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giving upon integration:
G
=
nRT ln P
+
g ( T , n )
(C.15)
where g ( T , n ) is the Gibbs' free energy of n moles of gas at unit pressure. Let us now
consider a system made up of several components (e.g. Na + ,Cl , and H 2 O for a salt
solution). The share of the total free enthalpy G of the system that can be assigned to each
component i having n i moles in the system is
μ i , which is obtained by writing:
G
=
μ i n i
(C.16)
i
where the sum relates to all the components of the system;
μ i is known as the chemical
potential of component i in the system. It is found, by taking the derivative of this relation
with respect to each variable, that
μ i is simply the derivative of G relative to n i , when T ,
P , and the number of moles of components other than i are kept constant. This yields the
general expression of G for a system whose temperature, pressure, and composition are
specified:
d G
=−
S d T
+
V d P
+
μ i n i
(C.17)
i
If we consider a mixture of ideal gases, i.e. gas molecules of species other than i which
do not interact with each other, the equation of state can be written as:
PV
=
( n i ) RT
(C.18)
i
where n is replaced by the sum of the numbers of moles of each species. The partial
pressure P i of gas i is defined as ( n i /
n ) P , and the Gibbs' free energy equation becomes:
n i RT ln P i + μ
i ( T )
0
=
G
(C.19)
i
0
where
μ
i ( T ) is the chemical potential in the standard state P i
=
1 atm. By reference to
(C.14) , the chemical potential
μ i of gas i in the mixture of gases is defined as:
0
μ i
= μ
i ( T )
+
RT ln P i
(C.20)
Let us now consider the following reaction in the gaseous state:
CH 4 +
2O 2
CO 2 +
2H 2 O
(C.21)
As the reaction progresses, the compounds are created and destroyed in proportions
dictated by the stoichiometric coefficients
ν
:
d n CH 4
d n O 2
d n CO 2
d n H 2 O
ν CH 4 =
ν O 2 =
ν CO 2 =
ν H 2 O =
ξ
d
(C.22)
where
measures the
progress of the reaction and varies between 0 and 1. The reaction will be at equilibrium
when the free energy of the reaction products (right-hand side) is equal to that of the reac-
tants (left-hand side), i.e. when the transfer of matter from one side to the other occurs
ν CH 4 =−
1,
ν O 2 =−
2,
ν CO 2 =+
1, and
ν H 2 O =+
2. The parameter
ξ
 
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