Carbon dioxide, which is recognized as the major contributor to global warming as a “greenhouse gas,” is formed when fossil fuels are combusted, as in electrical power plants fueled by coal, oil, or natural gas. One potential way to reduce the amount of CO2 added to the atmosphere is to store it as a compressed gas in underground formations. Consider a 1000-megawatt coal-fired power plant that produces about 6×106 tons of CO2 per year. a. Assuming ideal-gas behavior, 1.00 atm, and 27°C, calculate the volume of CO2 produced by this power plant.

Verified step by step guidance

1. Convert the temperature from degrees Celsius to Kelvin by adding 273.15 to the Celsius temperature: \( T(K) = 27 + 273.15 \).
2. Use the ideal gas law equation \( PV = nRT \) to find the volume \( V \). Rearrange the equation to solve for \( V \): \( V = \frac{nRT}{P} \).
3. Calculate the number of moles \( n \) of CO2 using the given mass and the molar mass of CO2 (approximately 44.01 g/mol). First, convert the mass from tons to grams, then use \( n = \frac{\text{mass in grams}}{\text{molar mass}} \).
4. Substitute the values into the ideal gas law equation: \( P = 1.00 \text{ atm} \), \( R = 0.0821 \text{ L atm/mol K} \), \( T \) in Kelvin, and \( n \) calculated in the previous step.
5. Calculate the volume \( V \) in liters, which will give you the volume of CO2 produced by the power plant under the given conditions.

Key Concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law allows us to predict the behavior of gases under various conditions, making it essential for calculating the volume of gases like CO2 produced in combustion processes.

Molar Volume of a Gas

The molar volume of a gas is the volume occupied by one mole of an ideal gas at standard temperature and pressure (STP), which is 0°C and 1 atm. At these conditions, the molar volume is approximately 22.4 liters. However, in this question, we are dealing with different conditions (27°C and 1 atm), so we must adjust our calculations using the Ideal Gas Law to find the volume of CO2 produced by the power plant.

Combustion of Fossil Fuels

The combustion of fossil fuels involves a chemical reaction where hydrocarbons react with oxygen to produce carbon dioxide and water, releasing energy. This process is a significant source of CO2 emissions, contributing to global warming. Understanding the amount of CO2 produced by such processes is crucial for developing strategies to mitigate climate change, such as carbon capture and storage.