Problem: The explosive nitroglycerin (C3H5N3O9) decomposes rapidly upon ignition or sudden impact according to the following balanced equation: 4 C3H5N3O9(l) → 12 CO2(g) + 10 H2O(g) + 6 N2(g) + O2(g), ΔH˚rxn = –5678 kJ. Calculate the standard enthalpy of formation ( H˚f) for nitroglycerin.

We are asked to calculate the standard enthalpy of formation ( H˚_f) for nitroglycerin.

Balanced reaction: 

4 C₃H₅N₃O₉(l) → 12 CO₂(g) + 10 H₂O(g) + 6 N₂(g) + O₂(g), ΔH˚_rxn = –5678 kJ

$\boxed{\mathbf{\Delta H}{\mathbf{°}}_{\mathbf{rxn}}\mathbf{=}\mathbf{\Delta H}{\mathbf{°}}_{\mathbf{f}\mathbf{,}\mathbf{ }\mathbf{prod}}\mathbf{-}\mathbf{\Delta H}{\mathbf{°}}_{\mathbf{f}\mathbf{,}\mathbf{ }\mathbf{react}}}$

Note that we need to multiply each ΔH˚_f by the stoichiometric coefficient since ΔH˚_f is in kJ/mol. 

Also, note that ΔH˚_f for elements in their standard state is 0.