Book Problem 4D.9

[Raya Amin 2A]

4D.9 The enthalpy of formation of trinitrotoluene (TNT) is -67 kJ/mol and the density of TNT is 1.65 g/cm^3. In principle, it could be used as a rocket fuel, with the gases resulting from its decomposition streaming out of the rocket to give the required thrust. In practice, of course, it would be extremely dangerous as a fuel because it is sensitive to shock. Explore its potential as a rocket fuel by calculating its enthalpy density (enthalpy change per liter) for the reaction:

4C7H5N3O6(s) + 21O2(g) -> 28CO2(g) + 10H2O(g) + 6N2(g)

For this question, I used enthalpies of formation to calculate the enthalpy of reaction and I got a negative enthalpy of reaction (-3292 kJ/mol). I then used this to calculate the enthalpy density, which was a negative value. The answer key has the exact same value that I do, but it is a positive value. Could anyone help me figure out how they got a positive value for this?

Thanks!

[Carissa Liu 3A]

You are correct in that the enthalpy of the reaction is exothermic (negative value). However, the rocket uses this reaction as fuel and consumes it. Therefore the rocket requires energy input (endothermic) and would have the opposite sign as the reaction.
H rocket + H reaction = 0
H rocket = -H reaction
H rocket = -(-H reaction)
Thus, the H value that the rocket consumes would be positive.

[Alyssa Gates 1H]

Could anyone explain the last part to this problem? I understand how to get to 3292 kJ but after that I don't know what to do.