Gibbs energy 219
compounds, e.g. if the system contained carbon monoxide, oxygen and carbon dioxide as
defined in eqn
(12.1),
then
it
is necessary
to define the
Gibbs
energy as
G=mg=mg(p, T,mi) where
m,
is the mass of component
i,
and
m=C mi.
The
significance of changes of composition on the value of the Gibbs energy of a mixture will
now be investigated.
If
G
=
mg
=
mg(
p, T,
m,)
(12.4)
and if it is assumed that G is a continuous function with respect to
p, and T and the masses
of constituents comprising the mixture, then the change of G with changes in the
independent variables is
dG
=
(
$)T,dp
+
(
$)p,ciT
+
(”)
dm,
+
...
(*)
drn,
(12.5a)
aml
p,T,m,,l
amn
p.T.m,,,
where dm,
.
.
.
dm, are changes in mass of the various constituents.
A
similar equation can
be written in terms of amount of substance n, and is
For the initial part of the development of these equations the mass-based relationship (eqn
(12.5a)) will be used because the arguments are slightly easier to understand. The term
represents the ‘quantity’ of Gibbs energy introduced by the transfer of mass dm, of
constituent 1 to the system. (This can be more readily understood by considering the
change in internal energy, dU, when the term (aU/am,)p,T,m,*,
dm, has a more readily
appreciated significance.)
The significance of the terms on the right of eqn (12.5a) is as follows: