Rate ratios

The equation does not take into account such pertubation factors as steric effects, solvent effects, and ion-pair formation. These factors, however, may be neglected when experiments are carried out in the same solvent at the same temperature and concentration for an homogeneous set of substrates. So, for a given ambident nucleophile the rate ratio kj/kj will depend on A and B, which vary with (a) the attacked electrophilic center, (b) the solvent, and (c) the counterpart cationic species of the anion. The important point in this kind of study is to change only one parameter at a time. This simple rule has not always been followed, and little systematic work has been done in this field (12) stiH widely open after the discovery of the role played by single electron transfer mechanism in ambident reactivity (1689). 

By protodetritiation of the thiazolium salt (152) and of 2 tritiothiamine (153) Kemp and O Brien (432) measured a kinetic isotope effect, of 2.7 for (152). They evaluated the rate of protonation of the corresponding yiides and found that the enzyme-mediated reaction of thiamine with pyruvate is at least 10 times faster than the maximum rate possible with 152. The scale of this rate ratio establishes the presence within the enzyme of a higher concentration of thiamine ylide than can be realized in water. Thus a major role of the enzyme might be to change the relative thermodynamic stabilities of thiamine and its ylide (432). 

Rates of debromination of bromonitro-thiophenes and -selenophenes with sodium thio-phenoxide and sodium selenophenoxide have been studied. Selenophene compounds were about four times more reactive than the corresponding thiophene derivatives. The rate ratio was not significantly different whether attack was occurring at the a- or /3-position. As in benzenoid chemistry, numerous nucleophilic displacement reactions are found to be copper catalyzed. Illustrative of these reactions is the displacement of bromide from 3-bromothiophene-2-carboxylic acid and 3-bromothiophene-4-carboxylic acid by active methylene compounds (e.g. AcCH2C02Et) in the presence of copper and sodium ethoxide (Scheme 77) (75JCS(P1)1390). 

Peroxy acid oxidation of (17) gave sulfoxide (18) whose F NMR spectrum showed equivalent CF3 groups even at —95 °C (76JA4325). Tlie rate ratio for the sulfur walk in (18/17) is an astounding 10 ° at 25 "C theoretical reasons for the difference have been discussed (80JA286i). 

To compare the results of the correlation presented in this article and an exact numerical solution, let us consider the case where air with a wet-bulb temperature of 70°F is used to cool water from 120°F to 80°F. Table 1 summarizes the results for different air-to-water flow rate ratios. 

Table 5.12. Tosylate/Bromide Rate Ratios for Solvolysis of RX in 80% Ethanol ...

In developing mathematieal expressions for seleetivities, knowledge of the rate equations are required. This is beeause the instantaneous seleetivity is defined in terms of the rate ratios. The parameters that affeet the instantaneous and the overall seleetivities are exaetly the same as those influeneing the reaetion rates, namely, the eoneentration, temperature, aetivation energy, time of reaetion (residenee time in flow reaetors), eatalysts, and the fluid meehanies. 

Calculating the heat capacity rates ratio gives... 

The largest known fluonne stenc effect is the rate ratio of lo" at 25 °C for the meta ring fhp m 20 [166 Other dynamic processes that reveal bona fide fluonne stenc effects are the bamers to i-C3H.j group rotation in 21 =69... 

The chemical and stochastic concentrations are related by [A] = ca, etc. Combining these equations and equating the chemical and stochastic rate ratios gives... 

It should be noted that positional selectivity is never complete even when a clean reaction gives only one isolated product.Reaction occurs at all positions in proportion to the ratio of the rate constants. The difference between a clean reaction (e.g., rate 9 times that of a competing reaction) and one giving a troublesome mixture can be merely a moderate quantitative increase in one rate (e.g., to a 9 7 rate ratio) or a change in both rates (e.g., to a 3 4 ratio). Work such as that of Kauffmann and Boettcher on heteroarynes illustrates the potential of modern forms of chromatography for determining the true proportion of even very minor products. 

