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Solution thermodynamics theory—Part IV

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1 Solution thermodynamics theory—Part IV
Chapter 11 Rahul Patel Rahul ahir Sanjay Khatri

2 When we deal with mixtures of liquids or solids
We define the ideal solution model Compare it to the ideal gas mixture, analyze its similarities and differences

3 Component i in a mixture of ideal gases
This eqn. is obtained by combining Now we define Ideal solution model

4 Other thermodynamic properties for the ideal solution: partial molar volume

5 partial molar entropy in the ideal solution

6 partial molar enthalpy in the ideal solution

7 Chemical potential ideal solution
Chemical potential component i in a Real solution Chemical potential Pure component i Subtracting: For the ideal solution

8 Lewis-Randall rule Lewis-Randall rule
(Dividing by Pxi each side of the equation)

9 When is the ideal solution valid?
Mixtures of molecules of similar size and similar chemical nature Mixtures of isomers Adjacent members of homologous series

10 Virial EOS applied to mixtures

11 How to obtain the cross coefficients Bij
Mixing rules for Pcij, Tcij, wij, to 11.73

12 Fugacity coefficient from virial EOS
For a multicomponent mixture, see eqn

13 problem For the system methane (1)/ethane (2)/propane (3) as a gas, estimate at T = 100oC, P = 35 bar, y1 =0.21, and y2 =0.43 Assume that the mixture is an ideal solution Obtain reduced pressures, reduced temperatures, and calculate

14 Results: methane (1) ethane (2) propane (3)
Virial model Ideal solution

15 Now we want to define a new type of residual properties
Instead of using the ideal gas as the reference, we use the ideal solution

16 Excess properties The most important excess function is
the excess Gibbs free energy GE Excess entropy can be calculated from the derivative of GE wrt T Excess volume can be calculated from the derivative of GE wrt P And we also define partial molar excess properties

17

18 Definition of activity coefficient

19 Summary

20 Summary

21 Note that:

22 problem a) Find expressions for ln g1 and ln g2 at T and P
The excess Gibbs energy of a binary liquid mixture at T and P is given by a) Find expressions for ln g1 and ln g2 at T and P Using x2 =1 – x1 GE/RT= x x x13

23 Since gi comes from We can use eqns and 11.16

24 then And we obtain

25 If we apply the additivity rule and the Gibbs-Duhem equation
At T and P (b and c) Show that the ln gi expressions satisfy these equations Note: to apply Gibbs-Duhem, divide the equation by dx1 first

26 THANK YOU


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