Chen-equation

Sun bleaching, in paper restoration, 11 414 Sun-Chen equation, 15 675 Sunett, 24 233 Sunfish... 

Figure 2.8 shows the enantiomeric excess of the remaining substrate A as a function of the conversion, for several values of the enantiomeric ratio, according to the Chen equation. When the selectivity of the enzyme is high ( =100), the remaining substrate is enantiopure from 50% conversion on. For lower selectivities, the yield of enantiopure substrate is lower. But sooner or later an enantiomeric excess of virtually 100% will be reached for the remaining substrate. At the moment that a sufficiently high ee has been obtained, the reaction should be terminated, because otherwise this enantiopure substrate will be converted further until racemic product remains. 

The enantiomeric excess of the product according to this second Chen equation (Figure 2.8) shows a very unpleasant featnre The first percentages of product already show an enantiomeric excess <100%, and during the conversion a decrease occurs. Only for very high values of E 100% enantiomeric excess is obtained. Typical practical values of E are 5-50. When >98% enantiomeric excess is desired, it is therefore better to concentrate on compounds which are remaining substrates of a reaction than on compounds which are products. 

A pure component constant that is occasionally used in property correlations is the enthalpy of vaporization at the normal boiling point, AHvbp. In addition, several special estimation methods are suggested. The Chen equation (15) gives a relation among the enthalpy of vaporization, the reduced vapor pressure, and the reduced temperature. When applied to the normal boiling point, Eq. 2 is obtained, with an average error of 2% ... 

Equation 3-14 is implicit in as it cannot be rearranged to derive directly and thus requires an iterative solution. Here, the Chen equation is used for calculating (i.e, = 4f(-). The Chen equation is explicit... 

Orbey, H., C.P. Bokis, and C.C. Chen, Equation of state modeling of phase equilibrium in the low-density polyethylene process The Sanchez-Lacombe, statistical associating fluid theory, and polymer-Soave-Redlich-Kwong equations of state. Industrial Engineering Chemistry Research, 1998. 37(11) p. 4481 491. 

The tendency to form organized monolayers improves with chain length. This is illustrated in a study of adsorption kinetics in alkanoic acid monolayers on alumina by Chen and Frank [36]. They find that the Langmuir kinetic equation, discussed in Section XVII-3, (see Problem XI-6)... 

In principle, Chen, given the flux relations there is no difficulty in constructing differencial equations to describe the behavior of a catalyst pellet in steady or unsteady states. In practice, however, this simple procedure is obstructed by the implicit nature of the flux relations, since an explicit solution of usefully compact form is obtainable only for binary mixtures- In steady states this impasse is avoided by using certain, relations between Che flux vectors which are associated with the stoichiometry of Che chemical reaction or reactions taking place in the pellet, and the major part of Chapter 11 is concerned with the derivation, application and limitations of these stoichiometric relations. Fortunately they permit practicable solution procedures to be constructed regardless of the number of substances in the reaction mixture, provided there are only one or two stoichiomeCrically independent chemical reactions. 

An equation that yields values of AFF P in units of kj/mol to within about 2% is Chen s equation (1) ... 

Annuli Approximate heat-transfer coefficients for laminar flow in annuh may be predicted by the equation of Chen, Hawkins, and Sol-berg [Tron.s. Am. Soc. Mech. Eng., 68, 99 (1946)] ... 

The results of computations of T o for an isolated fiber are dhistrated in Figs. 17-62 and 17-63. The target efficiency T t of an individual fiber in a filter differs from T o for two main reasons (Pich, op. cit.) (1) the average gas velocity is higher in the filter, and (2) the velocity field around the individual fibers is influenced by the proximity of neighboring fibers. The interference effect is difficult to determine on a purely theoretical basis and is usually evaluated experimentally. Chen (op. cit.) expressed the effecd with an empirical equation ... 

Bailey and Chen have improved on previous correlations with the following equations ... 

Chen, N. H., Liquid-Solid Filtration Generalized Design and Optimization Equations, Chem. Eng-., July 31, 1978, p. 97. 

Shell-side film coefficients can be conveniendy obtained from the charts of Chen, Figures 10-60, 10-61, and 10-62. These are based on Donohue s equation... 

The charts of Chen are also useful for solving the equations for condensing coefficients however, the correction for the effect of multiple fluid stream is not included. Therefore, the results should he conservative. 

Chen, N.H. New Equation Gives Tower Diameter, Chemical Engineering, Feb. 5, 1962, p. 109. Chart for Height of Transfer Unit in Wetted Wall Columns, Chemical Engineering, May 10, 1965, p. 193. 

Chen and Gross [48] derived equations to calculate partition coefficients for blood flow-limited compartments from either constant rate infusion (i.e., steady-state conditions) or intravenous bolus regimens. For a noneliminating organ under steady-state conditions,... 

Both the Chen and Gross [48] and the Gallo et al. [49] methods have been applied to eliminating compartments. Both derivation methods are based on the specific mass balance equations for the given model structure. Monte Carlo investigations have demonstrated that both methods provide reasonably accurate and precise estimates of partition coefficients from concentration-time data sets containing error, data one is likely to encounter from in vivo studies. 

Figure 9 compares Equation 20 with the recent pressure drop flow rate data of Friedmann, Chen, and Gauglitz (5) for a 1 wt% commercial sodium alkyl sulfonate dimer (Chaser SD-1000) stabilized foam in a Berea sandstone. These data are particularly useful because they have been corrected for foam blockage and therefore correctly reflect the flowing bubble regime. The solid line in Figure 9 is best fit according to Equation 20. Unfortunately, neither of the parameters c or 6 is available. Two sets of estimates are shown in Figure 9. When e - 0 (i.e., no surfactant effect) the bubble size is about 30% of a grain diameter. When — 0.1 mm (i.e., a value characteristic of those in Figure 8) the bubble size is about 10 grain diameters. We assert that Equation 20 not only predicts the correct velocity behavior of foam but it does so with reasonable parameter values (23).

Thermochemistry. Chen et al.168 combined the Kohn-Sham formalism with finite difference calculations of the reaction field potential. The effect of mobile ions into on the reaction field potential Poisson-Boltzman equation. The authors used the DFT(B88/P86)/SCRF method to study solvation energies, dipole moments of solvated molecules, and absolute pKa values for a variety of small organic molecules. The list of molecules studied with this approach was subsequently extended182. A simplified version, where the reaction field was calculated only at the end of the SCF cycle, was applied to study redox potentials of several iron-sulphur clusters181. 

The curves in Fig. 22 were calculated by means of the above equation, the points being experimental values. Figure 24 (Kwauk, Wang, Li, Chen and Shen, 1985) shows empirical correlations for the constants e and ea for FCC catalyst, fine and coarse alumina, pyrite cinder and iron ore concentrate. 

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