Lewis method

For these conditions there are two basic methods for determining the number of plates required. The first is due to Sorel(25) and later modified by Lewis126 , and the second is due to McCabe and Thiele(27). The Lewis method is used here for binary systems, and also in Section 11.7.4 for calculations involving multicomponent mixtures. This method is also the basis of modem computerised methods. The McCabe-Thiele method is particularly... 

Numerical values of Ss were obtained after replacing ps by fs according to Lewis method. Figure 5 shows that the entropy of the adsorbed phase always lies below that for gaseous phase compressed to the same density. Thus the adsorbed phase is more localized and has less freedom than the compressed phase. 

Fig. 18. Determination of copolymerization parameters by the Mayo-Lewis method. See p. 255 of ref. 170.

The classical Mayo-Lewis scheme relating comonomer feeds to relative reactivity ratios (5i) is often applied to copolymerization of cyclosiloxanes. This scheme presumes that no depropagation of the copolymer occurs, that the copolymerization rate constants depend only on the ultimate comonomer units, and that instantaneous comonomer feed ratios and copolymer compositions are used in the analysis of data. When these assumptions hold, the Mayo-Lewis method is very useful for the analysis of copolymerization data. 

The basicity of esters is similar to that of related ethers, therefore, in copolymerization random structures could be expected. THF (pKb = 5.0) and BCMO (pKb = 5.65) were copolymerized with e-caprolactone (eCL pKb = 5.31) and P-propiolactone (PPL, pKb = 10.06), eCL and cyclic ethers enter the copolymer with nearly the same rates. The reactivity ratios determined by the Mayo-Lewis method are rt(BCMO) = 0.24, r2(eCL) = 0.44 and rt(THF) = 0.7, r2(eCL) = 0.3 4C). r, should be higher for THF(Mj) because the reversibility of THF polymerization has not been taken into account (cf. Sect. 15.1.3.1). rt and r2 values suggest the formation of nearly random copolymers. The microstructure of BCMO-eCL copolymers was studied by NMR spectroscopy, and the new signals B and A due to heterodyad appeared [cf. Eq. (15-41)]. Simultaneously the ratio of signals C/D decreased from 2 to a lower value ... 

The Lewis method of formulation therefore shows more isomers than actually exist. The minimum in curve C is an energy minimum with respect to both electron distribution and atomic configuration, and hence represents a definite compound but one that cannot be represented by a single Lewis formula. This compound is a meso-meric one. We have represented its energy and atomic configura-... 

The copolymerization constants are estimated by the Mayo-Lewis method using the different means of linearization and optimization (most often the Fineman-Ross and Kelen-Tudos methods). We shall now consider the principal problems m the field of copolymerization of MCMs under the same conditions as for their homopolymerization. 

Under some circumstances it is also possible to use a modified Lewis method (50). This assumes a continuous function instead of a discrete realtion between B and n. Then if ... 

The modified Lewis method can easily be employed once the relationship between B and B is obtained provided that the condition in Eqn. (15) is satisfied. Juvekar and Sharma (50) listed expressions which were obtained from the modified Lewis method, for calculating the number of plates for cases 3,5,10,11 and 12 of Table 2. They compared the graphical results of Kawagoe et al. 

Exanqjle 4-1. Stage-by-stage calculations by the Lewis method... 

Use the Lewis method to find the number of equilibrium contacts required if the feed is input on the second stage from the top. 

B. Explore. Except for some slight changes in the feed tenperature and column pressure, this problem is very similar to Example. VI. The solution for B and D obtained in that exanple is still correct. B = 6667 k h, D = 3333 kg/h. Equilibrium data are available in weight fractions in Figure 2-4 and in mole fraction units in Figure 2-2 and Table 2-1. To use the Lewis method we must have CMO. We can check this by conparing the latent heat per mole of pure ethanol and pure water. (This checks the third and most inportant criterion for CMO. Since the column is well insulated, the first criterion, adiabatic, will be satisfied.) The latent heats are (Himmelblau. 1974) ... 

