where aand bare the coefficients of the balanced chemical reaction. The
chemical potentials can be written in terms of the standard chemical potential
° and a term involving a nonstandard pressure. If we assume ideal-gas be-
havior, we can use equation 4.56 to rewrite the above equation as(^) rxnGbB°RTln
p
p
B
°
aA°RTln
p
p
A
°
We can rearrange this expression algebraically and use properties of logarithms
to get
(^) rxnG(b B°a A°) RTln
(
(
pp
AB/
/
p
p°
°
)
)
b
a (5.5)The standard Gibbs free energy of reaction, (^) rxnG°, is defined as
(^) rxnG°b B°a A° (5.6)
As with Hand S, we also define (^) fG° for formation reactions. Because Gis a
state function, equation 5.6 can be written in a more useful form in terms of
the standard Gibbs free energies of formation:
(^) rxnG°b (^) fG°proda (^) fG°react
The quotient [(pB/p°)b]/[(pA/p°)a] is defined as the reaction quotient Q:
Q
(
(
pp
AB/
/
p
p°
°
)
)
b
aWe therefore write equation 5.5 as(^) rxnG rxnG°RTln Q (5.7)
The definitions of (^) rxnG° and Qcan be generalized for any number of reac-
tants and products.
(^) rxnG° (^) fG° (products) (^) fG° (reactants) (5.8)
0
iproducts
(pi/p°)^ i
Q (5.9)
jreactants
(pj/p°)^ j
Absolute values are used for the ’s because we are writing Qexplicitly as a
fraction. Using equation 5.8, standard Gibbs free energies of reactions can be
determined from the Gibbs free energies of formations. The (^) fG° values are
tabulated, along with the (^) fHvalues and absolute entropies. The stoichiome-
try of the chemical reaction must be used when applying equation 5.8, since
(^) fG’s are typically given as molar quantities (that is, as (^) fG).
We should clearly differentiate between (^) rxnGand (^) rxnG°. (^) rxnGcan have
various values, depending on what the exact conditions of the system are and
what the extent of the reaction is. (^) rxnG°, on the other hand, is the change in
Gibbs free energy between products and reactants when all reactants and prod-
ucts are in their standard states of pressure, form, and/or concentration (and
typically for a specified temperature, like 25°C). (^) rxnG° is a characteristic of a
reaction, whereas (^) rxnGdepends on what the exact state of the system is, or
what the individual states of the reactants and products are. For instance, equa-
tion 5.7 allows us to determine (^) rxnGfor any reaction under conditions other
than standard pressures, as shown in the following example.
124 CHAPTER 5 Introduction to Chemical Equilibrium