Relative reactivity wiU vary with the temperature chosen for comparison unless the temperature coefficients are identical. For example, the rate ratio of ethoxy-dechlorination of 4-chloro- vs. 2-chloro-pyridine is 2.9 at the experimental temperature (120°) but is 40 at the reference temperature (20°) used for comparing the calculated values. The ratio of the rate of reaction of 2-chloro-pyridine with ethoxide ion to that of its reaction with 2-chloronitro-benzene is 35 at 90° and 90 at 20°. The activation energy determines the temperature coefficient which is the slope of the line relating the reaction rate and teniperature. Comparisons of reactivity will of course vary with temperature if the activation energies are different and the lines are not parallel. The increase in the reaction rate with temperature will be greater the higher the activation energy. 

The effect of the leaving group is illustrated in the comparison of fluoro- and chloro-nitrobenzenes (Table VIII) in their reactions with ethoxide ion (lines 5 and 8) and with piperidine (lines 7 and 9). Rate ratios F Cl are 23 1 (opposing and entropy of activation changes) and 201 1 (E effect), respectively, for the two nucleophiles. For the reasons discussed in Section II, D, 1, a fluorine substituent produces a lower energy of repulsion of the nucleophile and thus facilitates reaction. 

Table XIV, line 3). The rates are equal (only at 20°) due to a large, compensating difference between the entropies of activation. In piperidino-dechlorination, 4-chloroquinoline (Table XI, line 3) has a higher and a lower rate (by about 200-fold at 20°) than 1-chloroisoquinoline (Table XIV, line 1). This reversal of reactivity and of the relationship of the activation energies is attributed to the factors in amination reactions mentioned above. The relative reactivity of the chloro groups in 2,4-dichloroquinoline with methanolic methoxide is given as a 2 1 rate ratio of 4- to 2-displacement. 

As already mentioned, there is a striking difference in the reactivity of 1- and 3-chloroisoquinoline the former reacts about 10 times faster than the latter with both piperidine and ethoxide ion at room temperature. The lower rate of ethoxy-dechlorination of the 3-isomer is due to an E which is 10 kcal higher. It is not justified to conclude that this isomer is virtually unactivated when its rate of ethoxylation is 100,000 times that of 2-chloronaphthalene and the E for this reaction is markedly decreased (by 7 kcal) relative to that of 2-chloronaphthalene. A direct comparison of reactivity with piperidine has not been made, but a rate ratio of 500 1 can be estimated by using a factor of one-fortieth (Table X, lines 1 and 4) to make the... 

The rate of amination and of alkoxylation increases 1.5-3-fold for a 10° rise in the temperature of reaction for naphthalenes (Table X, lines 1, 2, 7 and 8), quinolines, isoquinolines, l-halo-2-nitro-naphthalenes, and diazanaphthalenes. The relation of reactivity can vary or be reversed, depending on the temperature at which rates are mathematically or experimentally compared (cf. naphthalene discussion above and Section III,A, 1). For example, the rate ratio of piperidination of 4-chloroquinazoline to that of 1-chloroisoquino-line varies 100-fold over a relatively small temperature range 10 at 20°, and 10 at 100°. The ratio of rates of ethoxylation of 2-chloro-pyridine and 3-chloroisoquinoline is 9 at 140° and 180 at 20°. Comparison of 2-chloro-with 4-chloro-quinoline gives a ratio of 2.1 at 90° and 0.97 at 20° the ratio for 4-chloro-quinoline and -cinnoline is 3200 at 60° and 7300 at 20° and piperidination of 2-chloroquinoline vs. 1-chloroisoquinoline has a rate ratio of 1.0 at 110° and 1.7 at 20°. The change in the rate ratio with temperature will depend on the difference in the heats of activation of the two reactions (Section III,A,1). 

