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Chapter 18: Problem 79

In 1986 an electrical power plant in Taylorsville, Georgia, burned \(8,376,726\) tons of coal, a national record at that time. (a) Assuming that the coal was 83\(\%\) carbon and 2.5\(\%\) sulfur and that combustion was complete, calculate the number of tons of carbon dioxide and sulfur dioxide produced by the plant during the year. (b) If 55\(\%\) of the SO \(_{2}\) could be removed by reaction with powdered CaO to form \(\mathrm{CaSO}_{3},\) how many tons of \(\mathrm{CaSO}_{3}\) would be produced?

Short Answer

Expert verified
In 1986, the electrical power plant produced 25,597,760.06 tons of CO₂ and 418,836.3 tons of SO₂. If 55% of the SO₂ could be removed by reaction with powdered CaO, 431,174.93875 tons of CaSO₃ would be produced.

Step by step solution

01

Calculate tons of carbon and sulfur in coal

To calculate the mass of carbon and sulfur in the coal, we will first convert the percentage to a decimal and then multiply it by the total mass of the coal. Mass of carbon = (Percentage of carbon in coal) × (Total mass of coal) Mass of carbon = (0.83) × (8,376,726 tons) = 6,952,582.58 tons Mass of sulfur = (Percentage of sulfur in coal) × (Total mass of coal) Mass of sulfur = (0.025) × (8,376,726 tons) = 209,418.15 tons
02

Calculate tons of CO₂ and SO₂ produced

Complete combustion means that all carbon will convert to CO₂ and all sulfur will convert to SO₂. We will use the stoichiometry to calculate the mass of CO₂ and SO₂ produced. The balanced chemical equation for combustion of carbon and sulfur is as follows: C + O₂ → CO₂ S + O₂ → SO₂ Molar mass of C = 12 g/mol, Molar mass of CO₂ = 44 g/mol Molar mass of S = 32 g/mol, Molar mass of SO₂ = 64 g/mol Mass of CO₂ = (Mass of carbon) × (Molar mass of CO₂ / Molar mass of C) Mass of CO₂ = (6,952,582.58 tons) × (44/12) = 25,597,760.06 tons Mass of SO₂ = (Mass of sulfur) × (Molar mass of SO₂ / Molar mass of S) Mass of SO₂ = (209,418.15 tons) × (64/32) = 418,836.3 tons
03

Calculate the amount of SO₂ removed by reaction with CaO

To find the amount of SO₂ removed by reaction with CaO, we will first find the 55% of the total mass of SO₂ produced, and then use stoichiometry to calculate the mass of CaSO₃ formed. The balanced chemical equation for the reaction is as follows: SO₂ + CaO → CaSO₃ Mass of SO₂ removed = (Percentage of SO₂ removed) × (Total mass of SO₂ produced) Mass of SO₂ removed = (0.55) × (418,836.3 tons) = 230,359.965 tons
04

Calculate the mass of CaSO₃ produced

Now, we will use stoichiometry to calculate the mass of CaSO₃ produced from the reaction between SO₂ and CaO. Molar mass of CaO = 56 g/mol, Molar mass of CaSO₃ = 120 g/mol Mass of CaSO₃ produced = (Mass of SO₂ removed) × (Molar mass of CaSO₃ / Molar mass of SO₂) Mass of CaSO₃ produced = (230,359.965 tons) × (120/64) = 431,174.93875 tons The answers are: (a) 25,597,760.06 tons of CO₂, and 418,836.3 tons of SO₂ were produced. (b) 431,174.93875 tons of CaSO₃ would be produced if 55% of the SO₂ could be removed by reaction with powdered CaO.

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Most popular questions from this chapter

A reaction that contributes to the depletion of ozone in the stratosphere is the direct reaction of oxygen atoms with ozone: $$\mathrm{O}(g)+\mathrm{O}_{3}(g) \longrightarrow 2 \mathrm{O}_{2}(g)$$ At 298 \(\mathrm{K}\) the rate constant for this reaction is \(4.8 \times 10^{5}\) \(M^{-1} \mathrm{s}^{-1} .\) (a) Based on the units of the rate constant, write the likely rate law for this reaction. (b) Would you expect this reaction to occur via a single elementary process? Explain why or why not. (c) Use \(\Delta H_{f}^{\circ}\) values from Appendix \(C\) to estimate the enthalpy change for this reaction. Would this reaction raise or lower the temperature of the stratosphere?

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