Rate factors, partial

Partial rate factors (PRFs) are a quantitative way of describing directing effects in electrophilic aromatic substitution. If we take the data from Table 12.3, together with the fact that nitration of toluene proceeds 24 times faster than nitration of benzene, we can obtain an estimate of the relative reactivity of a specific site on toluene relative to a single site on benzene. Benzene has six identical protons that can be replaced, whereas toluene has two ortho-, two meta-, and one para-position. 

The value 0.58 comes from the fraction of the product that is substituted at the ortho-position, 24 from the relative rates of reaction of toluene and benzene, and 6/2 from the number of sites on benzene for substitution relative to the number of ortho positions on toluene. Similarly, 

The fact that the value for the mete-position is 1 reflects the overall increase in electron density in the aromatic ring although the intermediate for substitution at that position is not specifically stabilized, the more electron-rich ring in toluene is more nucleophilic than benzene. The greater PRF at the para-position is probably steric in origin. 

Notice that these values bear out our conclusions about the directing effect of the nitro group from studying the electronic effects in the resonance forms of the Wheland intermediates for the substitution. The mete-position is not favored it is simply the least disfavored option. This means that poiynitration of aromatics is iikeiy to be difficult your lab assignment 

FIGURE 12.40 Partial rate factors for raitration of nitrotoluerae. 

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TABLE 4.2 Nitration of aromatic compounds isomer proportions and partial rate factors ... 

Substituents in pyridinium salt Relative rates Isomer proportions (partial rate factors) i 0 p-ratio... 

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... 

Compound Position of substitution Partial rate factor Ref. 

TABLE 7.1 Partial rate factors for some electrophilic substitutions of toluene... 

Relative electrophilic localization energies vs. logarithms of partial rate factors for nitration (a) Hiickel, (6) PPP with fixed /3. (From Dewar Thompson. ) (iv) Plot of log K vs. AB c. (From Dewar. )... 

The applicability of the two-parameter equation and the constants devised by Brown to electrophilic aromatic substitutions was tested by plotting values of the partial rate factors for a reaction against the appropriate substituent constants. It was maintained that such comparisons yielded satisfactory linear correlations for the results of many electrophilic substitutions, the slopes of the correlations giving the values of the reaction constants. If the existence of linear free energy relationships in electrophilic aromatic substitutions were not in dispute, the above procedure would suffice, and the precision of the correlation would measure the usefulness of the p+cr+ equation. However, a point at issue was whether the effect of a substituent could be represented by a constant, or whether its nature depended on the specific reaction. To investigate the effect of a particular substituent in different reactions, the values for the various reactions of the logarithms of the partial rate factors for the substituent were plotted against the p+ values of the reactions. This procedure should show more readily whether the effect of a substituent depends on the reaction, in which case deviations from a hnear relationship would occur. It was concluded that any variation in substituent effects was random, and not a function of electron demand by the electrophile. ... 

The above proportionality can be expressed by the following equation, in which/p Me and/ j jyjg are the partial rate factors for substitution at p- and we-positions respectively. ... 

Although the partial rate factors for the alkylbenzenes vary somewhat with the experimental conditions, the main facts of the situation are perfectly clear ... 

Ratio toluene- /-f-butylbenzene. The partial rate factors are based on the relative rates for toluene benzene of ref. i. 

As has been noted above, there is no gross change in the mechanism of nitration of PhNH3+ down to 82 % sulphuric acid. The increase in o- andp-substitution at lower acidities has been attributed differential salt effects upon nitration at the individual positions. The two sets of partial rate factors quoted for PhNH3+ in table 9.3 show the effect of the substituent on the Gibbs function of activation at the m- and -positions to be roughly equal for reaction in 98 % sulphuric acid, and about 28 % greater at the -position in 82 % sulphuric acid. ... 

The isomer proportions for the nitration of the chlorotoluenes, to be expected from the additivity principle, have been calculated from the partial rate factors for the nitration of toluene and chlorobenzene and compared with experimental results for nitration with nitric acid at o °C. The calculated values are indicated in brackets beside the experimental values on the following structural formulae. In general, it can be... 

Here, and with the chlorotoluenes, the precise values for the calculated figures depend on the values adopted for the partial rate factors in the mono-substituted compounds. These and the relative rates do depend slightly on conditions. As has been pointed out several times previously, comparisons with benzene for nitration in sulphuric acid have to be made with care. 

