What is the minimum number of fuel canisters you must bring?The standard heat of formation of propane at 25°C is −103.8/kJmol

Question

On a 

12

 day wilderness expedition you'll need to heat 5.0kg

 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 25.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 −103.8/kJmol

.

Answer 1

5.0 kg H2O / day x 12 days = 60.0 kg H2O needed to be heated

q = mC∆T

q = heat = ?

m = mass = 60.0 kg

C = specific heat of water = 4.184 kJ/kgº

∆T = change in temperature = 100º - 25º = 75º (100º is the boiling point of H2O)

q = (60.0 kg)(4.184 kJ/kgº)(75º) = 18,828 kJ of heat energy needed

Combustion of propane:

1 mol C3H8 = 103.8 kJ

molar mass C3H8 = 44 g/mol

25 g C3H8 x 1 mol / 44 g = 0.568 moles C3H8 / canister

0.568 mol C3H8 / canister x 103.8 kJ / mol = 59. kJ / canister

18,828 kJ x 1 canister / 59 kJ = 319⁺ canisters needed

Minimum number of canisters needed = 320 canisters