Lewis number, definition

Langmuir-Hinshelwood kinetics adsorption inhibition, 62 consistency of, 66 rate-controlling step for, 60 two-step model for, 67 Langmuir-Hinshelwood mechanism, 60 Lewis acid, 6 Lewis number definition of, 107 stability as affected by, 266 Local activity factor, 465 Lumping, 81... 

Solutions of the complete transient equations (with the additional parameter, Lewis number Lw ) have not been studied very much because of the mathematical complexity. Lee and Luss [90] have shown for some cases that Lw > 1 (an author s definition of the Lewis number must be carefully checked—some use the reciprocal of our Lw ) can lead to limit-cycle and other complex behavior. However, Ray [132] estimates that for this to occur, considering reasonable values of jSand y, the critical values are Lw > 5-lOor larger. Thus, the conclusion from Table 3.7.a-l is that this is not at all likely, except perhaps for very high-pressure reactors. 

A transition in the behaviour of the flame is obtained for an equivalence ratio of 0.4. Below this value, the flame becomes unstable correlations of flame speeds and maximum reaction rates along the flame front change sign when the equivalence ratio goes from rich to lean. A similar transition was observed for simple chemistry situations but for a Lewis number of unity. The definition of a Lewis number in a real flame is difficult but in this case, the trend observed in simple chemistry cases (and predicted by asymptotic theories) is confirmed by complex chemistry computations. 

Here v and d represent dimensionless convection velocity and dimensionless thermal dif-fusivity, resp. (axial mass dispersion is neglected) B is dimensionless reaction enthalpy. Da is the Damkohler number and Le is the Lewis number. We have avoided the conventional introduction of the Peclet number since we would like to examine the effects of convection and thermal diffusion separately. Otherwise, the scaling of the variables and definitions of the dimensionless quantities are conventional, see e.g. (Nekhamkina et al. (2000)). 

Utilizing this definition, Eqs. 8.44 through 8.47 can be rewritten for a unit Lewis number as ... 

Comparing these forms with Equations (6) earlier, we can see definite and meaningful similarities. The Lewis number occurs in exactly the same way as the ratio of diffusion coefficients. The temperature rise can also be seen to provide an effective autocatalyst. In this case, the feedback is thermal rather than chemical, but enters the governing equation in exactly the same manner. 

This area of reactivity has been the subject of excellent reviews (J5). Silyl enol ethers are not sufficiently nucleophilic to react spontaneously with carbonyl compounds they do so under the influence of either Lewis acids or fluoride ion, as detailed above. Few clear trends have emerged from the somewhat limited number of definitive studies reported so far, with ambiguities in diastereoisomeric assignments occasionally complicating the issue even further. 

Before studying some examples more closely, let us consider some cases which are not listed in Table 13. There are numerous compounds SnX2 which are definitely monomeric but are nevertheless no carbene analogs since their valence electron number at the tin atom is at least eight. These compounds contain chelating ligands which can stabilize the carbenoid tin atom due to intramolecular Lewis acid-base interactions as shown by structure A and B (see also Chapter 3). 

This electrophile/nucleophile dichotomy can be looked upon as a special case of the acid/base idea. The classical definition of acids and bases is that the former are proton donors, and the latter proton acceptors. This was made more general by Lewis, who defined acids as compounds prepared to accept electron pairs, and bases as substances that could provide such pairs. This would include a number of compounds not previously thought of as acids and bases, e.g. boron trifluoride (39),... 

Perhaps the greatest area in which the Lewis acid-base approach is most useful is that of coordination chemistry. In the formation of coordination compounds, Lewis acids such as Cr3+, Co3+, Pt2+, or Ag+ bind to a certain number (usually 2, 4, or 6) of groups as a result of electron pair donation and acceptance. Typical electron pair donors include H20, NH3, F , CN , and many other molecules and ions. The products, known as coordination compounds or coordination complexes, have definite structures that are predictable in terms of principles of bonding. Because of the importance of this area of inorganic chemistry, Chapters 16 through 22 in this book are devoted to coordination chemistry. 

Some liquid covalent halides can act as nonaqueous solvents " based on Lewis acid-base behavior, according to the donor-acceptor definition. The self-dissociated ions consist of a cation formed by subtraction of a hahde ion from the neutral compound, while the anion is formed by its addition (equation 24). Salts derived from such covalent halides can be considered as titration products of the parent acidic and basic compounds (equations 25 and 26). In such cases, both the cation and the anion usually possess a stable coordination number with a high geometrical symmetry. 

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