Question

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 \(25 \%\) 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

(a) The plant produced approximately 25,677,893 tons of CO2 and 4,188,363 tons of SO2. (b) Around 3,460,299 tons of CaSO3 would be produced by removing 55% of the SO2.

Step-by-step solution

Understand and break down the problem

First, we will find out the total tons of carbon and the total tons of sulfur in the coal. Total coal burned in Taylorsville = 8,376,726 tons Percentage of Carbon = 83% Percentage of Sulfur = 25%

Calculate tons of Carbon and Sulfur

Tons of Carbon = (Total coal × Percentage of Carbon) / 100 Tons of Sulfur = (Total coal × Percentage of Sulfur) / 100

Calculate tons of Carbon Dioxide (CO2) and Sulfur Dioxide (SO2)

Now we need to convert the tons of carbon and sulfur into their respective dioxide forms. 1 mole of Carbon (C) = 12 g 1 mole of CO2 = 44 g Similarly, 1 mole of Sulfur (S) = 32 g 1 mole of SO2 = 64 g Since moles are proportional to mass in this case, Mass of CO2 = Mass of Carbon × (Mass of CO2 / Mass of C) Mass of SO2 = Mass of Sulfur × (Mass of SO2 / Mass of S)

Calculate the tons of Calcium Sulfite (CaSO3) produced

Given that 55% of the SO2 can be removed by reaction with powdered CaO to form CaSO3: 1 mole of CaO = 56 g 1 mole of SO2 = 64 g 1 mole of CaSO3 = 120 g Since moles are proportional to mass in this case, Mass of CaSO3 produced = Mass of SO2 (55%) × (Mass of CaSO3 / Mass of SO2) Now, let's substitute provided values and do the necessary calculations to find the final answers.

Calculations

Tons of Carbon = (8,376,726 × 83) / 100 = 6,952,782.18 tons Tons of Sulfur = (8,376,726 × 25) / 100 = 2,094,181.5 tons Mass of CO2 = 6,952,782.18 × (44 / 12) = 25,677,892.94 tons Mass of SO2 = 2,094,181.5 × (64 / 32) = 4,188,363 tons Mass of CaSO3 produced = 4,188,363 × 0.55 × (120 / 64) = 3,460,299.25 tons To summarize our findings: (a) Total tons of CO2 produced: approximately 25,677,893 tons. Total tons of SO2 produced: approximately 4,188,363 tons. (b) Total tons of CaSO3 produced: approximately 3,460,299 tons.

Key concepts

Combustion Reactions

A combustion reaction is a chemical process where a fuel combines with an oxidizer, typically oxygen, releasing energy in the form of heat and light. Most fuels are hydrocarbons, and when they burn completely, they produce carbon dioxide (CO₂) and water (H₂O). However, other elements like sulfur, when present, also combust and form other products, such as sulfur dioxide (SO₂). In our exercise, we look at coal combustion, which is primarily composed of carbon but can also contain other elements like sulfur.

In understanding a combustion reaction for a substance like coal, it's essential to consider the elements involved and the stoichiometric coefficients that help in balancing the chemical equation. The coefficients indicate the proportions in which the reactants combine to form products. For coal that is predominantly carbon but contains sulfur as well, we need to account for both the carbon and sulfur components when calculating the products formed during combustion.

Mole Concept

The mole concept is a fundamental cornerstone in chemistry, facilitating the understanding of chemical reactions on a quantitative level. It is essentially a counting unit for atoms, molecules, or formula units, much like a dozen represents a count of twelve items. One mole is defined as the amount of a substance that contains exactly 6.022×10²³ (Avogadro's number) of particles.

These particles could be atoms, molecules, ions, or electrons. In stoichiometry and chemical calculations, the molar mass (the mass of one mole of a substance) becomes especially crucial because it allows us to convert between the mass of a substance and the number of moles, and thus the number of atoms or molecules, it contains. For instance, when coal burns and produces CO₂ and SO₂, we use the molar masses of carbon, sulfur, carbon dioxide, and sulfur dioxide to work out how much of each product is formed from a certain amount of coal.

Chemical Calculations

Chemical calculations are vital for quantitatively describing the transformations that occur in chemical reactions. Through stoichiometry, which is the calculation of reactants and products in chemical reactions, we can determine the exact amounts of substances required or produced. The process involves using balanced chemical equations, which provide the mole ratio of the reactants and the products.

The exercise provided is a prime example of practical chemical calculations. Starting with the total tons of coal burned, we calculate the mass of carbon and sulfur in the coal. Using stoichiometry, we then determine the mass of CO₂ and SO₂ produced from these masses. Additionally, we can further calculate products of secondary reactions, such as the formation of calcium sulfite (CaSO₃) when calcium oxide (CaO) reacts with sulfur dioxide.

These calculations are not just abstract figures—they have real-world implications, such as environmental pollution assessment, resource management, and in this case, determining the potential impact of a power plant's emissions on the environment.