UNIQUAC: Difference between revisions
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The combinatorial contribution accounts for shape differences between molecules and affects the entropy of the mixture and is based on the lattice theory. |
The combinatorial contribution accounts for shape differences between molecules and affects the entropy of the mixture and is based on the lattice theory. |
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The excess entropy γ<sup>C</sup> is calculated exclusively from the pure chemical parameters, using the relative Van der Waals volumes ''r''<sub>''i''</sub> and surface areas q<sub>i</sub> of the pure chemicals. |
The excess entropy γ<sup>C</sup> is calculated exclusively from the pure chemical parameters, using the relative Van der Waals volumes ''r''<sub>''i''</sub> and surface areas q<sub>i</sub> <ref group="nb"> of the pure chemicals. |
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<math>\ln \gamma_i^C = (1 - V_i + \ln V_i) - \frac{z}{2} q_i \left( 1 - \frac{V_i}{F_i} + |
<math>\ln \gamma_i^C = (1 - V_i + \ln V_i) - \frac{z}{2} q_i \left( 1 - \frac{V_i}{F_i} + |
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Revision as of 22:46, 20 January 2012
UNIQUAC (short for UNIversal QUAsiChemical) is an activity coefficient model used in description of phase equilibria.[1] The model is a so-called lattice model and has been derived from a first order approximation of interacting molecule surfaces in statistical thermodynamics. The model is however not fully thermodynamically consistent due to its two liquid mixture approach. In this approach the local concentration around one central molecule is assumed to be independent from the local composition around another type of molecule.
It has been shown that while the local compositions are correlated, ignoring this correlation gives little effect on the correlation of activity coefficients.[2] Today the UNIQUAC model is frequently applied in the description of phase equilibria (i.e. liquid–solid,liquid–liquid or liquid–vapor equilibrium). The UNIQUAC model also serves as the basis of the development of the group contribution method UNIFAC, where molecules are subdivided in atomic groups. In fact, UNIQUAC is equal to UNIFAC for mixtures of molecules, which are not subdivided; e.g. the binary systems water-methanol, methanol-acryonitrile and formaldehyde-DMF.
A more thermodynamically consistent form of UNIQUAC is given by the more recent COSMOSPACE and the equivalent GEQUAC model.[3]
Equations
In the UNIQUAC model the activity coefficients of the ith component of a two component mixture are described by a combinatorial and a residual contribution.
The first is an entropic term quantifying the deviation from ideal solubility as a result of differences in molecule shape. The latter is an enthalpic [nb 1] correction caused by the change in interacting forces between different molecules upon mixing.
Combinatorial contribution
The combinatorial contribution accounts for shape differences between molecules and affects the entropy of the mixture and is based on the lattice theory.
The excess entropy γC is calculated exclusively from the pure chemical parameters, using the relative Van der Waals volumes ri and surface areas qi Cite error: A <ref> tag is missing the closing </ref> (see the help page).
- Extensions for better describing the temperature dependence of activity coefficients[4]
- Solutions for specific molecular arrangements.[5]
See also
- Chemical equilibrium
- Chemical thermodynamics
- Fugacity
- MOSCED, a model for estimating limiting activity coefficients at infinite dilution
- NRTL, an alternative to UNIQUAC of the same local composition type
Notes
- ^ Here it is assumed that the enthalpy change upon mixing can be assumed to be equal to the energy upon mixing, since the liquid excess molar volume is small and Δ Hex=ΔUex+Vex ΔP ≈ ΔU
References
- ^ Abrams D.S., Prausnitz J.M., “Statistical Thermodynamics of Liquid Mixtures: A New Expression for the Excess Gibbs Energy of Partly or Completely Miscible Systems”, AIChE J., 21(1), 116–128, 1975
- ^ McDermott (Fluid Phase Equilibrium 1(1977)33) and Flemr (Coll.Czech.Chem.Comm., 41(1976)3347)
- ^ Egner, K., Gaube, J., and Pfennig, A.: GEQUAC, an excess Gibbs energy model for simultaneous description of associating and non-associating liquid mixtures. Ber. Buns. Ges. 101(2): 209–218 (1997). Egner, K., Gaube, J., and Pfennig, A.: GEQUAC, an excess Gibbs energy model describing associating and nonassociating liquid mixtures by a new model concept for functional groups. Fluid Phase Equilibria 158–160: 381–389 (1999)
- ^ Cite error: The named reference
NewExtentionwas invoked but never defined (see the help page). - ^ Andreas Klamt, Gerard J. P. Krooshof, Ross Taylor “COSMOSPACE: Alternative to conventional activity-coefficient models”, AIChE J., 48(10), 2332–2349,2004