Enthalpy Diagrams 

The enthalpy relationships involved in adding thermochemical equations
are most easily visualized by means of an enthalpy diagram, such as the one
below. Horizontal lines in such a diagram correspond to different absolute
values of enthalpy, H. A horizontal line drawn higher in the diagram represents
a larger value of H. Changes in enthalpy, H, are represented by the
vertical distances between the lines. Take another look at the diagram below.
It shows all three of the CO_{2 }reactions already discussed. The
total decrease in energy, however, is the same regardless of which path
is taken, so the total energy evolved in the twostep path has to be the
same as in the onestep reaction. 



Law of Heat Summation (Hess's Law) For
any reaction that can be written in steps, the standard heat of reaction
is the same as the sum of the standard heats of reactions for the steps.


One of the most useful applications of Hess's law is the calculation
of the value of ΔH^{o }for a reaction whose ΔH^{o
}is unknown or cannot be measured. Hess's law says that we can
add thermochemical equations, including their values of ΔH^{o},
to obtain some desired thermochemical equation and its ΔH^{o}.


Example Problem: Consider the following thermochemical equations:
C(s) + ½O_{2}(g) > CO(g)
ΔH^{o }= 10.5 kJ 

Use them to find the H^{o }in kilojoules for the reaction.
C(s) + O_{2}(g) > CO_{2}(g) 

Solution  
This is a particularly simple problem, but it illustrates a few
important points about all such problems. Let's add the two given thermochemical
equations: 

C(s) + ½O_{2}(g) > CO(g)
ΔH^{o }= 10.5 kJ CO(g) + ½O_{2}(g) > CO_{2}(g) ΔH^{o }= 283.0 kJ C(s) + ½O_{2}(g)
+ ½O_{2}(g) + CO(g) > CO(g) + CO_{2}(g)


The resulting equations can be simplified. Cancel the CO(g) because
it appears on both sides. You can do this as long as you have the same chemical
in the same physical state. Add the two oxygen terms together. This gives
us the target equation. 

C(s) + ½O_{2}(g) > CO(g) ΔH^{o
}= 10.5 kJ CO(g) + ½O_{2}(g) > CO_{2}(g) ΔH^{o }= 283.0 kJ C(s) + O_{2 }(g) > CO_{2}(g) ΔH^{o }= 393.5 kJ 

Example Problem #2  
Carbon monoxide is often used in metallurgy to remove oxygen from
metal oxides and thereby give the free metal. The thermochemical equation
for the reaction of CO with iron(III) oxide, Fe_{2}O_{3},
is 

Fe_{2}O_{3}(s) + 3 CO(g) > 2 Fe(s) + 3 CO_{2
}(g) ΔH^{o
}= 26.74 kJ 

Use this equation and the equation for the combustion of CO
CO(g) + ½O_{2}(g) > CO_{2}(g)
ΔH^{o }= 283.0 kJ 

to calculate the value of H^{o }for the reaction
2 Fe(s) + 1½O_{2 }(g) > Fe_{2}O_{3}


Solution  
Combine the equations in such a way that we can add them to the
final target equation. Then we add the corresponding ΔH^{o}'s
to obtain the ΔH^{o }of the target equation.


