Solution Thermodynamics :
Theory
FUGACITY AND
FUGACITY COEFFICIENT:
SPECIES IN SOLUTION
The definition of the fugacity of a species in
solution is parallel to the definition of the pure
species fugacity
where
is the fugacity of species i in
solution, replacing the partial pressure yi P
Thus, multiple phases at the same T and
P are in equilibrium when the fugacity of
each constituent species is the same in
all phases.
For the specific case of multicomponent
vapor/liquid equilibrium:
Also,
For an ideal gas,
is necessarily zero;
therefore
, and
Also,
This equation demonstrates that
is a
partial property with respect to G R / RT
M = Σx i M i
GR
GR
= Σx i
= Σxi ln φˆi
RT
RT
To get
φˆi
use virial equation only.
THE IDEAL SOLUTION
Partial property
Total property from
summability
Enthalpy change of mixing:
∆Hmix= = Hid – ƩxiHi = 0
Entropy change of mixing:
∆Smix= = Sid – ƩxiSi = -RƩxilnxi
Gibbs energy change of mixing:
∆Smix= = Gid – ƩxiGi = RTƩxilnxi
Fugacity of component in ideal
solution
The LewisIRandall Rule
Division of both sides by Pxi
id
fˆi
xi f i
=
xi P xi P
EXCESS PROPERTIES
an excess property is defined as the
difference between the actual property value
of a solution and the value it would have as
an ideal solution at the same temperature,
pressure, and composition, thus,
EXCESS PROPERTIES
For example:
Also,
The Excess Gibbs Energy and the
Activity Coefficient
As,
[1]
[2]
[1]-[2]
G i − Gi
id
fˆi
= RT ln
xi f i
The activity coefficient of species i in solution
Thus,
For an ideal solution,
= 0, and therefore
is a partial property with respect to GE/ RT :
The following forms of the summability and
GibbsIDuhem equations:
To get
Using virial equation
(ex 11.9)
ϕˆ i
assuming ideal solution
Sheet 2
10. Two kmol/hr of liquid n-octane are
continuously mixed with four kmol/hr of liquid
iso-octane. The mixing process occurs at
constant T and P; mechanical power
requirements are negligible
a) Use an energy balance to determine the rate
of heat transfer
b) Use an entropy balance to determine the
rate of entropy generation (W K-1)
Sheet 3
Sheet 3
Sheet 3
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