Wohl equation

W2) Wobl Equation of State. It is the 4th degree in the volume virial equation proposed in 1914 by Wohl and described in Addnl Ref Aj. it was used by Joffe (Ref 2a) far calcn of parameters of some gases in order to compare the results with those obtd by using the eq (5) of Joffe with equation of Beattie-Bridgeman and vanderWaals Joffe gives (Ref 2a, p 541) for Wohl equation ... 

The form of the Wohl Equation which leads to the van Laar Equation is... 

Each equation used, whether for ((i°, f , or y, has its particular advantages and disadvantages, and limitations on its range of applicability these and other factors influence the selection of the equations, or particular combination of equations used. For example, in many Kellogg design applications the four-suffix Margules form of the Wohl equation for activity coefficients is... 

In all cases the Wohl equation was used for the activity coefficients,... 

Table VII shows results for the first system, isopropanol -isopropyl ether - water - propylene, in which the experimental compositions in each of the three phases are compared with the values predicted by the method just described. A modified Redlich-Kwong equation of state for vapor fugacity, Chao-Seader equation with adjusted parameters for liquid fugacity, and the Wohl equation for the activity coefficients were used. The predictions were based only on data for binary systems.

The first recorded correlation of dipole moments with substituent constants was observed by Taft (3), who reported results for alkyl cyanides, chlorides, iodides, and tertiary amines. Kross and Fassel (31) have reported the correlations of dipole moments for 4-substituted nitrobenzenes with the simple Hammett equation. Rao, Wohl, and Williams (32) have studied the correlation of dipole moments of disubstituted benzenes with eq. (1) and of monosubstituted benzenes with the equation... 

Wohl in 1919 reported that A -bromoacetamide (CH CONHBr) induced allylic bromination. " Then iV-bromosuccinimide (30) was described in 1942 by Ziegler and co-workers to be useful in such free radical bromination reactions (equation 41), " and this widely utilized procedure is known as the Wohl-Ziegler reaction. In 1963 the mechanism of the reaction was proposed to involve halogen atoms in the hydrogen abstraction step " " " instead of succinimidyl radicals as had been commonly supposed. The halogen atom mechanism had previously been proposed by Gosselain et al. for reactions of yV-chlorosuccinimide. " ... 

Wohl s compressibility equation, 67 work of formation of drop, 371 of steam, 346... 

There are many other equations, which have been proposed, that do not result from Wohl s method. Two of the most popular equations are the Wilson and the universal quasi-chemical theory (UNIQUAC) by Abrams and Prausnitz.These equations are based on the concept of local composition models, which was proposed by Wilson in his paper. It is presumed in a solution that there are local compositions that differ... 

Different forms of this equation have been proposed (Wohl, 1946). One of these is the three-suffix or third-degree form ... 

The Margules equation is generalized in its four-suffix form to multi-component mixtures as follows (Wohl, 1946) ... 

The multi-component van Laar equation takes the following form (Carlson and Colburn, 1942 Wohl, 1946 Prausnitz et al., 1967) ... 

The binary constants Ay and A are determined from binary VLE data. For a three-component system (Wohl, 1946), the liquid activity coefficients are calculated by Equation 1.35a ... 

Recently Wohl (30) reported on extensive studies on the competitive antagonism of Ca2+-induced rat aortic vasoconstriction in vitro by a series of 36 benzothiadiazines. The Extended Huckel Theory (EHT) was used to calculate the preferred tautomer in solution, and charges, etc., on all atoms. The final equation was fairly successful in predicting the activity of several moderately potent compounds not included in the original regression. 

In spite of the simplicity of this relationship, the expressions for computing the activity coefficients for multicomponent mixtures are quite cumbersome. Since the equations of Wohl,76 Van Laar,68 Margules,43 Scatchard and Hamer,57 Redlich and Kister,52 and others are well documented in the literature, a restatement of these equations is not presented. Instead, a brief introduction to the newer methods including the Wilson equation, the NRTL, UNIQUAC, ASOG, and the UNIFAC methods is presented. 

Because of its flexibility, simplicity, and ability to fit many systems well, the van Laar equation is widely used in practice. It can be derived from the general energy expansion of Wohl, which considers effective volume fractions and molecular interactions. The so-called Carlson and Colburn natural logarithm version of the van Laar equation is given in Table 5.3. However, a common logarithm form is more common. The Margules and Scatchard-Hamer equations in Table 5.3 can also be derived from the Wohl expansion by a set of different assumptions. 

Another equation frequently used is the Renon equation. This three-parameter equation is also very successful for systems where G is highly asymmetrical. Other equations due to Wohl and to Margules have been discussed in detail by Hala et al. It should be noted that all the equations for G are to some degree arbitrary. For mixtures which show unusual composition dependence, either the numerical integration method for (p,x) data or the differentiation method for (p,y) data is to be preferred since it is difficult to predict in advance if the deviations observed between the calculated and the experimental values are due to errors in the data or are due to an inadequate function for G. To determine the accuracy of G data it is necessary to consider the magnitude of the various terms in equations (2) and (3). For the case where pX = 100 kPa, = 60 kPa, p - pX = P - P% - 20 kPa, 5aa = bb =... 

The Wohl deffvdation, an alternative to the Ruff d radation, is nearly the reverse of the Kiliani-Fischer synthesis. The aldose carbonyl group is converted to the oxime, which is dehydrated by acetic anhydride to the nitrile (a cyanohydrin). Cyanohydrin formation is reversible, and a basic hydrolysis allows the cyanohydrin to lose HCN. Using the following sequence of reagents, give equations for the individual reactions in the Wohl degradation of D-arabiiK>se to D-erythrose. Mechanisms are not required. 

A good example of the use of quantum calculations to obtain a large number of electronic indices for a series of benzothiadiazine hypotensive agents was reported by Wohl 47). However, the large number of parameters which Wohl used to develop regression equations for a relatively small number of compounds precluded the effective use of regression analysis for this series of data. 

Virial equation Wohl method Correlation for second virial coefficients Worn, K Z. Phys. Chem. 2 (1929) 77... 

Method of Worn. (Van Laar, Mar- GULES, SCATCHARD- Hamer) Effective Volumetric Ratio Polynomial Equation for the excess Gibb s energy, interaction parameters, relatively simple to use WoHL, K., TYans. Am. Chem. Eng. 42 (1946) 215 [1.13]. 

Limitations. 1. The Margules equations are quantitatively most useful for relatively symmetrical systems, i.e.y where Aab nearly equals Aba-They are very flexible in that they can show maximum or minimum values of log 7t with concentration. Differentiation of the equation shows that a maximum (or minimum) can be expected Aba Aab > 2.0. Wohl has shown, however, that for systems of such dissymmetry the Margules equations fail quantitatively to follow the observed data and that a better criterion for the probable appearance of a maximum is when Aba/Aab > 2 + (2.3Aba/4). It is then clear that for systems of considerable dissymmetry without maxima the Margules equations will be inapplicable. If Aab = Abaj the equations reduce to the simple forms... 

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