The limited data available for 2,4-dichloroquinoline (Table X, line 9) show a substantially greater rate of methoxylation than for the 2- and 4-chloro analogs (Table X, line 6 and Table XI, line 2), as a result of activation (lowering of E ) by the additional chlorine substituent. Unequal mutual activation (cf. Section III, B, 2) by these substituents is indicated by the rate ratio of 1.9 1 for 4- to 2-substi-tution in the dichloro compound and of 25 1 for the two mono-chloro compounds. 

Phenylhydroxylamine rearranges in sulfuric acid to give mainly p-aminophenol. Industrial routes to this compound have been developed in which phenylhydroxylamine, formed by hydrogenation of nitrobenzene in sulfuric acid over platinum-on-carbon, is rearranged as it is formed. Conditions are adjusted so that the rate of rearran ment is high relative to the rate of hydrogenation of hydroxylamine to aniline (15,17,86). An easy way to obtain a favorable rate ratio is to carry out the reduction with about 1% DMSO present in the sulfuric acid (79,81). 

Either ring of an alkyl-substituted naphthalene may be reduced and the rate ratio depends both on the position of R and its size 2S). Naphthalenes... 

The rate ratio of hydrogenation to hydrogenolysis varies with the catalyst, substrate structure, and environment in a partially predictable way. 

For nonlinear systems, however, the evaluation of the flow rates is not straightforward. Morbidelli and co-workers developed a complete design of the binary separation by SMB chromatography in the frame of Equilibrium Theory for various adsorption equilibrium isotherms the constant selectivity stoichiometric model [21, 22], the constant selectivity Langmuir adsorption isotherm [23], the variable selectivity modified Langmuir isotherm [24], and the bi-Langmuir isotherm [25]. The region for complete separation was defined in terms of the flow rate ratios in the four sections of the equivalent TMB unit ... 

To determine the true overall temperature difference, the correction factors, F, shown in Figure 10-34 are used to correct for the deviations involved in the construction of multipasses on the shell and tube sides of the exchanger. Note that R of the charts represents the heat capacity rate ratio , and P is the temperature efficiency of the exchanger. 

Predominant formation of either complex fluoride or complex oxyfluoride depends on the interaction rates ratio of processes (25) and (26). The relatively high interaction rates of (27) and (28) lead to the synthesis of simple fluorides or oxyfluorides, respectively. With the availability of two or more cations in the system, the ammonium complex fluorometalates interact forming stable binary fluorides or oxyfluorides or mixtures thereof. 

Table 12-2 gives some of Sterba s results for 1-naphthol, resorcinol, 1-methoxy-naphthalene, 3-methoxyphenol and 1,3-dimethoxybenzene. The data in the table show that the 1-naphthoxide ion is 108 times more reactive than the undissociated naphthol, which is 102 times more reactive than 1-methoxynaphthalene. The rate ratios for the monoanion of resorcinol relative to resorcinol, 3-methoxyphenol, and 1,3-dimethoxybenzene are of similar magnitudes. The dissociation of both OH groups of resorcinol gives rise to a rate constant (2.83 X 109 m -1 s-1) which, in our opinion, is probably mixing- or diffusion-controlled (see Sec. 12.9). 

Analysis of the first-order rate coefficient in terms of the two consecutive reactions which were occurring, yielded values of 5.3 xlO-4 and 2.64 xlO-4 the latter value was confirmed as arising from reaction on the first reaction product, 3,4-dichlorodiphenylmethane, because separate 3,4-dichlorobenzylation of this gave a rate coefficient of 2.98 x 10-4. The first-order (overall) rate coefficients obtained at 15 °C (0.665 x 10-4) and 35 °C (6.1 x 10-4) yielded Ea = 19.6, and log A = 14.3, the rate ratio for the consecutive reactions being the same (0.5) at both temperatures later studies have tended to confirm this order of activation energy. 

The rate ratio is given by the first part of Eq.(5-24). If [OH ] and [C6H5S ] are sufficiently high so as to remain nearly constant, the product ratio is... 

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