Reaction rate comparison 79 second-order

What about reactions of the type A + B — C This is a second-order reaction, and the second-order rate constant has units of M min-1. The enzyme-catalyzed reaction is even more complicated than the very simple one shown earlier. We obviously want to use a second-order rate constant for the comparison, but which one There are several options, and all types of comparisons are often made (or avoided). For enzyme-catalyzed reactions with two substrates, there are two Km values, one for each substrate. That means that there are two kcJKm values, one for each substrate. The kcJKA5 in this case describes the second-order rate constant for the reaction of substrate A with whatever form of the enzyme exists at a saturating level B. Cryptic enough The form of the enzyme that is present at a saturating level of B depends on whether or not B can bind to the enzyme in the absence of A.6 If B can bind to E in the absence of A, then kcJKA will describe the second-order reaction of A with the EB complex. This would be a reasonably valid comparison to show the effect of the enzyme on the reaction. But if B can t bind to the enzyme in the absence of A, kcat/KA will describe the second-order reaction of A with the enzyme (not the EB complex). This might not be quite so good a comparison. 

Scheme 3 Dienophiles for tetrazine bioorthogonal reaction and corresponding second-order rate constant, a 7>ani-cyclooctene synthesis and rate constant comparison, b Bicyclononyne as a dienophile. c Recently reported dienophile mini-tags and their corresponding rate constant. 2 was measured by reacting with tetrazine 14 was measured by reacting with tetrazine 15 2 was measured by reacting with tetrazine 16...

A similar circumstance is detectable for nitrations in organic solvents, and has been established for sulpholan, nitromethane, 7-5 % aqueous sulpholan, and 15 % aqueous nitromethane. Nitrations in the two organic solvents are, in some instances, zeroth order in the concentration of the aromatic compound (table 3.2). In these circumstances comparisons with benzene can only be made by the competitive method. In the aqueous organic solvents the reactions are first order in the concentration of the aromatic ( 3.2.3) and comparisons could be made either competitively or by directly measuring the second-order rate constants. Data are given in table 3.6, and compared there with data for nitration in perchloric and sulphuric acids (see table 2.6). Nitration at the encounter rate has been demonstrated in carbon tetrachloride, but less fully explored. ... 

A comparison of the second-order rate coefficients for nitration of 2,4,6-tri-methylpyridine and 1,2,4,6-tetramethylpyridinium ion (both at the 3-position) shows similarity of profile in the common acidity region and a rapidly increasing rate with acidity for the trimethyl compound at acidities below 90 wt. % (where the usual maximum is obtained). These two pieces of evidence show reaction to occur on the conjugate acid as also indicated by the large negative entropy of activation. Surprisingly, the tetramethyl compound is less reactive than the trimethyl compound so maybe this is an example of steric hindrance to solvation. Calculation of the encounter rate also showed that reaction on the free base was unlikely. 

Bradfield et al.21g first studied the kinetics of molecular bromination using aromatic ethers in 50% aqueous acetic acid at 18 °C. They showed that the kinetics are complicated by the hydrogen bromide produced in the reaction which reacts with free bromine to give the tribromide in BrJ, a very unreactive electrophile. To avoid this complication, reactions were carried out in the presence of 5-10 molar excess of hydrogen bromide, and under these conditions second-order rate coefficients (believed to be I02k2 by comparison with later data) were obtained as follows after making allowance for the equilibrium Br2 + Br7 Bn, for which K = 50 at 18 °C 4-chloroanisole (1.12), 4-bromoanisole (1.20), 4-... 

There is one further piece of kinetic evidence which throws light on an aspect of the benzidine rearrangement mechanism, and this is comparison of the rates of reaction of ring-deuterated substrates with the normal H compounds. If the final proton-loss from the benzene rings is in any way rate-determining then substitution of D for H would result in a primary isotope effect with kD < kH. This aspect has been examined in detail42 for two substrates, hydrazobenzene itself where second-order acid dependence is found and l,l -hydrazonaphthalene where the acid dependence is first-order. The results are given in Tables 2 and 3. 

Ejfect ofSolvent. In addition to the solvent effects on certain SeI reactions, mentioned earlier (p. 764), solvents can influence the mechanism that is preferred. As with nucleophilic substitution (p. 448), an increase in solvent polarity increases the possibility of an ionizing mechanism, in this case SeI, in comparison with the second-order mechanisms, which do not involve ions. As previously mentioned (p. 763), the solvent can also exert an influence between the Se2 (front or back) and SeI mechanisms in that the rates of Se2 mechanisms should be increased by an increase in solvent polarity, while Sni mechanisms are much less affected. 

