Answer :
Final answer:
1 mole of gasoline releases 5010 kJ, while 1 mole of diesel releases 9905 kJ, with diesel having a higher energy output per mole due to its greater molecular weight and similar energy content per kilogram.
Explanation:
The student is asked to calculate and compare the energy released by burning 1 mole of gasoline and 1 mole of diesel, assuming specific molecular weights for each. To calculate the released energy, we need to know the energy density of the fuels, which is given as 50 MJ per kilogram for gasoline. First, we convert the molecular weight of gasoline (100.2 g/mol) into kilograms which gives us 0.1002 kg/mol. Thus, 1 mole of gasoline releases 50 MJ/kg × 0.1002 kg/mol = 5.01 MJ/mol, or 5010 kJ/mol, when burned.
Similarly, for diesel, if we assume a similar energy content as gasoline, at the molecular weight of 198.1 g/mol, we convert it to kilograms, obtaining 0.1981 kg/mol. Then, 1 mole of diesel releases 50 MJ/kg × 0.1981 kg/mol = 9.905 MJ/mol, or 9905 kJ/mol. Comparing the two, diesel releases more energy per mole than gasoline because its molecular weight and energy content per kilogram result in a higher value when both are considered.