One of the largest sources of SO2 to the atmosphere is coal-fired power plants. Calculate the volume of SO2 in liters produced by burning 1 kg of coal that contains 2% sulfur. Assume all the sulfur is converted to SO2.

Verified step by step guidance

Step 1: Determine the mass of sulfur in the coal. Since the coal contains 2% sulfur, calculate the mass of sulfur in 1 kg of coal by multiplying 1 kg by 0.02.

Step 2: Convert the mass of sulfur to moles. Use the molar mass of sulfur (approximately 32.07 g/mol) to convert the mass of sulfur obtained in Step 1 to moles.

Step 3: Use the stoichiometry of the reaction to find moles of SO2 produced. The balanced chemical equation for the conversion of sulfur to sulfur dioxide is S + O2 -> SO2. This indicates a 1:1 mole ratio between sulfur and SO2.

Step 4: Convert moles of SO2 to volume. Use the ideal gas law or the molar volume of a gas at standard temperature and pressure (STP), which is 22.4 L/mol, to convert the moles of SO2 to volume in liters.

Step 5: Summarize the process. Ensure all units are consistent and check calculations for accuracy, confirming the volume of SO2 produced from the given mass of coal.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It allows us to calculate the amounts of substances involved based on balanced chemical equations. In this case, understanding the stoichiometric conversion of sulfur to sulfur dioxide (SO2) is essential for determining the volume produced from burning coal.

Molar Volume of a Gas

The molar volume of a gas at standard temperature and pressure (STP) is approximately 22.4 liters per mole. This concept is crucial for converting moles of a gas into volume. In the context of the question, once the moles of SO2 produced from the sulfur in coal are calculated, this molar volume can be used to find the total volume of SO2 generated.

Percent Composition

Percent composition refers to the percentage by mass of each element in a compound. In this scenario, knowing that the coal contains 2% sulfur allows us to calculate the mass of sulfur in 1 kg of coal. This information is vital for determining how much sulfur is available to be converted into SO2 during combustion.

Recommended video:

Guided course

00:38

Mass Percent Calculation

Related Practice

Textbook Question

Titanium(III) chloride, a substance used in catalysts for preparing polyethylene, is made by high-temperature reaction of TiCl₄ vapor with H₂: 2 TiCl₄(g) + H₂(g) → 2 TiCl₃(s) + 2 HCl(g) (b) How many liters of HCl gas at STP will result from the reaction described in part (a)?

Textbook Question

A typical high-pressure tire on a bicycle might have a volume of 365 mL and a pressure of 7.80 atm at 25 °C. Suppose the rider filled the tire with helium to minimize weight. What is the mass of the helium in the tire?

Textbook Question

Assume that you have 1.00 g of nitroglycerin in a 500.0-mL steel container at 20.0 °C and 1.00 atm pressure. An explosion occurs, raising the temperature of the container and its contents to 425 °C. The balanced equation is 4 C3H5N3O91l2¡ 12 CO21g2 + 10 H2O1g2 + 6 N21g2 + O21g2 (c) What is the pressure in atmospheres inside the container after the explosion according to the ideal gas law?

Textbook Question

Natural gas is a mixture of many substances, primarily CH4, C2H6, C3Hg, and C4H10. Assuming that the total pressure of the gases is 1.48 atm and that their mole ratio is 94:4.0:1.5:0.50, calculate the partial pressure in atmospheres of each gas.

Textbook Question

A special gas mixture used in bacterial growth chambers contains 1.00% by weight CO2 and 99.0% O2. What is the partial pressure in atmospheres of each gas at a total pressure of 0.977 atm?