Chapter 5

1. Chapter 5 FUGACITY OF A COMPONENT IN A MIXTURE

2. Fugacity of pure species: (4.46) Fugacity of a component in a mixture: (5.1) where is the fugacity of species i in solution, replacing the partial pressure yiP. This definition of does not make it a partial molar property, and it is therefore identified by a circumflex rather than by an overbar.

3. Criteria for multi-componentphase equlibrium (5.2) (5.3) (I = 1, 2, . . . , N) (5.4) For the specific case of multi-component vapor/liquid equilibrium: (I = 1, 2, . . . , N) (5.5)

4. The definition of a residual property is: (3.41) Multiplied by n mol of mixture, it becomes Differentiation with respect to ni at constant T, P, and nj gives: (5.6)

5. For Gibbs energy: (5.7) (5.1) (4.45) ( – ) (5.8) where: (5.9)

6. FUNDAMENTAL RESIDUAL-PROPERTY RELATION In order to extend the fundamental property relation to residual properties, we transform eq. (3.34) into an alternative form through the mathematical identity (5.10) d(nG) is defined in eq. (4.13) (4.13)

7. So that: Remembering that G = H – TS (5.11)

8. For ideal gas: (5.12) Subtracting this equation from Eq. (5.11) gives (5.13) Eq. (5.13) is the fundamental residual-property relation.

9. Introducing eq. (5.8) into eq. (5.13) yields): (5.14) Division of Eq. (5.14) by dPand restriction to constant T and composition leads to: (5.15)

10. Division of Eq. (5.14) by dTand restriction to constant P and composition leads to (5.16) Division of Eq. (5.14) by dniand restriction to constant P, T, and nj leads to: (5.17)

11. FUGACITY COEFFICIENT FROM VIRIAL EOS The relation of Residual Gibbs energy with equation of state: (constant T) (3.50) For a mixture composed of n moles: (constant T) (5.18)

12. Differentiation gives: (constant T) (5.19) (5.20)

13. For 2-term virial eos (5.21)

14. Introducing eq. (5.21) into eq. (5.19) yields: As B is usually a function of T, the above equation can be integrated as: (5.22)

15. The second virial coefficient for a mixture For a binary mixture:

16. (5.23)

20. 5.1 (5.24)

21. (5.25) (5.26)

22. (5.26)

23. (5.27)