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 −103.85/kJmol.

Answer 1

Answer:

319 is the minimum number of fuel canisters.

Explanation:

$Q=mc\Delta T$

Where:

Q = heat absorbed or heat lost

c = specific heat of substance

m = Mass of the substance  

ΔT = change in temperature of the substance

Mass of water = 5.0 kg = 5000 g

Specific heat of water = c = 4.184 J/g°C

ΔT = change in temperature of the water during boiling ;p

= 100°C - 25°C = 75°C

Heat absorbed by 5000 g of water = Q

$Q=5000 g\times 4.184J/g^oC\times 75^oC=1,569,000 J$

1 J = 0.001 kj

Q =1,569,000 × 0.001 kJ = 1,569 kJ

Heat required in 12 days, Q' = 1,569 kJ × 12 = 18,828 kJ

The standard heat of formation of propane at 25°C = -103.85kJ/mol

The standard heat of formation of 1 gram of propane at 25°C :

=$\frac{-103.85 kJ/mol }{1 mol\times 44 g/mol}=-2.3602 kJ/g$

Heat released on burning of 1 grams of propane = 2.3602 kJ

Let the number of canister having 25 g of propane be x.

Total mass of propane , M= 25x

M amount of propane will give Q' amount of heat.

$25x \times 2.3602 kJ/g=Q'$

$25x\times 2.3602 kJ/g=18,828 kJ$

$x=\frac{18,828 kJ}{25x\times 2.3602 kJ}=319.09\approx 319$

319 is the minimum number of fuel canisters.