Reaction a is the reverse reaction for the formation of Fe 2 O 3 ; therefore, the
change in enthalpy for a is fH°[Fe 2 O 3 ]. Reaction b is the reverse reaction
for the formation of SO 3 (), and is multiplied by 3. Therefore, the change in
enthalpy for b is 3 fH° [SO 3 ()]. Reaction c is the formation reaction for
iron (III) sulfate. The change in enthalpy for c is fH°[Fe 2 (SO 4 ) 3 ]. You should
verify that the reactions a–c yield equation 2.54 when added together
algebraically.
The algebraic combination of the fH° values therefore yields the rxnH°
for equation 2.54. We get
rxnH°fH[Fe 2 O 3 ] 3 fH[SO 3 ()] + fH[Fe 2 (SO 4 ) 3 ]
Looking up the values in tables shows that fH°[Fe 2 O 3 ],fH° [SO 3 ()], and
fH°[Fe 2 (SO 4 ) 3 ] are 826,438, and 2583 kJ per mole of compound, re-
spectively. So the rxnH° for the reaction in equation 2.54 is
rxnH°443 kJ
for the formation of 1 mole of Fe 2 (SO 4 ) 3 from Fe 2 O 3 and SO 3 at standard
pressure.
The above example shows that the fH° values of the products are used
directly, that the fH° values of the reactants have changed sign, and that the
coefficients of the balanced chemical reaction are used as multiplicative factors
(the multiplier 3 for fHfor SO 3 and the 3 preceding SO 3 in the balanced
chemical reaction is not a coincidence). An understanding of these ideas allows
us to develop a short-cut that we can apply to the evaluation of the change in
enthalpy for any chemical reaction. (Or any other state function, for that mat-
ter, although so far we have internal energy as the only other state function.)
For a chemical process,
rxnH fH(products) fH(reactants) (2.55)
In each summation, the number of moles of each product and reactant in the
balanced chemical equation must be included. Equation 2.55 applies for any
set of conditions, as long as all fHvalues for all species apply to the same con-
ditions. We can also define the change in internal energy for a formation reac-
tion as fU. This energy change, the internal energy of formation, has a paral-
lel importance to fH and is also tabulated. There is also a simple
products-minus-reactants expression for the change in internal energy for any
chemical process, also based on the fUvalues:
rxnU fU(products) fU(reactants) (2.56)
Again, the general expression applies for both standard and nonstandard con-
ditions, as long as all values apply to the same set of conditions. Appendix 2
contains a large table of (standard) enthalpies of formation. This table should
be consulted for problems that require energies of formation reactions.
Equations 2.55 and 2.56 eliminate the need to perform a complete Hess’s-law
type of analysis on every chemical reaction.Example 2.17
The oxidation of glucose, C 6 H 12 O 6 , is a basic metabolic process in all life. In
cells, it is performed by a complex series of enzyme-catalyzed reactions. The
overall reaction is
C 6 H 12 O 6 (s) + 6O 2 (g) →6CO 2 (g) + 6H 2 O ()56 CHAPTER 2 The First Law of Thermodynamics