In order to determine the efficiency of the polymers as reagents in nucleophilic catalysis, it was decided to study the rate of quaternization with benzyl chloride. Table I shows the second-order-rate constants for the benzylation reaction in ethanol. Comparison with DMAP indicates that poly(butadiene-co-pyrrolidinopyridine) is the most reactive of all the polymers examined and is even more reactive than the monomeric model. This enhanced reactivity is probably due to the enhanced hydrophobicity of the polymer chain in the vicinity of the reactive sites. 

CO3 species was formed and the X-ray structure solved. It is thought that the carbonate species forms on reaction with water, which was problematic in the selected strategy, as water was produced in the formation of the dialkyl carbonates. Other problems included compound solubility and the stability of the monoalkyl carbonate complex. Van Eldik and co-workers also carried out a detailed kinetic study of the hydration of carbon dioxide and the dehydration of bicarbonate both in the presence and absence of the zinc complex of 1,5,9-triazacyclododecane (12[ane]N3). The zinc hydroxo form is shown to catalyze the hydration reaction and only the aquo complex catalyzes the dehydration of bicarbonate. Kinetic data including second order rate constants were discussed in reference to other model systems and the enzyme carbonic anhy-drase.459 The zinc complex of the tetraamine 1,4,7,10-tetraazacyclododecane (cyclen) was also studied as a catalyst for these reactions in aqueous solution and comparison of activity suggests formation of a bidentate bicarbonate intermediate inhibits the catalytic activity. Van Eldik concludes that a unidentate bicarbonate intermediate is most likely to the active species in the enzyme carbonic anhydrase.460... 

The reaction scheme of Schwarz, with the specific rates, is shown in Table 7.1. Comparison with later compilations (Anbar et al., 1973, 1975 Farhataziz and Ross, 1977) indicates that most of these rates are reasonable within the bounds of experimental error. Some of the rates are pH-dependent, and when both reactants are charged there is a pronounced ionic strength effect these have been corrected for by Schwarz. He further notes that the second-order rates are not accurate for times less than 1 ns if the reaction radius... 

Analysis of the variation of the overall rate constant of reaction with [surfactant] was discussed in Section 3 (p. 222) and the treatment allows calculation of the second-order rate constants of reaction in the micellar pseudophase. These rate constants can be compared with second-order rate constants in water provided that both constants are expressed in the same dimensions and typically the units are M-1 s-1. Inevitably the comparison... 

For a number of reactions in functional micelles and comicelles second-order rate constants are similar in micelles and in water. Except for aromatic nucleophilic substitution they are slightly smaller in the micelles than in water, and the pattern of behavior is exactly that found for reactions of organic nucleophilic anions in non-functional micelles. Some examples of these comparisons are in Table 9. 

The basicity constants in water and micelles then have the same units (M 1), and values of K and Kb are not very different for arenimidazoles and nitroindoles under a variety of conditions (Table 10). The comparisons suggest that inherent basicities are not very different in water and cationic micelles, but, as with second-order rate constants of bimolecular reactions (Section 5), there is a limited degree of specificity because K /Kb is slightly larger for the nitroindoles than for the arenimidazoles, almost certainly because of interactions between the cationic micellar head groups and the indicator anions. 

Intramolecular general base catalysed reactions (Section II, Tables E-G) present less difficulty. A classification similar to that of Table I is used, but since the electrophilic centre of interest is always a proton substantial differences between different general bases are not expected. This section (unlike Section I, which contains exclusively unimolecular reactions) contains mostly bimolecular reactions (e.g. the hydrolysis of aspirin [4]). Where these are hydrolysis reactions, calculation of the EM still involves comparison of a first order with a second order rate constant, because the order with respect to solvent is not measurable. The intermolecular processes involved are in fact termolecular reactions (e.g. [5]), and in those cases where solvent is not involved directly in the reaction, as in the general base catalysed aminolysis of esters, the calculation of the EM requires the comparison of second and third order rate constants. 

For several of these ligands the reaction is first order in ethene and thus it was suggested that the insertion of ethene in the titanacyclopentane ring is the rate-determining step, as was also found for the triazacyclohexane catalyst [13], Turnover numbers of the titanium catalyst are very high, but since some of the chromium catalysts have a second order dependency in ethene a comparison cannot be made at higher pressure these chromium catalysts will be more effective [7,17],... 

The comparison has to be made between a first-order rate constant for the unimolecular process and a second-order rate constant for the corresponding intermolecular reaction (Sec. 6.1.1). One may arbitrarily decide on a 1 M concentration of reagent NHj, in which... 

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