The enthalpy of combustion for octane (C8H18(l)), a key component of gasoline, is –5074 kJ/mol. The reaction equation is: C8H18(l) + 12.5O2(g) ( RIGHT ARROW) 8CO2(g) + 9H2O(g). What is the (TRIANGLE)Hf for this reaction?
16CO2(g) + 18H2O(g) (RIGHT ARROW) 2C8H18(l) + 25O2(g)

kj

10,148 kJ

Explanation:  The heat released in the comnbustion of C8H18 is -5074 kJ/mole.  The negative sign indicates this is an exothermic reaction - heat is released by the bonds in this conbustion process:

C8H18(l) + 12.5O2(g) ⇒ 8CO2(g) + 9H2O(g)   -5074 kJ/mole C8H18

If we assume we are working with 1 mole of C8H18, then the total energy for the reaction is -5074 kJ.

The second reaction is the reverse:

16CO2(g) + 18H2O(g) ⇒ 2C8H18(l) + 25O2(g)

This will require energy to remake the bonds, so it is an endothermic process.  The energy released in the first reaction will be be the same that is required to reform the bonds.  +5074 kJ/mole.

But in this second case we are forming twice as many bonds, since the product has 2 C8H18 (2 moles of product).  So we need to double the enthalpy value for this system (2moles)*(5074 kJ/mole C8H18) = 10,148 kJ