Physical Chemistry , 1st ed.

or, integrating:
AUTS (4.12)

Similarly, for the Gibbs free energy:

GHTS

dGdHT dSS dT

dGdHT dS for an isothermal change

We integrate to get

GHTS (4.13)

Both equations 4.12 and 4.13 are for isothermal changes. They also allow us to
calculate Aor Gif changes in other state functions are known.
Just as we can determine U,H, and Sfor chemical processes using a
Hess’s-law approach, we can also determine G and Avalues for chemical re-
actions using a products-minus-reactants scheme. Because Gis a more use-
ful state function, we focus on that. We define free energies of formationfG
similarly to the enthalpies of formation, and tabulate those. If the fGvalues
are determined at standard thermodynamic conditions, we use the ° superscript
and label them fG°. We can then determine the Gof a reaction,rxnG, just
like we did the enthalpies of reactions. However, with Gwe have two ways to
calculate the free energy change for a reaction. We can use the rxnGvalues and
a products-minus-reactants approach,orwe can use equation 4.13. The choice
of which to use depends on the information given (or the information you are
able to get). Ideally, both approaches should give you the same answer.
Note that the above paragraph implies that fGfor elements in their stan-
dard states is exactly zero. The same is true for fA. This is because a forma-
tion reaction is defined as the formation of a chemical species from its con-
stituent chemical elements in their standard states.

Example 4.3

Determine rxnG(25°C 298.15 K) for the following chemical reaction us-

ing both methods for determining rxnG, and show that they yield the same

answer. Assume standard conditions. Appendix 2 in the back of the book lists

the various thermodynamic data.

2H 2 (g) O 2 (g) →2H 2 O ()

Solution

The following data were obtained from Appendix 2:

H 2 (g) O 2 (g) H 2 O ()

fH, kJ/mol 0 0 285.83

S, J/mol K 130.68 205.14 69.91

fG, kJ/mol 0 0 237.13

We begin by calculating rxnH:

rxnH2(285.83) (2 0     1 0)

rxnH571.66 kJ

Now, we calculate rxnS:

rxnS2(69.91) (2 130.68 205.14)

4.3 The Gibbs Free Energy and the Helmholtz Energy 95