Competition method

Occasionally it is as useful to obtain relative constants for a series of reactants acting on a common substrate, as it is to have actual rate values. Relative rate constants are obtained by competition methods, which avoid the kinetic approach entirely. The method is well illustrated by considering the second-order reactions of two Co(III) complexes Co and Cob (which might, for example, be Co(NH3)5CP and Co(NH3)5Br +), with a common reductant (Cr(II) (leading in this case to CrCU and CrBr + respectively)  

The reaction of pM concentrations of OH radicals (produced by pulse radiolysis) with substrates such as Co(en)3 produces very small absorbance changes. The reaction of OH with SCN on the other hand k = 6.6 x 10 M s at 25°C) yields the highly absorbing (SCN)f. Competition of Co(en)j with SCN for OH can be used to measure the relative rate constants and hence the value for OH with Co(en)3+ Ref. 354, 355. This approach is useful for the study of reactions of and Oj with pairs of reactants. 

All spectroscopic techniques involve production or deactivation of excited states, normally by the interaction between electromagnetic radiation and molecules. The excited states have finite lifetimes, determined by radiative and non-radiative relaxation to the ground state. Kinetic information can be obtained by comparison of the rates of these processes with those of chemical reactions in competition with them. We will consider two of these processes, involving nuclear spin and electronic excited states. However, the same ideas are applicable to other types of spectroscopic transition. 

From the Heisenberg uncertainty principle, a magnetic nucleus will always give an NMR absorption band with finite width, even if it is not involved in a chemical exchange reaction. The minimum bandwidth can be related to the spin-lattice relaxation time, Tj, since the mean lifetime of the excited spin state cannot exceed Ti, 

However, normally the bandwidth at half maximum can be related to the spin-spin relaxation time, T2, 

In the intermediate chemical exchange condition, the total relaxation frequency is given by the sum of the spin-spin relaxation, as above, together with the relaxation owing to chemical exchange, r, given by. 

knowing the value of Av,/j, which can be obtained by cooling the system such that the exchange becomes slower, and using the value of Av y obtained experimentally, we can obtain r. If the fractional occupation of the sites is 

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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. ... 

It may seem, at first sight, paradoxical that a competition reaction carried out under conditions in which the measured rate is independent of the concentration of the aromatic can tell us about the relative reactivities of two aromatics. Obviously, the measured rate has nothing to do with the rate of the product-determining step, and what is important in determining relative reactivities is the ratio of the values of ( 3.2.4) for two compounds. The criteria to be met for a correct application of the competitive method are well understood. ... 

Quantitative eomparisons of aromatic reactivities were made by using the competitive method with solutions of nitronium tetrafluoroborate in sulpholan, and a concentration of aromatic compounds 10 times that of the salt. To achieve this condition considerable proportions of the aromatic compoimds were added to the medium, thus depriving the sulpholan of its role as true solvent thus, in the nitration of the alkyl- and halogeno-benzenes, the description of the experimental method shows that about 50-60 cm of mixed aromatic compounds were dissolved in a total of 130 cm of sulpholan. 

As a means of determining relative reactivities, the competition method using nitronium tetrafluoroborate in sulpholan has been criticised as giving results which arise from incomplete mixing of the reagents before reaction is complete. The difficulty of using the competition method when the rate of reaction is similar to, or greater than,... 

The most notable studies are those of Ingold, on the orienting and activating properties of substituents in the benzene nucleus, and of Dewar on the reactivities of an extensive series of polynuclear aromatic and related compounds ( 5.3.2). The former work was seminal in the foundation of the qualitative electronic theory of the relationship between structure and reactivity, and the latter is the most celebrated example of the more quantitative approaches to the same relationship ( 7.2.3). Both of the series of investigations employed the competitive method, and were not concerned with the kinetics of reaction. 

Characteristics of the system as nitrating reagents Wibaut, who introduced the competitive method for determining reactivities (his experiments with toluene, benzene and chlorobenzene were performed under heterogeneous conditions and were not successful), pointed out that solutions of nitric acid in acetic anhydride are useful in making comparisons of reactivities because aromatic compounds are soluble in them. ... 

