How do you determine heat change in one reaction from a series other of reactions?

Question

Here's the problem:

You are given the following data.

Fe2O3(s) 3 CO(g) 2 Fe(s) 3 CO2(g) ΔH° = -23 kJ

3 Fe2O3(s) CO(g) 2 Fe3O4(s) CO2(g) ΔH° = -39 kJ

Fe3O4(s) CO(g) 3 FeO(s) CO2(g) ΔH° = 18 kJ

Calculate ΔH° for the following reaction.

FeO(s) CO(g) Fe(s) CO2(g)

Answer 1

You can use the equations of the reactions you're given.  Add and subtract them (reversing one will change the sign of the delta-H) until you get them to produce the one you're trying to calculate.

In this case, numbering the reactions from top to bottom, and using a negative to indicate reversing the reaction.. the one you want is:

-3-2+1.   Or close to that.  Start adding and canceling like terms until it balances!