1. Fugacity coefficient[P(T,v)]
Solve for dP as a function of dV

2. Vapor Fugacity
From EOS

3. Consider a pure system
IG P (P=0) as reference state
Consider how we do departure functions (residual properties)
Take a path

4. Departure (residual) Gibb’s Free Energy [v(T,P)]

5. Departure (residual) Gibb’s Free Energy [v(T,P)]

6. Fugacity coefficient[P(T,v)]

7. Fugacity Coefficient from EOS
IF v(T,P) [i.e. virial EOS]
IF P(T,v) [i.e. SRK EOS]

8. Practice problem (virial)
Z=1+BP/RT
Find the fugacity coefficient

9. Practice problem step 1-3
Recognize it is a vapor fugacity problem
Recognize it is for a pure system
Recognize I want EOS (not steam or correlation tables)

10. Practice problem – step 4
Choose the CORRECT equation

11. Practice problem – step 5
Plug in EOS into correct equation

12. Practice problem – step 6
Integrate and simplify

13. Practice problem (VDW)
Z=v/(v-b)-a/RTv
Find the fugacity coefficient

14. Practice problem step 1-3
Recognize it is a vapor fugacity problem
Recognize it is for a pure system
Recognize I want EOS (not steam or correlation tables)

15. Practice problem – step 4
Choose the CORRECT equation

16. Practice problem – step 5
Plug in EOS into correct equation

17. Practice problem – step 6
Integrate and simplify

18. Practice problem – step 6
Integrate and simplify

19. How does your book do it? vo=RT/Plow Solve for fi
Set limit of Plow  0
Solve for

20. What about mixtures? Let’s look at pure for an analogue
Change to partial molar properties

21. For P(T,v), do some manipulation
Let’s look at the other one for a start point
Change dP to dV (cyclic rule)

22. For P(T,v), do some manipulation
Let’s look at the other one for a start point
Change dP to dV (cyclic rule)

23. For P(T,v), do some manipulation
Let’s look at the other one for a start point
Plug both the real and ideal back in and adjust for difference in departure functions gdep(T,v)=gdep(T,p)+RTlnz and divide by RT to simplify into z/

24. Fugacity Coefficient from EOS
IF v(T,P) [i.e. virial EOS]
IF P(T,v) [i.e. SRK EOS]

25. What do they do in your book?
Similar to pure but different EQ

26. Practice problem (VDW)
Find the fugacity coefficient

27. Practice problem step 1-3
Recognize it is a vapor fugacity problem
Recognize it is for a mixed system
Recognize I want EOS (not correlation tables)

28. Practice problem – step 4
Choose the CORRECT equation

29. Practice problem step 5
Convert to z, multiply by n and take the proper derivative
Keep constants and n together

30. Practice problem step 6
Integrate and simplify

31. Practice problem step 6
Integrate and simplify

32. How does your book do it? Vo=nTRT/Plow Solve for fi
Set limit of Plow  0
Solve for

33. Summary
Recognize it is a vapor fugacity, whether it is a mixture or pure, and that I want you to use an EOS
Based on the EOS, choose the right equation

34. Summary For mixtures first take the appropriate derivative
Plug everything in, integrate, and simplify
Let’s do some CW