Ingold and his co-workers used the competitive method in their experiments, in which nitration was brought about in acetic anhydride. Typically, the reaction solutions in these experiments contained o-8-I 4 mol of nitric acid, and the reaction time, depending on the reactivities of the compounds and the temperature, was 0-5-10 h. Results were obtained for the reactivities of toluene, > ethyl benzoate, the halogenobenzenes, ethyl phenyl acetate and benzyl chloride. Some of these and some later results are summarized in table 5.2. Results for the halogenobenzenes and nitrobiphenyls are discussed later ( 9.1.4, lo.i), and those for a series of benzylic compounds in 5,3.4. 

Dewar and his co-workers, as mentioned above, investigated the reactivities of a number of polycyclic aromatic compounds because such compounds could provide data especially suitable for comparison with theoretical predictions ( 7.2.3). This work was extended to include some compounds related to biphenyl. The results were obtained by successively compounding pairs of results from competitive nitrations to obtain a scale of reactivities relative to that of benzene. Because the compounds studied were very reactive, the concentrations of nitric acid used were relatively small, being o-i8 mol 1 in the comparison of benzene with naphthalene, 5 x io mol 1 when naphthalene and anthanthrene were compared, and 3 x io mol 1 in the experiments with diphenylamine and carbazole. The observed partial rate factors are collected in table 5.3. Use of the competitive method in these experiments makes them of little value as sources of information about the mechanisms of the substitutions which occurred this shortcoming is important because in the experiments fuming nitric acid was used, rather than nitric acid free of nitrous acid, and with the most reactive compounds this leads to a... 

Davies and Warren have investigated the nitration of naphthalene, ace-naphthene and eight dimethylnaphthalenes in acetic anhydride at o °C. Rates relative to naphthalene were determined by the competition method, and the nitro-isomers formed were separated by chromatographic and identified by spectrophotometric means. The results, which are summarised in the table, were discussed in terms of various steric effects, and the applicability of the additivity rule was examined. For the latter purpose use was made of the data of Alcorn and Wells (table 10.2) relating to the nitration of monomethyl-naphthalenes at 25 °C. The additivity rule was found to have only limited utility, and it was suggested that the discrepancies might be due in part to the... 

The overall reactivity of the 4- and 5-positions compared to benzene has been determined by competitive methods, and the results agreed with kinetic constants established by nitration of the same thiazoles in sulfuric acid at very low concentrations (242). In fact, nitration of alkylthiazoles in a mixture of nitric and sulfuric acid at 100°C for 4 hr gives nitro compounds in preparative yield, though some alkylthiazoles are oxidized. Results of competitive nitrations are summarized in Table III-43 (241, 243). For 2-alkylthiazoles, reactivities were too low to be measured accurately. 

Absolute rate data for Friedel-Crafts reactions are difficult to obtain. The reaction is complicated by sensitivity to moisture and heterogeneity. For this reason, most of the structure-reactivity trends have been developed using competitive methods, rather than by direct measurements. Relative rates are established by allowing the electrophile to compete for an excess of the two reagents. The product ratio establishes the relative reactivity. These studies reveal low substrate and position selectivity. 

Structure-reactivity relationships can be probed by measurements of rates and equiUbria, as was diseussed in Chapter 4. Direct comparison of reaction rates is used relatively less often in the study of radical reactions than for heterolytic reactions. Instead, competition methods have frequently been used. The basis of competition methods lies in the rate expression for a reaction, and the results can be just as valid a comparison of relative reactivity as directly measured rates, provided the two competing processes are of the same kinetic order. Suppose that it is desired to compare the reactivity of two related compounds, B—X and B—Y, in a hypothetical sequence ... 

The study of relative rates by the competitive method can be useful. The principle was discussed in Section 3.1 in the context of parallel reactions, for which the ratio of the product concentrations is equal to the ratio of rate constants (provided the concentrations are under kinetic control). 

This is a steady-state competitive method, applicable when a solute is capable of fluorescing. We consider the simplest case. The solute A undergoes excitation to the excited singlet state A upon absorption of radiation of frequency... 

This is sometimes described as a competitive method, the coupling species O being involved in two separate reactions. 

The competitive method employed for determining relative rates of substitution in homolytic phenylation cannot be applied for methylation because of the high reactivity of the primary reaction products toward free methyl radicals. Szwarc and his co-workers, however, developed a technique for measuring the relative rates of addition of methyl radicals to aromatic and heteroaromatic systems. - In the decomposition of acetyl peroxide in isooctane the most important reaction is the formation of methane by the abstraction of hydrogen atoms from the solvent by methyl radicals. When an aromatic compound is added to this system it competes with the solvent for methyl radicals, Eqs, (28) and (29). Reaction (28) results in a decrease in the amount... 

