SO}}_{\text{2}}{}_{\text{(g)}}\text{+}{\text{O}}_{\text{2}}{}_{\text{(g)}}\to {\text{SO}}_{\text{3}}{}_{\text{(g)}}$

${\text{SO}}_{\text{3}}{}_{\text{(g)}}\text{+}{\text{H}}_{\text{2}}{\text{O}}_{\text{(l)}}\to {\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}{}_{\text{(aq)}}$

When ${\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}$ react with the marble to form ${\text{CaSO}}_{\text{4}}$ , ${\text{H}}_{\text{2}}\text{O}\text{and}{\text{CO}}_{\text{2}}$ through this way marble is destroyed. The chemical reaction equation for this process is,

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

Destruction of marble by acid rain produces carbon dioxide in great extent. This is one of the important greenhouse gases. Greenhouse gases are the gases that trap heat in the atmosphere.

Global warming is a serious environmental issue, in which there is an increase in the overall temperature of the earth by various factors. Presence of greenhouse gases like ${\text{CO}}_{\text{2}}$ will promote global warming.

Therefore the ${\text{CO}}_{\text{2}}$ liberated from limestone (it is also similar to marble with chemical formula ${\text{CaCO}}_{\text{3}}$ ) contributes to global warming.