Combining enthalpy changes

Reaction enthalpies depend on the state of reactants and of products, not the pathway between them.

Calculation of Δ_rH for formation of SO₃(g) from its elements can be based on:

Direct pathway: or Indirect pathway:

S(s) + 3/2 O2(g) SO3(g) SO2(g)

The enthalpy change for direct pathway equals the enthalpy change for the indirect pathway because the products and reactants of both pathways are the same. 

The equations in the indirect pathway simply add to give the desired overall reaction, and their enthalpy changes add to give the overall enthalpy change.
 

(1)	S(s) + O2(g)		SO2(g)
plus		ΔrH° = Δ1H°
(2)	SO2(g) + ½O2(g)		SO3(g)
equals		ΔrH° = Δ2H°
(3)	S(s) + 3/2 O2(g)		SO3(g)
	ΔrH° = Δ3H° = Δ1H° + Δ2H°

If reactions having known enthalpy changes do not simply sum to give the desired overall reaction, they (and their enthalpy changes) must be modified before summing.  To do this consider the relationship of each contributing equation to the desired equation, and the following guidelines.
 

1. Reverse any contributing equations having substances in the overall equation appearing on the wrong side
2. Change the sign of the enthalpy change for any that are reversed.
3. multiply contributing equations by factors so that coefficients on substances that are reactants and products in the overall equation are the same as they are in the overall equation
4. Multiply the enthalpy changes for these reactions by the same factors.
5. Check that the modified contributing equations add to give the overall equation
6. Add the modified enthalpy changes for the contributing equations.