Problem 98 - Chemistry: The Central Science in SI Units, Global Edition

Question

One method proposed for removing \(\mathrm{SO}_{2}\) from the flue gases of power plants involves scrubbing with an alkali solid such as calcium carbonate to form calcium sulfite and carbon dioxide gas. (a) Write a balanced chemical equation for the reaction. (b) What mass of \(\mathrm{CaCO}_{3}\) would be required to remove the \(\mathrm{SO}_{2}\) formed by burning \(1000 \mathrm{~kg}\) of coal containing \(8.0 \% \mathrm{~S}\) by mass? (c) What volume of \(\mathrm{CO}_{2}\) is formed under standard temperature and pressure? Assume that all reactions are \(100 \%\) efficient.

Step-by-Step Solution

Answer

(a) The balanced chemical equation for the reaction is: \(CaCO_{3} + SO_{2} \rightarrow CaSO_{3} + CO_{2}\). (b) The mass of CaCO3 required to remove the SO2 formed by burning 1000 kg of coal containing 8.0% S by mass is 250 kg. (c) The volume of CO2 formed under standard temperature and pressure is 56,000 L.

Step 1: Write the balanced chemical equation

The reaction between calcium carbonate (CaCO3) and sulfur dioxide (SO2) produces calcium sulfite (CaSO3) and carbon dioxide (CO2), as mentioned in the problem statement. Thus, the balanced chemical equation for this reaction is: \(CaCO_{3} + SO_{2} \rightarrow CaSO_{3} + CO_{2}\)

Step 2: Find the mass of sulfur in the coal

We are given that the coal contains 8.0% sulfur by mass. So, we need to find the mass of sulfur in 1000 kg of coal: Mass of sulfur = (Percentage of sulfur / 100) × Total mass of coal Mass of sulfur = (8.0 / 100) × 1000 kg = 80 kg

Step 3: Calculate the moles of sulfur

Now, we need to convert the mass of sulfur to moles. The molar mass of sulfur (S) is 32 g/mol, so: Moles of sulfur = (Mass of sulfur) / (Molar mass of sulfur) Moles of sulfur = 80,000 g / 32 g/mol ≈ 2500 moles

Step 4: Calculate the moles of SO2

When the coal burns, each mole of sulfur (S) forms one mole of sulfur dioxide (SO2). So, the moles of SO2 are the same as the moles of sulfur: Moles of SO2 = Moles of sulfur = 2500 moles

Step 5: Calculate the mass of CaCO3 required

From the balanced chemical equation, we see that one mole of SO2 reacts with one mole of CaCO3. So, the moles of CaCO3 required are the same as the moles of SO2: Moles of CaCO3 = Moles of SO2 = 2500 moles Now, we convert moles of CaCO3 to mass. The molar mass of CaCO3 is 100 g/mol, so: Mass of CaCO3 = (Moles of CaCO3) × (Molar mass of CaCO3) Mass of CaCO3 = 2500 moles × 100 g/mol = 250,000 g = 250 kg

Step 6: Calculate the moles of CO2 produced

From the balanced chemical equation, one mole of SO2 produces one mole of CO2. So, the moles of CO2 produced are the same as the moles of SO2: Moles of CO2 = Moles of SO2 = 2500 moles

Step 7: Calculate the volume of CO2 produced at STP

At standard temperature and pressure (STP), one mole of any gas occupies a volume of 22.4 liters. So, the volume of CO2 produced is: Volume of CO2 = (Moles of CO2) × (Volume of 1 mole of gas at STP) Volume of CO2 = 2500 moles × 22.4 L/mol ≈ 56,000 L To summarize the results: (a) The balanced chemical equation for the reaction is: \(CaCO_{3} + SO_{2} \rightarrow CaSO_{3} + CO_{2}\) (b) The mass of CaCO3 required to remove the SO2 formed by burning 1000 kg of coal containing 8.0% S by mass is 250 kg. (c) The volume of CO2 formed under standard temperature and pressure is 56,000 L.

Key Concepts

Sulfur Dioxide Removal

Sulfur dioxide ( SO₂ ) is a significant pollutant produced by burning fossil fuels, especially coal, which is often high in sulfur content. One effective method to remove SO₂ from emissions is using an alkali solid like calcium carbonate ( CaCO₃ ). In this process, when SO₂ gases pass through CaCO₃ , they react to form calcium sulfite ( CaSO₃ ) and carbon dioxide ( CO₂ ). By converting SO₂ to a less harmful form (as CaSO₃ ), its environmental impact, such as acid rain, is significantly reduced. This approach is beneficial in power plants and industrial settings to comply with environmental regulations and reduce air pollution.

In the described process, SO₂ removal through scrubbing involves:

• The reaction: CaCO₃ + SO₂ → CaSO₃ + CO₂
• Simplicity: Utilizes readily available materials, making it cost-effective.
• Efficiency: Potentially 100% effective, converting all SO₂ to CaSO₃ .

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions, crucial for understanding reactions like the SO₂ removal through scrubbing. It helps determine the exact amounts needed for a reaction to occur without excess reactants or products. This calculation involves converting mass to moles using the molar mass and understanding the mole ratio from the balanced chemical equation.

In our given problem:

• Determine the mass of sulfur in the coal: 8% of 1000 kg = 80 kg sulfur.
• Convert to moles of sulfur: with a molar mass of 32 g/mol, we get 2500 moles of S .
• Since one mole of sulfur produces one mole of SO₂ , we have 2500 moles of SO₂ .
• From the chemical equation: 1 mole of CaCO₃ reacts with 1 mole of SO₂ , hence 2500 moles needed of CaCO₃ .

This stoichiometric calculation ensures that SO₂ is completely scrubbed, leaving minimal environmental impact and achieving regulatory compliance.

Balanced Chemical Equation

A balanced chemical equation is fundamental in stoichiometry, ensuring mass conservation in reactions. Each atom must have the same number on both sides of the equation, reflecting that mass cannot be created or destroyed.

For the scrubbing of SO₂ with CaCO₃ , the balanced equation is: CaCO₃ + SO₂ → CaSO₃ + CO₂ Elements are balanced as follows:

• 1 Calcium (Ca) atom on each side.
• 1 Carbon (C) atom on each side.
• 2 Oxygen (O) atoms from SO₂ and 3 from CaCO₃ , balancing with 3 in CaSO₃ and 1 in CO₂ .
• 1 Sulfur (S) atom on each side.

Balancing chemical equations allows accurate predictions of reactants needed and products formed, foundational for chemical engineering and environmental chemistry.