Solution Thermodynamics : Theory - UniMasr · Solution Thermodynamics : Theory ... solution is...
Transcript of Solution Thermodynamics : Theory - UniMasr · Solution Thermodynamics : Theory ... solution is...
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Solution Thermodynamics : Theory
FUGACITY AND
FUGACITY COEFFICIENT:
SPECIES IN SOLUTION
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� 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
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� 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:
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� Also,
� For an ideal gas, is necessarily zero;
therefore , and
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� Also,
� This equation demonstrates that is a
partial property with respect to G R / RT
� To get use virial equation only.
iiMxM Σ=
ii
R
i
R
xRT
Gx
RT
Gφ̂lnΣ=Σ=
iφ̂
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THE IDEAL SOLUTION
Total property from
summability
Partial property
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� 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
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Fugacity of component in ideal solution
� The LewisIRandall Rule
� Division of both sides by Pxi
Px
fx
Px
f
i
ii
i
id
i =ˆ
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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,
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EXCESS PROPERTIES
� For example:
� Also,
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The Excess Gibbs Energy and the Activity Coefficient
� As, [1]
� [2]
� [1]-[2]ii
iid
iifx
fRTGG
ˆ
ln=−
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� The activity coefficient of species i in solution
� Thus,
� For an ideal solution, = 0, and therefore
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� is a partial property with respect to GE/ RT :
� The following forms of the summability and
GibbsIDuhem equations:
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� To get
Using virial equation assuming ideal solution
(ex 11.9)
iϕ̂
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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)
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Sheet 3
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Sheet 3
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Sheet 3
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Sheet 3