Question

On a 7 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.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.

Answer 1

Answer:

38 canisters

Explanation:

The combustion of propane can be represented by the equation below:

C₃H₈ (g) + O₂ (g) → CO₂ (g) + H₂O(g)     ΔHc = -103.85 kJ/mol

The boiling of water is represented below:

H₂O(l) → H₂O(g)    ΔH = Q = mcΔT

The heat necessary to make water reach the boiling point is Q, which is calculated with the mass of water (m = 4.0 kg), its specif heat capacity ( c = 4.200 J/kg°C) and temperature variation (ΔT = 100 - 25)

Therefore, ΔH = Q = 4.0 kg x 4.200 kJ/kg°C x 75 °C

ΔH = Q = 1260.0 kJ

This is the amount of heat necessary to heat the water every day. Since the expedition will last 7 days, the total heat will be 8820 kJ

Now we need to calculate the amount of propane needed to generate this heat:

1 mol C₃H₈ _______ 103.85 kJ

X                 _______ 8820 kJ

x = 84.9 mol C₃H₈

1 mol C₃H₈ _____ 44 g

84.9 mol C₃H₈ ___ x

x = 3735.6 g

1 canister _____ 100 g C₃H₈

x               _____ 3735.6 g

x = 37.3 canisters

The minimum number of fuel canisters I must bring is 38 canisters.