Another approach to calculations for cycles

While display of both the direct and the indirect pathway between reactants and products as a cycle is a useful representation for visualisation, you may find a different strategy more useful when calculating an enthalpy change for one component of a cycle.  This involves

1. writing the equation for the reaction having the unknown enthalpy change
2. combining equations having known enthalpy changes so that their sum gives the equation in Step 1.  Consider the example below:
    

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

The example is a simple one where the contributing equations simply add to give the desired equation. In most cases it is necessary to reverse some of the equations and/or multiply all components of the equation by a common factor before they will add to give the desired equation.  One general approach to choosing appropriate modifications is given below.
 
Step 1: 
Identify contributing equations having reactants/products which are the same as in the overall equation.
Reverse any equations having substances appearing in the overall equation on the wrong side of the equation.
Change the sign of the enthalpy change for any that are reversed. 

Step 2: 
Multiply contributing equations which have reactants/products in the overall equation by factors to make the coefficients on these reactants/products the same as they are in the overall equation. 
Multiply the enthalpy changes for these equations by the same factor.


Step 3: 
Check that the modified contributing equations add to give the overall equation. 
Adjust either the equations or their enthalpy changes as necessary and add.