Prof'G M Madhu

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Prof.G M Madhu Department of Chemical
Engineering R V College of Engineering, Bangalore
Session-16
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For binary mixture
At constant Temperature and pressure
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Problem The Gibbs free energy of a binary
solution is given by
(a)    Find the partial molar free energies of
the components at x20.8 and also at infinite
dilution. (b)   Find the pure component
properties
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Substitute
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To find the partial molar properties of
components 1 and 2 x20.8, x11-0.8 0.2
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At infinite dilution
or x20
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To find the pure component property
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Problem The enthalpy at 300K and 1 bar of a
binary liquid mixture is
Where H is in J/mol. For the stated temperature
determine 1.Expression in terms of and
in terms of x1. 2.Numerical Values of pure
component enthalpies. 3. Numerical values for
partial molar properties at infinite dilution.
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Solution
Substitute
11
At infinite dilution
or x20
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To find the pure component property
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Chemical Potential

• It is widely used as a thermodynamic property. It
  is used as a index in chemical equilibrium, same
  as pressure and temperature.

The chemical potential of component i
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For closed system there will be no exchange of
constituents (n is constant)
at constant temperature
at constant pressure
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At constant temperature and pressure
For binary solution
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Effect of temperature and pressure on chemical
potential
Effect of temperature
----------(1)
differentiating equation (1) with respect to T at
constant P
----------(2)
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---------(3)
differentiating equation (3) with respect to T at
constant P
differentiating again w r t ni
is partial molar entropy of component i
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In terms of partial molar properties
This equation represents the effect of
temperature on chemical potential.
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Effect of Pressure  
-------------------(4)
differentiating equation (4) with respect to T at
constant P
---------------------(5)
---------(3)
differentiating equation (3) with respect to P at
constant T
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differentiating again w r t ni
This equation represents the effect of pressure
on chemical potential
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Fugacity in solutions

• For pure fluids fugacity is explained as

The fugacity of the component i in the solution
is defined as analogously by
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is Chemical potential
is partial molar fugacity
For ideal gases
PT Total pressure.
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Fugacity in Gaseous solutions
We know that
------(1)
differentiating equation (1) with respect to T at
constant P
-----(2)
-----(3)
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differentiating equation (3) with respect to P at
constant T
differentiating again w r t ni
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Subtracting both sides by
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Composition is constant dln yi0
The above equation can be written as
Modifying equation (a)
- Represents fugacity of the component i in the
solution.
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Ideal solutions
An ideal mixture is one, for which there is no
change in volume due to mixing. In other words
for an ideal solution, partial molar volume of
each component will be equal to its pure
component volume at same temperature and
pressure.
--- Raoults law
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Ideal solutions are formed when similar
components or adjacent groups of group are mixed
Eg Benzene-Toluene, Methanol- Ethanol, Hexane-
Heptane
Solution undergo change in volume due to mixing
are known as non ideal solutions
Eg Methanol-Water Ethanol-water.