Question

The automobile fuel called E85 consists of 85% ethanol and 15% gasoline. E85 can be used in so-called flex-fuel vehicles (FFVs), which can use gasoline, ethanol, or a mix as fuels. Assume that gasoline consists of a mixture of octanes (different isomers of C8H18 ), that the average heat of combustion of C8H18(l) is 5400 kJ/mol , and that gasoline has an average density of 0.70 g/mL . The density of ethanol is 0.79 g/mL .

A. How many gallons of E85 would be needed to provide the same energy as 40 gal of gasoline?

Express your answer to two significant figures and include the appropriate units.

B.

If gasoline costs $ 3.88 per gallon in the United States, what is the break-even price per gallon of E85 if the same amount of energy is to be delivered?

Express your answer using three significant figures.

Answer 1

Answer

1 gallon = 3.7854 L

i.e. 40 gallons = 40*3.7854 * 1000 mL

density of Octane = 0.70 g/mL

Molecular wt of Octane = 114.23 gm/mole

wt. 40 gallons octane = 40*3.7854 * 1000*0.70 gm

moles of Octane = 40*3.7854 * 1000*0.70/114.23 = 927.88 moles

Energy og 40 gallons octane = 5400 kJ/mol * 927.88 mol

                                               = 5010552 kJ

1 gallon of E85 contains 0.85 gallons of ethanol and 0.15 gallons of gasoline

Mol wt.of ethanol = 46.068

Energy of ethanol = 1368 kJ/mol

Moles of ethanol and gasoline in 1 gallon E85:

Moles of gasoline = (3.7854*0.15)*0.70*1000/114.23 = 3.48

Moles of ethanol = (3.7854*0.85)*0.79*1000/46.068 = 55.7

Energy of 1 gallon E85 = (3.48*5400) + (55.7* 1368) = 94989.6 kJ

Therefore, amount of E85 required to give 40 gallons of gasoline    

                                                                                      = 5010552/94989.6

                                                                                      = 52.75 gallons