On a 5 day wilderness expedition you\'ll need to heat 4.0kg of water to the boil

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 butane C4H10 fuel, which you'll burn to heat the water. Each canister has 50.g of butane in it. What is the minimum number of fuel canisters you must bring? The standard heat of formation of butane at 25°C is ?125.7/kJmol. You'll probably find other helpful data in the ALEKS Data resource.

Explanation / Answer

mass of water = 4.0 kg = 4000 g

water boiling point = 100 oC (Tf)

water initial temperature = 25 oC (Ti)

water specific heat capacity (Cs) = 4.184 J/g.oC

energy (q) = m x Cs x (Tf - Ti) = 4000 g x 4.184 J/g.oC x (100 - 25) oC

q = 1255200 J per day

for 5 days q = 5 x 1255200 J = 6276000 J

each canister has 50 g butane

balanced chemical reaction equation is

C4H10(g) + 13/2 O2(g) --> 4 CO2(g) + 5 H2O(l)

moles present in 50 g butane = 50 g / 58.1222 g/mol = 0.86 mol

enthalpy of combustion = [products] - [reactants] = [( 4 x -393.5) + ( 5 x -285.8)] - [1 x -125.7) + (13/2 x 0)]

dHrxn = -2877.3 kJ = 2877300 J energy released.

1 mol butane gives 2877300 J energy

how many moles of butane required to produce 6276000 J energy = 6276000 J / 2877300 J = 2.18 mol

we know each canister has 0.86 mol of butane, we need 2.18 mol of butane

hence required canisters = 2.18 / 0.86 = 2.53 (we cannot use half due to the requirement of answer in integers)

Final answer: the minimum number of fuel canisters you must bring = 3

Important Note: You have not provided Aleks data, hence i have used sapling values, please make sure that my values are correct to your Aleks data since experts are not allowed to access Aleks data. Below link i have used Thermodynamis data.

https://sites.google.com/site/chempendix/thermo

Hope this helped you!

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