Combining equations and their enthalpies

The previous page showed how the enthalpy change for reaction (3) could be calculated by simply summing the enthalpy changes for reactions (1) and (2).

ΔH° = Δ1H° 2
ΔH° = Δ2H° 2
Δ3H° = Δ1H° + Δ2H°
(1) S(s) + O2(g) → SO2(g)
(2) SO2(g) + ½O2(g) → SO3(g)2
(3) S(s) + 3/2 O2(g) → SO3(g)     and2 23
233
plus3
equals2

Often the reactions for which enthalpy changes are known do not simply sum to give the overall equation, and they (and their enthalpy changes) must be modified accordingly.

One general approach to manipulating the equations is to consider the relationship of each contributing equation to the overall equation and
  1. reverse any contributing equations which have substances appearing in the overall equation on the wrong side.
    Change the sign of the enthalpy change for any that are reversed.
  2. multiply contributing equations and their enthalpy changes by factors to make the coefficients on substances which are reactants and products in the overall equation the same as they are in the overall equation
  3. check that the modified contributing equations add to give the overall equation