Final answer:
In a closed room with 40 m³ of air, the mass of combustible fuel needed to create an incapacitating atmosphere is calculated by determining the volume of CO₂ and H₂O gas produced when the fuel is burned. The correct option for the mass of fuel required to incapacitate people in 30 minutes and 10 minutes is 3.84 kg and 1.28 kg respectively.
Step-by-step explanation:
To determine the amount of combustible fuel needed to create an atmosphere that might incapacitate people in a closed room, we need to calculate the volume of CO₂ and H₂O gas produced when the fuel is burned. First, we need to convert the volume of the room from cubic meters to liters. 40 m³ = 40,000 L. Then, we can use the equation V = nRT/P to calculate the moles of gas produced.
We assume that CO₂ and H₂O are the only products of combustion. Since propane (C₃H₈) is a typical combustible fuel, the combustion reaction can be written as: C₃H₈ + 5O₂ → 3CO₂ + 4H₂O. By stoichiometry, 1 mole of C₃H₈ produces 3 moles of CO₂. The molar mass of propane is 44.1 g/mol. So, the mass of propane needed to produce enough CO₂ to incapacitate people in 30 minutes can be calculated. Since propane is combusted completely, the amount of fuel required for incapacitation in 10 minutes can be calculated by dividing the mass of fuel for 30 minutes by 3 since the reaction is a first-order reaction.
Therefore, the correct option is b. 3.84 kg for 30 minutes, 1.28 kg for 10 minutes.