4) An Environmental Issue Background: Most cars convert liquid fuel into gases a

Question

4) An Environmental Issue Background: Most cars convert liquid fuel into gases at high temperature. The expanding gases and heat are converted to work to turn the wheels. In that case the heat content of fuel is important. Gasoline is a great fuel since it is easy to transport and has high heat 'density. However, long term solutions are needed to wean us off our dependence on gasoline. One proposed solution is to run cars on ethanol derived mainly from corn. Some cars currently run on E85 (85% ethanol and 15% gasoline). The Problem: Use thermochemistry to calculate the anticipated miles per gallon (mpg) for a car running on 100% ethanol if it gets 20 mpg on 100% gasoline. Required information is that ethanol (C2HsOH) and gasoline (which can be thought of as octane, CsHis) are both combusted with oxygen to form CO2(g) and H2O(g). The densities are 0.79 g/mL (ethanol) and 0.69 g/mL (gasoline) and i gallon = 3.79 Liters. Ultimately, it will come down to comparing the heat released by a gallon of each. Octane-CsH 18(1)--250 kJ/mol Ethanol = C2H5OH(1)--277 kJ/mol CO2(g)393.5 kJ/mol H20(g)--241.8 kJ/mol 0g) 0 kJ/mol Required Hof values:

Explanation / Answer

The reaction for Ethanol will be

C2H5OH(l) + O2(g) ------ > CO2(g) + H2O(g)

Balancing the reaction will yield

C2H5OH(l) + 3.5O2(g) ------ > 2CO2(g) + 3H2O(g)

Delta H(rxn) = 2 * Hf(CO2) + 3 * Hf(H2O) - Hf(C2H5OH)

=> 2(-393.5) + 3(-241.8) + 277

=> -1235.4 kJ/mol

The reaction for Octane will be

C8H18(l) + O2(g) ------ > CO2(g) + H2O(g)

Balancing the reaction will yield

C8H18(l) + 12.5O2(g) ------ > 8CO2(g) + 9H2O(g)

Delta H(rxn) = 8 * Hf(CO2) + 9 * Hf(H2O) - Hf(C8H18)

=> 8(-393.5) + 9(-241.8) + 250

=> -5074.2 kJ/mol

1 gallon = 3.79 Liters = 3790 mL

For gasoline, Mass = Density * Volume = 2615.1 grams

For ethanol, Mass = Density * Volume = 2994.1 grams

Number of moles of ethanol = Mass/molar mass = 2994.1/46 = 65.089 moles

Number of moles of gasoline = Mass/molar mass = 2615.1/114 = 22.939 moles

Heat released in ethanol per gallon = 65.089 * (-1235.4 kJ) = -80410.95 kJ

Heat released in octane per gallon = 22.939 * (-5074.2 kJ) = -116397.07 kJ

Miles per gallon in case of ethanol = 20 mpg * 80410.95/116397.07 = 13.816 mpg

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