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.

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.

37.35 canisters will be required to boil 4kg water for 7 days.

The combustion reaction of propane,

The energy require to boil the water

Where,

Q is energy required

m- mass =4kg

c - specific heat capasity =

hence the enrgy required for 7 days will be 8820 kJ

As we know,

The molar mass of  propane = 44g/mol

1mol of propane generate 103.85 kJ of heat.

1 canister = 100 g

To genrate 8820 kJ of energy  84.9 moles of propane will needed.

Hence we need  3735.6 g of propane.

The number of canisters we need,

So we can say that we need 37.35 canisters to boil 4kg water for 7 days.

To know more about Specific heat capacity, refer to the link:

link

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