Solution Thermodynamics: Applications

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Presentation transcript:

Solution Thermodynamics: Applications Chapter 12-Part IV

Other models for GE/RT

The Van-Laar equation

Local composition theory There are cases where the cross-parameter may be a function of composition. A12 = A12(x) So, there could be “local” compositions different than the overall “bulk” compositions. For example (if coordination number is 8) AAAAAAA AABBAAA xAB = ; xBB = “A around B” or “B around B”

examples Specific interactions such as H-bonding and polarity

Nomenclature x21 = mole fraction of “2” around “1” x11 + x21 =1 112211 111111 x12 = mole fraction of “1” around “2” x22 = mole fraction of “2” around “2” x22 + x12 =1 Local compositions are related to overall compositions: If the weighting functions are =1 random solutions

Key are the Wij weighting factors If Wij =1 => random mixture

Wilson equation Wilson assumes that the weighting functions are functions of size and energetic interactions: z is the coordination number for atom i even if eij =eji (this is not always the case), the Lij parameters may be different, why?

Intermolecular pair potential Uij eij

Wilson’s equation for a binary For infinite dilution:

NRTL (non-random, two-liquid) Actual parameters: a, b12 and b21 See Table 12.5, page 474 Renon and Prausnitz, 1968

page 474

UNIQUAC equation UNIversal QUAsi Chemical model (Abrams and Prausnitz, AIChE J. 21:116 (1975) Uses surface areas (qi) to represent shapes qi is proportional to the surface area of i z is the coordination number

UNIQUAC cont. coordination number, z = 10 qj accounts for shape, rj accounts for size Energetic parameters tji=exp-(eji-eii)/RT= exp [(-aji)/RT] Pure species molecular parameters (in tables): r1, r2, q1, q2 ri are molecular size parameters relative to –CH2-

Activity coefficients from UNIQUAC

UNIFAC (UNIQuac Functional Activity Coefficient model) The solution is made of molecular fragments (subgroups) New variables (Rk and Qk) Combinatorial part is the same as UNIQUAC where Fk and qk are the volume fractions and surface fractions

Residual part of UNIFAC is different i identify species # of subgroups k in molecule i Be careful, this q is different than the surface fraction !!

Property changes of mixing We showed that for ideal solutions: From these properties we can evaluate ME = M - Mid

Property changes of mixing Let’s define:

Property changes of mixing This means that the excess properties and the properties change of mixing can be calculated from each other What are the DM for ideal solutions?

Mixing process at T and P