Balanced chemical equations can be treated in very similar ways to mathematical equations, as they represent ratios between the various components in the reaction. 
The law of conservation of energy
"Energy can be neither created nor destroyed; it can be transformed from one form of energy to another".
The significance of this law is that any energy change resulting from a physical, or chemical process, must be the same regardless of how many steps are taken from the initial to the final situation.
This was recognised by Germain Henri Hess, a Swissborn Russian chemist,
who formulated the eponymous law.
Hess' law
In any process the energy change between two situations is independent of the route taken between them.
In some ways it is similar to a journey taken from one town to another. The route between the two towns can never affect the real distance between them.
The beauty of this concept is that if we cannot measure the energy change using one route, we can always select other routes and add up all of the energy changes to obtain the results for the original route.
Energy calculations
In the previous section we saw how energy cycles and diagrams can be used to determine energy changes for processes. Energy changes can also be calculated mathematically by manipulation of equations.
We know that energy is an extensive characteristic of matter, i.e. the quantity of energy depends on the amount of matter involved. The equation for the formation of ammonia as written below releases 92 kJ of energy.
N_{2} + 3H_{2} 2NH_{3}ΔH = 92 kJ 
However, if the equation is written to form 1 mole of ammonia, exactly half the quantity of energy is released.
½N_{2} + 1½H_{2} NH_{3}ΔH = 46 kJ 
It should be apparent that the first equation is simply two times the second equation. Manipulation of equations in this way is perfectly valid and very useful in the application of Hess' law.
Equation manipulation
Chemical equations represent a physical reality and consequently can have any of the four rules of number operations applied. The main thing to bear in mind is that whatever is done to an equation must also be done to the energy change value.
Simply rearranging an equation does not affect the energy change, but performing any of the four rules of number, mutiplying, dividing, adding or subtracting does affect the energy.
The operations that can be carried out are summarised below.
operation

energy change


rearrangement  has no effect on the energy change 
reversing the equation  changes the sign of the energy change 
mutiplication  the energy change is mutiplied 
division  the energy change is also divided 
adding two equations  the energy changes are added together 
subtracting two equations  the energy changes are subtracted 
Operations not affecting the energy change
Rearrangement of an equation by moving a component from one side to the other, while changing its sign, does not affect the energy of the reaction.
Example: The first ionisation energy of sodium can be represented by the following equation: Na(g) Na^{+}(g) + 1e ΔH = +496 kJ This equation can be rearranged to: Na(g)  1e Na^{+}(g) ΔH = +496 kJ Notice that this rearrangement does not affect the energy change. 
Operations affecting the energy change
1 Reversing the equation
Reversing an equation also reverses the sign of the energy change. For example, the enthalpy of vaporisation of water, ΔH(vap), is represented by the following equation:
H_{2}O(l) H_{2}O(g)ΔH = +40.65 kJ 
The reverse process is the enthalpy change of condensation:
H_{2}O(g) H_{2}O(l)ΔH = 40.65 kJ 
Reversing the equation has changed the sign of the enthalpy change from positive to negative.
2 Adding together two equations
When two (or more) equations are added together the energy is also added. The equation produced may not have any physical reality in that it may be chemically impossible, but this does not alter the energetic validity of the procedure.
2C(s) + 2O_{2}(g)
2CO_{2}(g)ΔH
= 787.0 kJ H_{2}(g) + 2C(s) + 2½O_{2}(g) 2CO_{2}(g) + H_{2}O(l) ΔH = 1072.8 kJ 
3 Subtracting two equations
The energy changes are subtracted, taking care to note that subtraction of a negative value is the same as addition, i.e. () = +. In the example below the second equation 2 is subtracted from the first equation 1.
The energy change calculation is 1072.8  1410.0 = 1072.8 + 1410.0 = +337.2.
1 H_{2}(g) + 2C(s) + 2½O_{2}(g)
2CO_{2}(g) +
H_{2}O(l) ΔH
= 1071.8 kJ 2 C_{2}H_{2}(g) + 2½O_{2}(g) 2CO_{2}(g) + H_{2}O(l) ΔH = 1410.0 kJ H_{2}(g) + C(s)  C_{2}H_{2}(g) zero ΔH = +337.2 kJ 
The 'zero' indicates that there is nothing on the right hand side of the equation. However, notice that the term  C_{2}H_{2}(g) is negative and so rearrangement, by changing this component to the right hand side, gives:
H_{2}(g) + C(s) C_{2}H_{2}(g)ΔH = +337.2 kJ 
This is the equation representing the enthalpy of formation of ethyne, ΔHf.