The relative reactivities obtained by the method of competitive reactions corresponded to the values of the separately obtained rate and adsorption constants. The reactivities obtained by the competitive method differ, of course, from the ratio of the rates of the separately studied single reactions this difference increases with the difference in the values of the adsorption coefficients of competing substances. 

Olivier and Berger335, who measured the first-order rate coefficients for the aluminium chloride-catalysed reaction of 4-nitroben2yl chloride with excess aromatic (solvent) at 30 °C and obtained the rate coefficients (lO5/ ) PhCI, 1.40 PhH, 7.50 PhMe, 17.5. These results demonstrated the electrophilic nature of the reaction and also the unselective nature of the electrophile which has been confirmed many times since. That the electrophile in these reactions is not the simple and intuitively expected free carbonium ion was indicated by the observation by Calloway that the reactivity of alkyl halides was in the order RF > RC1 > RBr > RI, which is the reverse of that for acylation by acyl halides336. The low selectivity (and high steric hindrance) of the reaction was further demonstrated by Condon337 who measured the relative rates at 40 °C, by the competition method, of isopropylation of toluene and isopropylbenzene with propene catalyzed by boron trifluoride etherate (or aluminium chloride) these were as follows PhMe, 2.09 (1.10) PhEt, 1.73 (1.81) Ph-iPr, (1.69) Ph-tBu, 1.23 (1.40). The isomer distribution in the reactions337,338 yielded partial rate factors of 2.37 /mMe, 1.80 /pMe, 4.72 /, 0.35 / , 2.2 / Pr, 2.55337 339. 

Gallium bromide was used as the catalyst in a determination346 of the partial rate factors, by the competition method, for ethylation of some substituted benzenes in 1,2-dichloroethane at 25 °C. No direct rate measurements were made and the results, summarised in Table 80, show the low selectivity and high steric hindrance in the reaction. 

Since there is inherent in reactions which give low selectivities, the possibility that non-competitive conditions are responsible, Olah and Overchuck359 have measured directly the rates of benzylation, isopropylation, and fer/.-butylation of benzene and toluene with aluminium and stannic chlorides in nitromethane at 25 °C. Apparent second-order rate coefficients were obtained (assuming that the concentration of catalyst remains constant), but it must be admitted that the kinetic plots showed considerable departure from second-order behaviour. The observed rate coefficients and kreh values determined by the competition method are given in Table 88, which seems to clearly indicate that the competitive ex-... 

The greater steric hindrance to acetylation was also shown by a comparison of the rate of (103At2) of acetylation of toluene (0.763), ethylbenzene (0.660), i-propylbenzene (0.606) and f-butylbenzene (0.462) with those (determined by the competition method) for benzoylation both sets of data (Table 112) were obtained with dichloroethane as solvent at 25 °C, all reagent concentrations being 0.1 A/421. Relative rates of acylation other aromatics under the same conditions have also been obtained and are given in Table 113422. The different steric requirements for acetylation and benzoylation are further shown by the following respective relative rates for acylation of naphthalene derivatives in chloroform at 0 °C naphthalene (1 position) 1.00,1.00, (2 position) 0.31,0.04 2,3-dimethylnaphthalene (1 position) 1.59, 172, (5 position) 7.14, 38.2, (6 position) 3.68, 7.7422a. 

These and other competition methods can provide only the ratios of rate constants, not absolute values. Provided each ratio is referred to a common standard, the set of values defines the reactivity pattern of the given species. Of course, if it becomes feasible to measure any one of the rate constants, then the entire set can be placed on an absolute scale. 

The pKa value of the equilibrium was found to be equal to 10.2. Meissner and coworkers36 studied also the reaction of OH radicals with DMSO, however, the product of this reaction has no optical absorption in the range 270-800 nm and they measured only the rate of this reaction by a competition method and obtained k = 4.2 x 109m-1s-1. 

