Please provide a detailed solution for the above example. Butanol (C4HoOH is bei

Question

Please provide a detailed solution for the above example.

Butanol (C4HoOH is being combusted to generate heat. Unfortunately, the system does not achieve full combustion and 25% (in molar terms) of the resulting carbon is in the form of carbon monoxide (CO). A community will use the butanol to produce 25GJ of energy every week. Calculate how many liters of butanol they need to burn every week. Also, calculate how much it will cost the community if they are able to obtain the butanol at US $2/liter. Is this a reasonable number? Answer: 1051.2 L: US$2102.5 per week

Explanation / Answer

C4H9OH +   6O2 --> 4CO2 + 5H2O

C4H9OH +   2.5O2 --> CO + 5H2O

Now, combustion enthalpy = -2760 kJ/mol

We need 25 GJ. Thus, moles required = 25 x 106/2760 = 9058 moles.

However, since efficiency = 0.75, actual moles required = 9058/0.75 = 12077.33 moles = 12077.33 mol x 0.074 kg/mol = 893.722 kg

Density of butanol (from internet) = 849 kg/m3

Thus, volume required per week = 893.722 kg/849 kg/m3 = 1.0523 m3 = 1052.3 L

Cost = 1052.3 L x $2 = $2104.6/week

The slight variation may be due to some discrepency in density value.

The number obtained is quite reasonable, since a large community might require about 1000 L fuel every week. However, even efficient heating mediums could be used.

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