The answer is negative because you used a negative number for the kJ/mol. While the negative number is a true representation of an exothermic reaction you are not being consistent. You have two choices:
1. Disregard the negative sign for the -41663 or treat both numbers the same; i.e.,
2. Recognize that the 1E5 kJ you are producing is exothermic, also, and make that a negative number so that dividing a - by a - gives a plus.
As it is you are treating the 4153 as an exothermic reaction (which it is) but you are treating the 1E5 as an endothermic number but the question is asking for the amount of hexane needed to PRODUCE 1E5 (that's exothermic) so you should have a negative sign there too.
Personally, I simply ignore the sign for the 4163 because we know the mols needed must be positive.
C6H14 + 19/2 O2 -> 6 CO2 + 7H2O delta H = -4163 kJ
What mass of hexane is required to produce 1.0E5 kJ of heat by complete combustion?
-4163 kJ/mol x mol C6H14 = 1E5/-4163 kJ/mol
Mol = 1E5/-4163 kJ/mol
Mol = -24 mol
I know I can do m=n x MM now, but shouldn't the value of mol in the above be positive? Or do you just take the absolute value?
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