As a result of the conclusions reached in these studies, a simple competition method was devised 12, 32) to determine relative rates of hydride transfer reactions rather accurately. For example, to obtain relative reaction rates of ethyl ions with various additives, a suitable source of fully deuterated ethyl ions such as C3D8 or iso-C4Di0 was irradiated in the presence of a perprotonated additive (RH), leading to the formation of C2D6 and C2D5H by Reactions 2 and 3. 

For a detailed discussion the reader is referred to a number of recent monographs [9,10,23] and review articles [50,226-231]. The role of electrochemistry in waste water and effluent treatment is still queried, as remarked by Pletcher and Walsh [10]. One answer would be, relatively small since there are many competitive methods which are cheaper on a large scale and use less energy. Principle types of processes used in local-authority sewage works are listed in Table 14. 

Since the bond to the isotopic atom is not formed or broken in the transition state of the rate-determining step of the reaction, the difference between the rate constant for the reaction of the undeuterated and deuterated substrates is usually small. As a result, secondary deuterium KIEs are usually close to unity, i.e. the maximum secondary deuterium KIE is 1.25 per deuterium (Shiner, 1970a) and most of these KIEs are less than 1.10 (Westaway, 1987a). Therefore, careful kinetic measurements with an error of approximately 1 % in each rate constant or specially designed competitive methods are required to determine them with an acceptable degree of accuracy. 

Secondary isotope effects are small. In fact, most of the secondary deuterium KIEs that have been reported are less than 20% and many of them are only a few per cent. In spite of the small size, the same techniques that are used for other kinetic measurements are usually satisfactory for measuring these KIEs. Both competitive methods where both isotopic compounds are present in the same reaction mixture (Westaway and Ali, 1979) and absolute rate measurements, i.e. the separate determination of the rate constant for the single isotopic species (Fang and Westaway, 1991), are employed (Parkin, 1991). Most competitive methods (Melander and Saunders, 1980e) utilize isotope ratio measurements based on mass spectrometry (Shine et al., 1984) or radioactivity measurements by liquid scintillation (Ando et al., 1984 Axelsson et al., 1991). However, some special methods, which are particularly useful for the accurate determination of secondary KIEs, have been developed. These newer methods, which are based on polarimetry, nmr spectroscopy, chromatographic isotopic separation and liquid scintillation, respectively, are described in this section. The accurate measurement of small heavy-atom KIEs is discussed in a recent review by Paneth (1992). 

The rate constants for reaction of Bu3SnH with the primary a-alkoxy radical 24 and the secondary ce-alkoxy radical 29 are in reasonably good agreement. However, one would not expect the primary radical to react less rapidly than the secondary radical. The kinetic ESR method used to calibrate 24 involved a competition method wherein the cyclization reactions competed with diffusion-controlled radical termination reactions, and diffusional rate constants were determined to obtain the absolute rate constants for the clock reactions.88 The LFP calibrations of radical clocks... 

Conceptually, the simplest way to measure a kinetic isotope effect (KIE) is to use a non-competitive method, in which two separate kinetic runs are carried out, each starting with a different isotopomer of the reactant. The rate constants for both species are determined and the kinetic isotope effect (KIE) is the ratio of the two rate constants. This procedure is frequently referred to as the direct method . 

This non-competitive method has several practical limitations. Since the ordinary precision of determination of rate constants, (8kL/kL) or (Ske/kn), is on the order of a few percent, the method is limited as a practical matter to large, primary kinetic isotope effects, generally of hydrogen. This, because deuterium, the common heavy isotopomer for hydrogen, is available at 100% abundance at reasonable cost, and for hydrogen KIE s are usually large enough to constrain the relative error, 8(kL/kH)/(kL/kH), to acceptable values. 

One disadvantage of the non-competitive method is the necessity to synthesize samples of isotopically pure (or at least highly enriched) reactants, and this can be tedious and expensive. Since light and heavy isotopomers are very often obtained using different synthetic pathways (in order to optimize isotopic yield), they may carry different impurities or different concentrations of the same impurity. Therefore it is necessary to meticulously purify both samples before running experiments. In this... 

While competitive methods to determine KIE s are free from errors due to differences in reaction conditions (impurities, temperature, pH, etc.) they do require access to equipment that allows high precision measurements of isotope ratios. The selection of an appropriate analytical technique depends on the type of the isotope and its location in the molecule. For studies with stable isotopes the most commonly used technique (and usually the most appropriate) is isotope ratio mass spectrometry (IRMS). 

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