Disproportionality proportionality

Verhaltnis, n, proportion ratio, rate relation sit iation, connection, circumstance condition, consistency, -anzeiger, m. (Math.) exponent, -gleichheit, /, proportion. verhaltnis-mSssig, a. proportional, proportionate relative commensurable, commensurate. — adv. proportionately, relatively, -widrig, a. disproportionate. 

If termination were to occur in part by disproportionation, would still be proportional to v but the constant of proportionality would lie between one and two, its exact value depending on the fraction of termination which occurs by combination. The assumption that the reactions considered above suffice for the interpretation not only of the polymerization rate but also of the degree of polymerization requires in any case that Xn be proportional to v. 

Now consider the other extreme condition where diffusion is rapid relative to chemical reaction [i.e., hT( 1 — a) is small]. In this situation the effectiveness factor will approach unity for both the poisoned and unpoisoned reactions, and we must retain the hyperbolic tangent terms in equation 12.3.124 to properly evaluate Curve C in Figure 12.11 is calculated for a value of hT = 5. It is apparent that in this instance the activity decline is not nearly as sharp at low values of a as it was at the other extreme, but it is obviously more than a linear effect. The reason for this result is that the regions of the catalyst pore exposed to the highest reactant concentrations do not contribute proportionately to the overall reaction rate because they have suffered a disproportionate loss of activity when pore-mouth poisoning takes place. 

Westerhausen and co-workers developed synthetic routes for heteroleptic diorganozinc compounds that rely on either the steric bulk of the organic substituents or on Lewis basicity to prevent disproportionation.82,83 The chelating TMEDA prevented even heteroleptic diorganozinc compounds bearing small methyl groups from dis-proportionating (Scheme 33). 

The reverse of disproportionation is referred to as com-proportionation. A special case of disproportionation (or dismutation) is radical disproportionation which serves as a termination process in the fate of free radicals. For example, 2 CH3CH2- CH3CH3 + CH2=CH2. 

This would indicate either that disproportionation is the preferred route of termination for the ketyl radicals or that the pinacol is unstable and dis-proportionates to acyloin and ketone under the reaction conditions. 

The most universal and facile techniques for the preparation ofthe derivatives of all three types of complexes are reactions of co-proportionation of TiHal4 with Ti(OR)4 [1204,1199] and also of action of AcOHal on Ti(OR)4 (in 1 1, 1 2 and 1 3 ratios). In the latter case the crystallization of solvates of TiCln(OR)4 AcOR composition is observed [215]. The preparation ofalkox-ofluorides has been achieved also with the use of SbF3 instead ofAcOF [259], The vacuum distillation of alkoxide chlorides is often accompanied by their disproportionation, and the separation in the form of adducts with pipyridine C5H10NH has been therefore proposed as an alternative [1204],... 

Infrared spectral studies on molybdenum hexacarbonyl-alumina were reported by Davie, Whan, and Kemball 78). Without any activation procedure they obtained a sharp carbonyl frequency corresponding to unchanged hexacarbon-yl on the support. This material was not active for disproportionation. After treatment for one hour under vacuum at 373 °K the catalyst had lost the sharp carbonyl band but showed two wider and broader bands and was active for dis-proportionating propylene. The authors stated that the active catalyst clearly had a lower symmetry than the hexacarbonyl and must have lost one or more of the carbonyl groups. After exposure of the activated catalyst to air, the catalyst was inactive and showed no absorption in the carbonyl region. 

In 1984, the first very effective example of metathesis (disproportionation) of vinylsubstituted silicon compounds catalyzed by ruthenium complexes was reported [33]. It opened a new route of great synthetic importance and has allowed synthesis of a series of unsaturated silicon compounds according to the following equations, with the yield predominantly higher than 70%. Numerous reports on vinylsilane disproportionation (Eq. 21) [5, 33-38] and its co-dis-proportionation with olefins (Eq. 22) [37-44] have been published. 

Disproportionation and proportionation reactions occur when there exist situations of the type shown in Fig. 2.10. It is easy to predict these reactions from the diagrams. It should be noted, however, that these are thermodynamic predictions and kinetics can cause the reactions to... 

Fig. 2.10. Oxidation state diagrams for (a) proportionation—C is below straight line linking A and B (b) disproportionation—C is above the straight...

In a DISP 2 mechanism the second-order disproportionation step is rate limiting (see Section 2). An example of such a process involves the photoreduction of the dye fluorescein in basic aqueous solutions at mercury electrodes (Compton etal., 1988b). The photoreduction of benzophenone (86) and fluorobenzophenone in acetonitrile also proceeds via a DISP 2 type mechanism as verified by channel electrode voltammetry (Leslie et al., 1997). The rate-limiting step is electron transfer (86c) between photoexcited radical anion and the initial anionic species formed on electron transfer at the electrode surface. This process is further complicated by significant con-proportionation (86e) and quenching of the benzophenone excited state (86f). 

The biochemical fractions of the serum alkaline phosphatase in cirrhosis are listed in Table 13 according to blood types A and 0. It may be advantageous to compare the various moieties in these patients with the data on normal subjects of corresponding blood type (Table 10). In some cases (4, 5, 14) the elevation is proportionate in the LPSAP and non-LPSAP moieties, whereas in others (1, 2, 3, 9, 10, 12, 13, 15) there is a disproportionate elevation in the LPSAP fraction. Subject 7 exhibits the largest contribution of LPSAP (60%). There appears to be no similarity of the heat sensitivities of LPSAP and non-LPSAP in subjects 4, 5, 7, 14, and 15 with total LPSAP hyperphosphatasemia. In fact, the relatively high heat inactivation of sera 5, 6, 7, and 12 would register negatively for liver in a heat-inactivation test of total alkaline phosphatase (P19). 

The most obvious and frequently used route to sub-valent species in molten halide solution is the reduction of a normal-valent halide with its parent metal, i.e. sym-proportionation reactions such as (2). This methodology is natural, since it disfavors disproportionation of the sub-valent compound to the zero-valent state according to (1). In addition, the methodology minimizes the number of components in the system. Post-transition metal-molten salt systems from which solid, sub-valent compounds have been isolated through symproportionation reactions are summarized in Table 1. 

To the extent a deterrence theory relies on threatening a painful response to any attack, there remains the issue of proportionality, and whetha a deterrent response can be exercised within the confines of humanitarian law targeting rules. David Kretzmer suggests the [u]se of force that seems to be largely punitive, the primary motive of which is deterrence or which has wide political aims will be regarded as disproportionate. Deterrence is a concept that raises the issue of how the civilian population, including the political leadership, can be lawfully... 

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