5.3  Hess' law 
5.3.1: Determine the enthalpy change of a reaction that is the sum of two or three reactions with known enthalpy changes. Students should be able to construct simple enthalpy cycles and enthalpy level diagrams and to manipulate equations. Students will not be required to state Hess' law.
This topic is best addressed using examples
Example 1
Monoclinic sulphur is formed in volcanic regions by reaction between sulphur dioxide and hydrogen sulphide according to the equation:
SO_{2} + 2H_{2}S > 2H_{2}O + 3S
Draw an enthalpy diagram or cycle and calculate the standard enthalpy change for this reaction.
Here are some values.
Standard enthalpy of formation (all in kJ)
 H_{2}O(l) 286
 H_{2}S(g)  20.2
Standard enthalpy of combustion of S (monoclinic) = 297.2kJ
equation 2: H_{2} + S > H_{2}S 20.2
equation 3: S + O_{2} > SO_{2} 297.2
multiply E2 by 2
2H_{2} + 2_{2} > 2H_{2}S 40.4
add E3
equation 4: 2H_{2} + 3S + O_{2} > SO_{2} + 2H_{2}S
337.6
multiply E1 by 2
equation 5: 2H_{2} + O_{2} > 2H_{2}O
572 kJ
subtract 4 from 5
 3S > 2H_{2}O  SO_{2}  2H_{2}S 234.4
kJ
rearrange
SO_{2} + 2H_{2}S > 2H_{2}O + 3S
234.4 kJ
Example 2:
Calculate the enthalpy change in the reaction:
2KHCO3 (s) > K_{2}CO3 (s) + CO_{2} (g) + H_{2}O (l)
Hess' law by manipulation of the equations...
2KHCO3 > K_{2}CO3 + CO_{2} + H_{2}O
2K + H2 + 2C + 3O_{2} > 2KHCO3 ΔH = 2(959) = 1918
2K + C + 3/2O_{2} > K2CO3 ΔH = 1146
SUBTRACT
H2 + C + 3/2O2 > 2KHCO3  K2CO3 ΔH = 772
H2 + 1/2O2 > H2O ΔH = 286
SUBTRACT
C + O2 > 2KHCO3  K2CO3  H20 ΔH = 486
C + O2 > CO2 ΔH = 394
SUBTRACT
ZERO > 2KHCO3  K2CO3  H20 CO2 ΔH = 92
REARRANGE
K2CO3 + H20 + CO2 > 2KHCO3 ΔH = 92
THEREFORE
2KHCO3 > K2CO3 + H20 + CO2 ΔH = +92
This makes the enthalpy change
ΔH = sum ΔHf (Products)  sumΔHf (Reactants)
note that we use the actual values of the sum ΔHf (Products) and the negative of the sumΔHf (Reactants)
does that make it clearer?
you can think of any reactant as having to be broken down into its elements which then must be reformed as the products...
Hence sum of the ΔHf of the left hand side (reactants) but with the opposite sign (because they're being broken up)
Then they are reformed into the products > hence sum of the ΔHf of the products but with the correct sign this time
Simply add up the two sets of enthalpy sums to give you the reaction enthalpy
 sum ΔHf (Reactants) + sum ΔHf (Products) = Reaction enthalpy
of course the books usually just state the rearranged form
Reaction enthalpy = sum ΔHf (Products)  sum ΔHf (Reactants)
Which does not particularly help in the understanding of WHY this is the case...
Don't worry about the exam just remember that you have to break the reactants down to the elements in the first stage (sum the enthalpies of formation and change sign)and then build them back up to the products in the second stage (sum the enthalpies of formation)
Then add it all up!
Bond breaking = endothermic as you would expect
I made a mistake when I did the original calculation and got an exothermic value. I knew that it could not be the answer as simple inspection tells me that it is a decomposition and is overwhelmingly likely to be endothermic.
Always useful to consider the likelihood of ANY answer.
Resources

