Question

On a 5 day wilderness expedition you'll need to heat 4.0kg of water to the boiling point each day. The air temperature will average 25°C. You have available canisters of compressed propane C3H8 fuel, which you'll burn to heat the water. Each canister has 100.G of propane in it. What is the minimum number of fuel canisters you must bring? The standard heat of formation of propane at 25°C is −103.85/kJmol. You'll probably find other helpful data in the ALEKS Data resource.

Answer 1

To heat 4 kg of water from 25°C to 100°C for a 5-day period, you would need 30 canisters of propane, as each canister can provide 235.74 kJ of energy and each day requires approximately 1,254 kJ.

Step-by-step explanation:

To determine the minimum number of fuel canisters you must bring for a 5-day wilderness expedition to heat 4.0 kg of water to the boiling point daily, you'll need to consider the energy needed to heat the water and the energy provided by the combustion of propane. First, to heat 1 kg of water by 1°C (1 Kelvin), it takes 4.184 kJ. The water needs to be heated from 25°C to 100°C, which is a 75°C increase. Therefore, for 4 kg of water, the energy required per day is 4 kg × 75°C × 4.184 kJ/kg°C = 1,254 kJ.

Each mole of propane (C3H8) releases −103.85 kJ of energy upon combustion. Considering the molar mass of propane is approximately 44.1 g/mol, 100 g of propane contains about 100 g / 44.1 g/mol = 2.27 mol. Thus, each canister releases 2.27 mol × 103.85 kJ/mol = 235.74 kJ of energy.

To meet the daily energy requirement, you would need 1,254 kJ / 235.74 kJ/canister ≈ 5.32 canisters per day. Since you can't bring a fraction of a canister, you'll need 6 canisters per day. For a 5-day trip, 6 canisters/day × 5 days = 30 canisters. Consequently, the minimum number of fuel canisters to bring is 30.