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Chapter 18: Problem 81

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 \(\mathrm{SO}_{2}\) could be removed by reaction with powdered \(\mathrm{CaO}\) to form \(\mathrm{CaSO}_{3},\) how many tons of \(\mathrm{CaSO}_{3}\) would be produced?

Short Answer

Expert verified
The mass of carbon and sulfur in the coal are calculated as \(Mass\_Carbon = 8376726 * 0.83\) tons and \(Mass\_Sulfur = 8376726 * 0.025\) tons, respectively. The mass of CO₂ produced is \( Mass\_CO2 = Mass\_Carbon * \frac{Molar\_Mass\_CO2}{Molar\_Mass\_C} \) tons, and the mass of SO₂ produced is \( Mass\_SO2 = Mass\_Sulfur * \frac{Molar\_Mass\_SO2}{Molar\_Mass\_S} \) tons. By removing 55% of the SO₂, the mass of SO₂ removed is \( Mass\_SO2\_Removed = Mass\_SO2 * 0.55 \) tons. Finally, the mass of CaSO₃ produced is \( Mass\_CaSO3 = Mass\_SO2\_Removed * \frac{Molar\_Mass\_CaSO3}{Molar\_Mass\_SO2} \) tons.

Step by step solution

01

Calculate the mass of carbon in the coal

To find the mass of carbon in the coal, multiply the total mass burned by the percentage of carbon in it (83%). \[Mass\_Carbon = 8376726 * 0.83\]
02

Calculate the mass of sulfur in the coal

To find the mass of sulfur in the coal, multiply the total mass burned by the percentage of sulfur in it (2.5%). \[Mass\_Sulfur = 8376726 * 0.025\]
03

Calculate mass of CO₂ produced

In the complete combustion of carbon, one mole of carbon reacts with one mole of oxygen to produce one mole of CO₂. Therefore, the mass of CO₂ produced is related to the mass of carbon through their molar masses: \[ Mass\_CO2 = Mass\_Carbon * \frac{Molar\_Mass\_CO2}{Molar\_Mass\_C} \]
04

Calculate mass of SO₂ produced

In the complete combustion of sulfur, one mole of sulfur reacts with one mole of oxygen to produce one mole of SO₂. Thus, the mass of SO₂ produced is related to the mass of sulfur through their molar masses: \[ Mass\_SO2 = Mass\_Sulfur * \frac{Molar\_Mass\_SO2}{Molar\_Mass\_S} \]
05

Calculate mass of SO₂ removed

We are told that 55% of the SO₂ can be removed by reaction with CaO. Thus, multiply the mass of SO₂ produced by 55% to calculate the mass of SO₂ removed. \[ Mass\_SO2\_Removed = Mass\_SO2 * 0.55 \]
06

Calculate mass of CaSO₃ produced

In the reaction between SO₂ and CaO, one mole of SO₂ reacts with one mole of CaO to produce one mole of CaSO₃. Therefore, the mass of CaSO₃ is related to the mass of SO₂ removed through their molar masses: \[ Mass\_CaSO3 = Mass\_SO2\_Removed * \frac{Molar\_Mass\_CaSO3}{Molar\_Mass\_SO2} \] With these calculations we have found the number of tons of CO₂ and SO₂ produced during the year and the number of tons of CaSO₃ produced after removing 55% of SO₂ by reaction with powdered CaO.

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