The Lewis method is obviously much faster and more convenient than the Sorel method. It is also easier to program on a conputer or in a spreadsheet, hi addition, it is easier to understand the physical reasons why separation occurs instead of becoming lost in the algebraic details. However, remember that the Lewis method is based on the assunption of CMO. If CMO is not valid, the answers will be incorrect. 

If the calculation procedure in the Lewis method is confusing to you, continue on to the next section. The graphical McCabe-Thiele procedure explained there is easier for many students to understand. After completing the McCabe-Thiele procedure, return to this section and study the Lewis method again. 

McCabe and Thiele (1925) developed a graphical solution method based on Lewis method and the observation that the operating Eqs. t4-12b) and (4-14) plot as straight lines (the operating lines) on a y-x... 

Since the boilup ratio, V/B, was not specified, we cannot directly calculate L/V, which is the slope of the bottom operating line. Instead, we need to utilize the condition of the feed to determine flow rates in the stripping section. The same procedure used with the Lewis method can be used here. The feed quality, q. 

Determine the number of stages required, using the Lewis method and the McCabe-Thiele method... 

The Lewis method for binary distillation is easy to program on a spreadsheet using Visual Basic for Applications (VBA). If you are not familiar with VBA, read Appendix 4.B. Part 1. If you are familiar witii VBA, you can skip Part 1 and proceed to Part 2. 

The basic assumption in the potential theory approach to predicting the adsorption equilibria of a gas mixture is that the adsorption data for all pure components on the same adsorbent will fall on the same line when plotted on some appropriate coordinate (coalescing) [39,631. This principle is reflected in the Lewis method [64] and in the Grant-Manes (G-M) method [65] and its modification by Metha and Danner [66]. 

The Lewis method is used not only because of its simplicity of expression but also because much of the chemistry of the atom is directly associated with the electrons in the outermost energy level. Figure 11.4 shows Lewis structures for the elements hydrogen through calcium. 

Determinations of the refractive index and thickness of oxide films formed by various methods on silicon have been made by Archer and by Claussen and Flower " using ellipsometry. Archer found a refractive index of 1.362 for an oxide film formed in an aqueous solution of 0.1 M sodium borate and 0.1 M boric acid. Claussen and Flower found that the refractive index of the oxide formed in 0.0025 N KNO3 anhydrous N-methylacetamide was 1.468 and that of films formed in 0.04 iV KNO3 in N-methylace-tamide with 6-8% water was 1.417. Zobel and Young using Lewis method " with liquids of known refractive index, and ellipsometry, have observed a refractive index for films formed in the above aqueous borate solution of about 1.4. Care has to be taken to check that film breakdown effects do not render the film untypical. 

M. W. FreyerandE. A. Lewis, Methods Cell Biol, 200S,S4, 79. 

The relation [3.87] hnks the solutions described by the Lewis method of coefficients of activity and the excess Gibbs energy method. Both methods are therefore equivalent. 

Sorel-Lewis Method. As an illustration of the Sorel-Lewis method, consider the rectification of a 50 mol per cent benzene and 50 mol per cent toluene mixture into a product containing 5 mol per cent toluene and a bottoms containing 5 mol per cent benzene. The feed will enter as a liquid sufficiently preheated so that its introduction into the column does not affect the total mols of vapor passing the feed plate f.e., such that Fn Fm. A reflux ratio 0 /Z), equal to 3, will be employed, and the column wilt dj Hte with a total condenser and indirect heat in the still. The y x equilibrium curve is given in Fig. 7-2. 

McCabe and Thiele Method (Ref. 11). By the Sorel-Lewis method, the relation between and Xn+i is a straight line, and the equation of this line may be plotted on the y,x diagram. Thus, for the example worked in the preceding section,... 

Lewis Method. Lewis (Ref. 8) expresses the rate of increase of concentration of the liquid in the column from one plate to the next by the differential dx/dn-, therefore,... 

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