textbook 4D.9

[JaylinWangDis1L]

The enthalpy of formation of trinitrotoluene (TNT) is −67kJ⋅mol^−1, and the density of TNT is 1.65g⋅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

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

[SophiaBarden 2E]

Using the link that the question provided, you need to calculate the Enthalpies of formation for each product and then add all of these values up. Example: If the enthalpy of formation for H2O is -241.82 then remember to multiply it by 10 for this particular reaction.
The sum of enthalpies for the reaction is -13168 and represents the amount of energy released per 4 moles of TNT. So the amount of energy per one mole of TNT is -13168/4 = 3292 kj.mol-1.
We are trying to calculate the energy density in kJ per L. To do this, we convert 3292 kJ.mol into kJ.L using the molar mass of TNT and conversions of grams into cm^3 into Liters.

[Kaiya_PT_1H]

Thanks Sophia, this was super helpful!

[Charlotte Chen 3B]

Using the link that the question provided, you need to calculate the Enthalpies of formation for each product and then add all of these values up. Example: If the enthalpy of formation for H2O is -241.82 then remember to multiply it by 10 for this particular reaction.
The sum of enthalpies for the reaction is -13168 and represents the amount of energy released per 4 moles of TNT. So the amount of energy per one mole of TNT is -13168/4 = 3292 kj.mol-1.
We are trying to calculate the energy density in kJ per L. To do this, we convert 3292 kJ.mol into kJ.L using the molar mass of TNT and conversions of grams into cm^3 into Liters.

Why does the energy per one mole of TNT become positive if the energy released per mol of reaction (-13168kJ) is negative?

[Isabella Chou 1A]

I had the same question too ^ why does the enthalpy change per liter that we calculated become positive in the end?

[Neel Bonthala 2G]

Yeah, why exactly does the final enthalpy change for a mole of TNT become positive? Shouldn't the combustion of TNT also release energy, so it should be a negative value?