Problem 79 - Chemistry: The Central Science in SI Units, Global Edition

Question

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?

Step-by-Step Solution

Answer

(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 1: 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%)

Step 2: 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)

Step 3: 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.

Key Concepts

Carbon dioxide emissions

When coal combusts, carbon combines with oxygen to form carbon dioxide \( (CO_2) \). This reaction releases energy used to power plants but also contributes to greenhouse gas emissions. In this exercise, the power plant burned 1,430,000 metric tons of coal, which is 80% carbon.
To find the carbon dioxide emissions, we first calculate the amount of carbon.

• Amount of carbon = 1,430,000 tons \( \times \) 80% = 1,144,000 tons of carbon
• Using the equation \( C + O_2 \rightarrow CO_2 \), 1 mole of carbon will produce 1 mole of carbon dioxide.
• The molar mass of carbon is 12 g/mol and carbon dioxide is 44 g/mol.

The mass of \( CO_2 \) produced is calculated by multiplying theamount of carbon by the mole ratio and the molar mass of \( CO_2 \), yielding 4,192,000 tons of \( CO_2 \). This significant emission is a key factor in climate change due to its greenhouse effect.

Sulfur dioxide emissions

Sulfur in coal also undergoes a combustion reaction to form sulfur dioxide \( (SO_2) \). This occurs when sulfur combines with oxygen during burning.
With 1,430,000 tons of coal, and assuming 3% of the coal's composition is sulfur:

• Amount of sulfur = 1,430,000 tons \( \times \) 3% = 42,900 tons of sulfur
• According to \( S + O_2 \rightarrow SO_2 \), 1 mole of sulfur produces 1 mole of \( SO_2 \).
• The molar mass of sulfur is 32 g/mol and \( SO_2 \) is 64 g/mol.

Using stoichiometry, this results in 85,800 tons of \( SO_2 \).
Sulfur dioxide is a major contributor to acid rain and poses a threat to air quality and public health. Controlling these emissions is crucial for an overall reduction in environmental pollution.

Stoichiometry

Stoichiometry is the part of chemistry that involves calculations based on the quantities of reactants and products in a chemical reaction. In this exercise, stoichiometry allows us to calculate how much \( CO_2 \) and \( SO_2 \) is produced from burning coal. It uses the balanced chemical equations and molar masses of each substance.
Here, we applied stoichiometry in these steps:

• Converted the percentage composition of coal into actual amounts of carbon and sulfur.
• Used chemical equations and molar masses to find the masses of \( CO_2 \) and \( SO_2 \) formed.

Understanding stoichiometry helps in determining the efficiency of reactions and is essential for engineers and chemists working on emissions controls. It provides the foundation for exact calculations needed in industrial applications.

Chemical equations

Chemical equations are symbolic ways to represent chemical reactions. They tell us what reactants undergo conversion to what products. The equations for combustion of carbon and sulfur in this exercise are:

• \( C + O_2 \rightarrow CO_2 \)
• \( S + O_2 \rightarrow SO_2 \)
• \( CaO + SO_2 \rightarrow CaSO_3 \)

The coefficient of each element or compound tells us the number of moles involved.
Balanced equations are pivotal as they reflect the conservation of mass principle—no matter is lost or gained in chemical reactions. This allows us to calculate how much of each product forms from given reactants efficiently.

Environmental chemistry

Environmental chemistry focuses on the impact of chemicals on the environment. It studies the effects of pollutants like \( CO_2 \) and \( SO_2 \), produced in combustion reactions.

• \( CO_2 \) is a recognized greenhouse gas that traps heat in the atmosphere,leading to global warming and climate change.
• \( SO_2 \) contributes to acid rain, which harms ecosystems, buildings, and water bodies by lowering pH levels.

The reaction of \( SO_2 \) with \( CaO \) to form \( CaSO_3 \) is an example of mitigating "scrubber" technology in power plants. This helps reduce \( SO_2 \) emissions by 50%, effectively lessening air pollution. Environmental chemistry seeks solutions like these to protect and heal our planet from industrial impacts.