Introduction to Chemical Engineering Thermodynamics
Chapter 11
KFUPM Housam Binous CHE 303 1 single phase open system
Total differential of nG=g(P,T,n1,n2…ni…)
KFUPM Housam Binous CHE 303 2 chemical potential of species i
KFUPM Housam Binous CHE 303 3 G is a generating function:
KFUPM Housam Binous CHE 303 4 Chemical potential and Phase Equilibria
Equilibrium ↔ chemical potential of each species is the same in all phases
KFUPM Housam Binous CHE 303 5 Partial properties:
Partial molar Gibbs energy
Summability:
solution properties KFUPM Housam Binous CHE 303 6 KFUPM Housam Binous CHE 303 7 Gibbs/Duhem equation:
or
KFUPM Housam Binous CHE 303 8 Relations among partial properties :
KFUPM Housam Binous CHE 303 9 Gibbs’s theorem:
A partial molar property (other than volume) of a constituent species in an ideal-gas mixture is equal to the corresponding molar property of the species as a pure ideal gas at the mixture T but at a pressure equal to its partial pressure in the mixture, pi.
KFUPM Housam Binous CHE 303 10 KFUPM Housam Binous CHE 303 11 using summability to get solution’s properties:
KFUPM Housam Binous CHE 303 12 Enthalpy change of mixing for ideal gases is zero
Entropy change of mixing for ideal gases is always positive
KFUPM Housam Binous CHE 303 13 KFUPM Housam Binous CHE 303 14 Application of summability:
KFUPM Housam Binous CHE 303 15 because absolute values of Gibbs free energy are unknown, the same is true for chemical potentials. Also,
Thus, we introduce a more convenient property called the fugacity, fi, of a pure species i:
KFUPM Housam Binous CHE 303 16 residual Gibbs energy
KFUPM Housam Binous CHE 303 17 for constant T from chapter from chapter 6
KFUPM Housam Binous CHE 303 18 Virial EOS
KFUPM Housam Binous CHE 303 19 Cubic EOS
(see chapter 6 for definition of βi, qi and Ii)
KFUPM Housam Binous CHE 303 20 For a pure species, coexisting liquid and vapor phases are in equilibrium when the two phases have the same P, T, and fugacity or fugacity coefficients:
KFUPM Housam Binous CHE 303 21 Fugacity of a pure liquid
Poynting factor
KFUPM Housam Binous CHE 303 22 Virial EOS
KFUPM Housam Binous CHE 303 23 Definition of the fugacity of species i in solution of liquids or mixture of real gases:
If same T and P then equilibrium reached when fugacity of each constituent species is the same in all phases
KFUPM Housam Binous CHE 303 24 partial residual Gibbs energy measures departure from ideal-gas values
KFUPM Housam Binous CHE 303 25 If ideal-gas mixture:
KFUPM Housam Binous CHE 303 26 KFUPM Housam Binous CHE 303 27 KFUPM Housam Binous CHE 303 28 Virial EOS for mixtures:
For binary mixtures:
KFUPM Housam Binous CHE 303 29 For binary mixtures:
KFUPM Housam Binous CHE 303 30 For multicomponent mixtures:
KFUPM Housam Binous CHE 303 31 Kesler/Lee correlation for pure gases only:
Use Appendices E13 to E16
KFUPM Housam Binous CHE 303 32 Extension of Virial EOS to allow fugacity calculations of gas Mixtures:
KFUPM Housam Binous CHE 303 33 realistic only for ideal gases
Ideal solution defined by:
Gibbs energy of pure i in its real physical state of gas, liquid or solid application mainly for liquids
KFUPM Housam Binous CHE 303 34 KFUPM Housam Binous CHE 303 35 Application of Summability relation
KFUPM Housam Binous CHE 303 36 Lewis/Randall rule: composition dependence of the fugacity of a species in an ideal solution
KFUPM Housam Binous CHE 303 37 Excess Properties
KFUPM Housam Binous CHE 303 38 ideal-gas mixture = ideal solution of ideal gases
remember we had also :
KFUPM Housam Binous CHE 303 39 fundamental excess-property relation remember we had also:
KFUPM Housam Binous CHE 303 40 KFUPM Housam Binous CHE 303 41 ideal solution
KFUPM Housam Binous CHE 303 42 when
recover ideal solution and Lewis/Randall rule
KFUPM Housam Binous CHE 303 43 conceptual development:
KFUPM Housam Binous CHE 303 44 KFUPM Housam Binous CHE 303 45 <<
effect of pressure on activity coefficient and excess Gibbs energy is usually neglected
KFUPM Housam Binous CHE 303 46 Summability and Gibbs/Duhem equations
KFUPM Housam Binous CHE 303 47