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Chapter 18: Problem 79

A 500 megawatt electrical power plant typically burned 1,430,000 metric tons of coal in a year. (a) Assuming that the coal was \(80 \%\) carbon and \(3 \%\) 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 \(50 \%\) 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
(a) The amount of CO2 produced is 824,000 tons, and the amount of SO2 produced is 30,780 tons. (b) The amount of CaSO3 produced when 50% of the SO2 is removed is 15,390 tons.

Step by step solution

01

Determine the amount of carbon and sulfur in coal

First, we need to find out how much carbon and sulfur are present in the coal. According to the problem, the coal is 80% carbon and 3% sulfur. To find the amount of carbon and sulfur in the 1,430,000 metric tons of coal burned, we need to multiply the total amount of coal by the percentage of carbon and sulfur. Amount of carbon = (1,430,000 tons of coal) x (80%) Amount of sulfur = (1,430,000 tons of coal) x (3%)
02

Calculate the amount of CO2 and SO2 produced

Now, we will use the stoichiometry of the combustion reactions of carbon and sulfur to determine the mass of CO2 and SO2 formed. The balanced chemical equations for the reactions are: \(C + O_2 \rightarrow CO_2\) \(S + O_2 \rightarrow SO_2\) The molar masses are: C = 12 g/mol, O2 = 32 g/mol, CO2 = 44 g/mol, S = 32 g/mol, and SO2 = 64 g/mol. Using the stoichiometry of the reactions, we can calculate the mass of CO2 and SO2 produced. Mass of CO2 = (Amount of carbon) x (ratio of moles of CO2 to moles of C) x (molar mass of CO2) Mass of SO2 = (Amount of sulfur) x (ratio of moles of SO2 to moles of S) x (molar mass of SO2)
03

Calculate the amount of CaSO3 produced

Now, we need to determine how much CaSO3 will be produced if 50% of the SO2 is removed by a reaction with CaO. The balanced chemical equation for the reaction is: \(CaO + SO_2 \rightarrow CaSO_3\) The molar masses are: CaO = 56 g/mol and CaSO3 = 120 g/mol. Using the stoichiometry of the reaction, we can calculate the mass of CaSO3 that would be produced by reaction with 50% of the SO2 formed. Mass of CaSO3 = (50% of the mass of SO2) x (ratio of moles of CaSO3 to moles of SO2) x (molar mass of CaSO3) Now, calculate the values in each step and find the desired amounts of CO2, SO2, and CaSO3 produced.

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