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Figure 10.6
Equilibrium reaction stoichiometry.
10.4 RGibbs BLOCK
The RGibbs block can be used to establish the chemical equilibrium composition
between reactants and products. Consider the reaction of isomer A to isomer B at a
given temperature and pressure. For an
n
-component mixture where
x
i
is the mole
fraction of component
i
, the Gibbs free energy
g
mix
is given by
g
mix
=
x
i
+
RT x
i
ln
x
i
(10.9)
Differentiating equation (10.9) with respect to
x
a
and recognizing that for a two-
component mixture
x
b
=
−
x
a
, one obtains
1
dg
mix
dx
a
x
a
1
−
x
a
=
g
a
−
g
b
+
RT
ln
(10.10)
The minimum of
g
mix
can be found by setting equation (10.10) to zero and solving
for
x
a
. The same approach can be taken for complex chemical and phase equilibria.
This method is especially useful for liquid-liquid equilibrium, as it does not produce
spurious solutions as may be the case for models such as Decant and Flash3, which
solve the describing equations with the appropriate activity coefficient equations.
An example of the use of the RGibbs block for the chlorination of benzene is given at
Examples/RGibbsExample1. Figure 10.7 shows the basic setup and calculation options
available. Figure 10.8 shows detailed specifications and product options. It is important
to note that no reactions need to be defined. One may optionally choose to eliminate
from consideration components from the mixture. Examples/RgibbsExample2 is used
to illustrate the possibility of excluding a possible product. In this case the component
