How do you find the enthalpy for the overall reaction?

Question

Given 

Fe2O3+3CO—> 2Fe+3CO2 ΔH=-23.44 kJ

Fe3O4+CO—> 3FeO+CO2 ΔH=21.79 kJ

Fe+CO2–>FeO+CO ΔH=-10.94 kJ

How do you find the enthalpy for the overall reaction:

3Fe2O3+CO—>2Fe3CO4+CO2?

Answer 1

I have found that the fastest way to do Hess's Law Problems is to figure out the combination of reactions that gets the final chemicals you want and you do to the heats of reaction what you did to the equations. You can trust that they gave you a set of equations that work.

3Fe₂O₃ requires that equation 1 is times 3 (the chemical is unique to this equation)

Here's where I notice the Fe₃CO₄ which should be Fe₃O₄ Given that this is true, this requires that the second equation be flipped and times two or time a -2.

You can balance one of the other compounds, but easiest here is to remove the intermediate FeO which comest in as 6 FeO on the reactant side (from -2 * rxn 2), so we need to multiply rxn 3 by 6 to bring in 6FeO on the product side. 3*rxn1 + (-2) rxn2 +6 * rxn 3.