Problem 70 - Chemistry: The Central Science

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 \(2.5 \%\) 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?

Step-by-Step Solution

Answer

The tons of CO2 and SO2 produced by the power plant are calculated using the stoichiometry of the combustion reactions: \(Tons\,of\,CO2 = 6,952,484\,tons\) and \(Tons\,of\,SO2 = 209,418\,tons\). When 55% of the SO2 is removed by reaction with CaO, the amount of CaSO3 produced is \(Tons\,of\,CaSO3 = 169,546\,tons\).

Step 1: Determine the tons of coal burned for each element

: First, let's find out the tons of coal burned for carbon and sulfur, using their respective percentages in the coal. For Carbon: \( Tons\,of\,carbon =Total\,tons\,of\,coal \times \% carbon \) \( Tons\,of\,carbon = 8,376,726 \times 0.83 \) For Sulfur: \( Tons\,of\,sulfur = Total\,tons\,of\,coal \times \% sulfur \) \( Tons\,of\,sulfur = 8,376,726 \times 0.025 \)

Step 2: Calculate the tons of CO2 and SO2 produced

: Now, let's calculate the tons of CO2 and SO2 produced by using the stoichiometry of the combustion reaction. For Carbon dioxide (CO2): The stoichiometry of the reaction is 1 mol of C produces 1 mol of CO2. So, using the molar masses of C and CO2, we can find the tons of CO2 produced. \( Tons\,of\,CO2 = \frac{Molar\,mass\,of\,CO2}{Molar\,mass\,of\,C} \times Tons\,of\,carbon \) For Sulfur dioxide (SO2): The stoichiometry of the reaction is 1 mol of S produces 1 mol of SO2. So, using the molar masses of S and SO2, we can find the tons of SO2 produced. \( Tons\,of\,SO2 = \frac{Molar\,mass\,of\,SO2}{Molar\,mass\,of\,S} \times Tons\,of\,sulfur \)

Step 3: Calculate the tons of CaSO3 produced

: Lastly, we have to calculate the tons of calcium sulfite (CaSO3) produced when 55% of the SO2 is removed by reaction with CaO. The stoichiometry of the reaction is 1 mol of SO2 reacts with 1 mol of CaO to form 1 mol of CaSO3. So, we'll use the molar masses of SO2 and CaSO3 to find the amount of CaSO3 produced. \( Tons\,of\,CaSO3 = \frac{Molar\,mass\,of\,CaSO3}{Molar\,mass\,of\,SO2} \times Tons\,of\,SO2\,removed \) where \(Tons\,of\,SO2\,removed = 0.55 \times Tons\,of\,SO2\)

Key Concepts

Combustion Reactions

Combustion reactions are a type of chemical reaction where a substance combines with oxygen to release energy in the form of heat and light. Typically, these substances are organic, like coal or gasoline, containing carbon and hydrogen. When they burn, they predominantly produce carbon dioxide (CO2) and water (H2O).

The process of burning fossil fuels, such as coal in our exercise, is crucial to understand as it links to environmental concerns. Complete combustion requires an abundant supply of oxygen; otherwise, incomplete combustion occurs which can produce toxic byproducts such as carbon monoxide (CO) and soot. Calculating the products of combustion reactions, such as CO2 and sulfur dioxide (SO2) from coal, requires an understanding of stoichiometry, which helps predict the amount of reactants and products in a chemical reaction.

Molar Mass Calculations

Molar mass is the weight of one mole (6.022 × 10²³ particles) of a substance and is expressed in grams per mole (g/mol). During calculations, understanding the molar mass of a compound is essential in converting between mass and number of moles.

In our example, calculating the mass of carbon dioxide or sulfur dioxide produced from burning coal hinges on the molar masses of carbon (C), sulfur (S), CO2, and SO2. These values can be found on the periodic table and are vital for accurate stoichiometric calculations. For carbon, the molar mass is approximately 12.01 g/mol, while sulfur's is about 32.06 g/mol. Knowing these allows us to convert tonnes of carbon and sulfur to moles, then to the mass of the respective oxides.

Chemical Stoichiometry

Chemical stoichiometry involves the quantitative relationship between reactants and products in a chemical reaction. This concept is foundational for performing calculations like those in the Taylorsville power plant's coal combustion.

To do this, we must balance chemical equations and use ratios of reactants and products, referred to as stoichiometric coefficients, to ensure the mass conservation law is respected. Starting with a balanced equation allows us to relate moles of one substance to moles of another. In our exercise, the stoichiometry of combustion was used to calculate tons of CO2 and SO2 produced from the given tons of coal. In later steps, understanding the reaction between SO2 and CaO to form CaSO3, including the 55% efficiency in SO2 removal, applies stoichiometry to predict the amount of byproduct formed. This is integral for process planning and environmental compliance.