Ethanol, $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH},$ is used as a fuel for motor vehicles, particularly in Brazil

(a) Write the balanced equation for the combustion of ethanol to $\mathrm{CO}_{2}(g)$ and $\mathrm{H}_{2} \mathrm{O}(g),$ and, using the data in Appendix G, calculate the enthalpy of combustion of 1 mole of ethanol.

(b) The density of ethanol is 0.7893 $\mathrm{g} / \mathrm{mL}$ . Calculate the enthalpy of combustion of exactly 1 $\mathrm{L}$ of ethanol.

(c) Assuming that an automobile's mileage is directly proportional to the heat of combustion of the fuel, calculate how much farther an automobile could be expected to travel on 1 1 $\mathrm{L}$ of gasoline than on 1 of ethanol. Assume that gasoline has the heat of combustion and the density of n-octane, $\mathrm{C}_{8} \mathrm{H}_{18}\left(\Delta H_{\mathrm{f}}^{\circ}=-208.4 \mathrm{kJ} / \mathrm{mol} ; \text { density }=0.7025\right.$ $\mathrm{g} / \mathrm{mL}$ .