Recall that:

$\mathbf{density}\mathbf{=}\frac{\mathbf{mass}}{\mathbf{volume}}$

- Average heat of combustion ethanol = 1370 kJ/mol
- Molar mass C
_{8}H_{18}(gasoline) =114.23 g/mol - Molar mass C
_{2}H_{5}OH (ethanol) = 46.07 g/mol

a)${\mathbf{E}}_{\mathbf{gasoline}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{}\overline{)\mathbf{L}}\mathbf{\times}\mathbf{0}\mathbf{.}\mathbf{70}\frac{\mathbf{g}}{\overline{)\mathbf{mL}}}\mathbf{\times}\frac{\mathbf{1}\mathbf{}\overline{)\mathbf{mL}}}{{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\overline{)\mathbf{}\mathbf{L}}}\mathbf{\times}\mathbf{5400}\mathbf{}\frac{\mathbf{kJ}}{\overline{)\mathbf{mol}}}\mathbf{\times}\frac{\mathbf{1}\mathbf{}\overline{)\mathbf{mol}\mathbf{}{\mathbf{C}}_{\mathbf{8}}{\mathbf{H}}_{\mathbf{18}}}}{\mathbf{114}\mathbf{.}\mathbf{23}\mathbf{}\overline{)\mathbf{g}\mathbf{}{\mathbf{C}}_{\mathbf{8}}{\mathbf{H}}_{\mathbf{18}}}}$

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 C_{8}H_{18}), that the average heat of combustion of C_{8}H_{18}(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) By using the information given as well as data in Appendix C, compare the energy produced by combustion of 1.0 L of gasoline and of 1.0 L of ethanol.

(b) Assume that the density and heat of combustion of E85 can be obtained by using 85% of the values for ethanol and 15% of the values for gasoline. How much energy could be released by the combustion of 1.0 L of E85?

(c) How many gallons of E85 would be needed to provide the same energy as 40 gal of gasoline?

**(d) 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?**

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