n-Alcohols: lg^," = -0.420 + 0.517«, +—--(27)
n-Aldehydes: lg/," =-0.650 + 0.517«, + ^^ (28)
where the coefficient B is the same in both cases.
5.2.2. Parachor method
Activity coefficients at infinite dilution are obtained from the following relationship:
where Uf is potential energy of component i, All' is enthalpy of evaporation, C is a constant, a function of temperature, the parachor ratio of the two components, and the number of carbon atoms in the solute and solvent molecules, T is the absolute temperature, and R is gas constant. The same variety of systems covered in the Pierrotti-Deal-Derr method is also included in this approach.
Starting with the Hildebrand-Schatchard model for non-polar mixtures, Weimer and Prausnitz developed an expression for evaluating values of hydrocarbons in polar solvents:
RT\nr; =F2[ai-l2)2+r,2-2^,2] + tfr[hi^ + l--^] (31)
i i where Vj is the molar volume of pure component i, A, is the non-polar solubility parameter, r, is the polar solubility parameter, T is the absolute temperature, and R is gas constant. The subscript 1 represents the polar solvent and subscript 2 is the hydrocarbon solute with Vn = krf (32)
Later Helpinstill and Van Winkle suggested that Eq. (31) is improved by considering the small polar solubility parameter of the hydrocarbon (olefins and aromatics):
RT\nY; =V2[(Ai -A2)2 +(ti -t2)2 - 2y/n] + RT[\n^- +1 --p-] (33)
For saturated hydrocarbons,
For unsaturated hydrocarbons, y/n = 0.388(r, -r,)2 (36)
The term y/n corresponds to the induction energy between the polar and non-polar components. Since no chemical effects are included, the correlation should not be used for solvents showing strong hydrogen bonding.
Unfortunately, the parameters of these three methods are limited, which leads to their very narrow application in extractive distillation. So these methods are rarely reported in the recent references.
However, CAMD based on group contribution methods is very desirable. By means of CAMD, the experiment working is greatly decreased in a search for the best solvents. CAMD as a useful tool plays an important role in finding the solvent and shortening the search time. It is believed that with the development of CAMD, it would be possible to be extended and applied in many more fields.
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