Chapter 21, Problem 21.40QP

Calcium oxide or quicklime (CaO) is used in steelmaking, cement manufacture, and pollution control. It is prepared by the thermal decomposition of calcium carbonate.

$Cac{O}_3(s)\to CaO\left(s\right)+C{O}_2\left(g\right)$

Calculate the yearly release of CO₂ (in kilograms) to the atmosphere if the annual production of CaO in the United States is 1.7 × 10¹⁰ kg.

Interpretation Introduction

Interpretation: The yearly release of ${\text{CO}}_{\text{2}}$ into the atmosphere when given amount of $\text{CaO}$ is produced in US should be determined using given balanced equation.

Concept Introduction:

Balanced Equation: A chemical reaction is considered as balanced equation if all the number of atoms, the charge and the mass of elements on both reactant and the product side are equal in the reaction.

Moles: It is the number of particles present in the given specific substance. The formula used to identify the moles present in given mass of a compound is as follows,

$\text{x}\text{moles}\text{=}\frac{\text{Given}\text{mass}\text{of}\text{the}\text{sample}}{\text{Molecular}\text{mass}\text{of}\text{the}\text{sample}}$

Molar mass: It is the total mass of the substance including all the number and the mass of the elements present in substance.

Greenhouse effect:

The heat near the earth surface gets trapped by the gases present in the earth atmosphere. The carbon dioxide is the primary gas that traps more heat. The earth’s atmosphere contains gases that radiate energy in all directions in which the part of the energy gets imparted into the earth surface.

The imparted energy makes the earth surface to have high temperature.

Conditions that greenhouse gas should fulfil is as follows,

The gas is considered as greenhouse gas if it possesses dipole moment or the vibrational motions of the gases should create some temporary dipole moment.

Atmosphere: The atmosphere is defined as air that is layer of gases which surrounds the earth due to gravity of earth.

The earth atmosphere consists of layers such as thermosphere, mesosphere, stratosphere and troposphere depending on the temperature and its composition.

To determine: The amount of ${\text{CO}}_{\text{2}}$ released during $\text{CaO}$ production under given conditions.

Answer to Problem 21.40QP

There are about $1.3{\text{×10}}^{\text{10}}\text{kg}\text{of}{\text{CO}}_{\text{2}}$ released during production of $\text{1}{\text{.7×10}}^{\text{10}}\text{kg}\text{of}\text{CaO}$ considering the given balanced equation.

Explanation of Solution

Consider the balanced equation.

$\begin{array}{l}\text{x}\text{moles}\text{=}\frac{\text{Given}\text{mass}\text{of}\text{the}\text{sample}}{\text{Molar}\text{mass}\text{of}\text{the}\text{sample}}\\ 1\text{moles}\text{of}\text{CaO}=\frac{\text{1}{\text{.7×10}}^{\text{13}}\text{g}\text{of}\text{CaO}}{\text{56}\text{.08}\text{g}\text{/mol}\text{of}\text{CaO}}\\ 1\text{moles}\text{of}{\text{CO}}_{\text{2}}=\frac{\text{x g}\text{of}{\text{CO}}_{\text{2}}}{\text{44}\text{.01}\text{g}\text{/mol}\text{of}{\text{CO}}_{\text{2}}}\\ \text{Hence,}\\ \frac{\text{1}{\text{.7×10}}^{\text{13}}\text{g}\text{of}\text{CaO}}{\text{56}\text{.08}\text{g}\text{/mol}\text{of}\text{CaO}}=\frac{\text{x g}\text{of}{\text{CO}}_{\text{2}}}{\text{44}\text{.01}\text{g}\text{/mol}\text{of}{\text{CO}}_{\text{2}}}\\ \end{array}$

Considering the given balanced equation, it is clear that one mole of ${\text{CaCO}}_{\text{3}}$ gives one mole of $\text{CaO}$ and ${\text{CO}}_{\text{2}}$ which shows that one mole of $\text{CaO}$ is equal to one mole of ${\text{CO}}_{\text{2}}$.

Determine the amount of ${\text{CO}}_{\text{2}}$ released.

$\begin{array}{l}\text{x}\text{moles}\text{=}\frac{\text{Given}\text{mass}\text{of}\text{the}\text{sample}}{\text{Molar}\text{mass}\text{of}\text{the}\text{sample}}\\ \text{Mass}\text{of}{\text{CO}}_{\text{2}}\text{=}\frac{\text{1}{\text{.7×10}}^{\text{13}}\text{g}\text{of}\text{CaO}}{\text{56}\text{.08}\text{g}\text{/mol}\text{of}\text{CaO}}\times 44.01\text{g/mol}{\text{CO}}_{\text{2}}\\ =1.3{\text{×10}}^{\text{13}}\text{g}\text{of}{\text{CO}}_{\text{2}}\\ =1.3{\text{×10}}^{\text{10}}\text{kg}\text{of}{\text{CO}}_{\text{2}}\\ \\ \text{1kg}\text{=}\text{1000}\text{g}\\ {\text{=10}}^{\text{3}}\text{g}\end{array}$

The amount of ${\text{CO}}_{\text{2}}$ released during the production of $\text{CaO}$ is obtained by substituting the given values like mass of $\text{CaO}$ and the molar mass values of $\text{CaO}$ and ${\text{CO}}_{\text{2}}$

Conclusion

The mass of ${\text{CO}}_{\text{2}}$ released during $\text{CaO}$ production is determined.