Ethanol (CH3CH2OH) has been suggested as an alternative fuel source. Ethanol's enthalpy of combustion is Hcomb = - 1368 kJ/mol. What volume of ethanol (d = 0.789 g/mL) is required to produce the same amount of energy as 1 gallon of gasoline, which can be modeled as isooctane (C8H18) with an energy density of 32.9 kJ/mL? (1 gal = 3.785 L; d = 0.703 g/mL)

a. 1.41 gal

b. 0.85 gal

c. 1.00 gal

d. 1.15 gal

d. 0.90 ga

a) V = 1.41 gal

Explanation:

Ethanol:

∴ Hcomb = - 1368 KJ/mol ... (-) exothermic reaction

∴ δ = 0.789 g/mL

∴ Mw Ethanol = 46.07 g/mol

⇒ Eδ = (1368 KJ/mol) (mol/46.07 g) (0.789 g/mL) = 23.4285 KJ/mL

isooctane:

∴ Eδ = 32.9 KJ/mL

∴ δ = 0.703 g/mL

1 gal = 3785 mL

⇒ E = (32.9 KJ/mL) (3785 mL) = 124526.5 KJ

Volume of Ethanol:

⇒ (Eδ) (V) = 124526.5 KJ

⇒ V = (124526.5 KJ) / (23.4285 KJ/mL) = 5315.167 mL

⇒ V = (5315.167 mL) (gal/3785 mL) = 1.404 gal ≅ 1.41 gal