Using the partial rate factors for nitration of chlorobenzene, Ridd and de la Mare calculated the relative rates of nitration of the dichlorobenzenes, with respect to /)-dichlorobenzene, with the results shown below. Also given are results based on more recent nitrations in mixed... 

Compound Relative ratef Partial rate factors ... 

Any attempt to calculate partial rate factors for the i-oxides being The encounter rate criterion ( 8.2.3) is ambiguous for these compounds. 

Despite the considerable amount of work which has been reported, our knowledge of the nitration of biphenyl is not in a satisfactory state. The 0 p-T3.tw varies considerably with the conditions of nitration, and the cause of the variation is not fully understood. Nitrations with solutions prepared from nitric acid and acetic anhydride have generally given o -ratios greater than unity, the most consistent value being 2-2, obtained at o °C. The corresponding partial rate factors are reported later. 

The nitration of nitro- and dinitro-biphenyls has been examined by several workers. i - As would be expected, nitration of the nitro-biphenyls occurs in the phenyl ring. Like a phenyl group, a nitrophenyl group is 0 -directing, but like certain substituents of the type CH CHA ( 9.1.6) it is, except in the case of w-nitrophenyl, deactivating. Partial rate factors for the nitration at o °C of biphenyl and the nitro-biphenyls with solutions prepared from nitric acid and acetic anhydride are given below. The high o p-v2X o found for nitration of biphenyl... 

Partial rate factors are from ref. 2 and (in parentheses) ref. 4. o />-Ratios are from ref. 2 and relative rates are calculated from the partial rate factors. For biphenyl Dewar et give partial rate factors= 305/4 = 18. Recalculation of their results gives... 

These partial rate factors have been recalculated from the experimental data of Dewar and Urch. Their reported values for diphenylmethane are not seriously discrepant with the values now given, but this is not so for the values for fluorene. As given, and copied in the literature, the values were /j = 2040 / = 60 fi = 944. There are consequent errors in table 8 and figs. 16 (reproduced as fig. 9. i of this volume) and 32 of ref. 22. 

The significance of Dewar s results for a series of polynuclear hydrocarbons, as well as for various compounds containing hetero atoms, has been discussed ( 5.3.2). Though the differences are not often important, we have not in all cases been able to reproduce the values for the partial rate factors reported by these authors, by recalculation from their reported results in table 5.3 the figures in parentheses are some examples of our recalculations. 

The nitration of phenylpyridines and related compounds has attracted attention for a long time, and measurements of isomer proportions have been made for several compounds of this type. Nitration occurs in the phenyl ring. For 2-phenylpyridine and 2-phenylpyridine i-oxide measurements of the dependence of rate of nitration upon acidity in 75-81 % sulphuric acid at 25 °C show that both compounds are nitrated as their cations (table 8.1). The isomer distribution did not depend significantly upon the acidity, and by comparison with the kinetic data for quinolinium ( 10.4.2) the partial rate factors illustrated below were obtained.They should be compared with those for the nitration of 2-nitrobiphenyl ( 10.1). The protonated heterocyclic groups are much... 

The first quantitative studies of the nitration of quinoline, isoquinoline, and cinnoline were made by Dewar and Maitlis, who measured isomer proportions and also, by competition, the relative rates of nitration of quinoline and isoquinoline (1 24-5). Subsequently, extensive kinetic studies were reported for all three of these heterocycles and their methyl quaternary derivatives (table 10.3). The usual criteria established that over the range 77-99 % sulphuric acid at 25 °C quinoline reacts as its cation (i), and the same is true for isoquinoline in 71-84% sulphuric acid at 25 °C and 67-73 % sulphuric acid at 80 °C ( 8.2 tables 8.1, 8.3). Cinnoline reacts as the 2-cinnolinium cation (nia) in 76-83% sulphuric acid at 80 °C (see table 8.1). All of these cations are strongly deactivated. Approximate partial rate factors of /j = 9-ox io and /g = i-o X io have been estimated for isoquinolinium. The unproto-nated nitrogen atom of the 2-cinnolinium (ina) and 2-methylcinno-linium (iiiA) cations causes them to react 287 and 200 more slowly than the related 2-isoquinolinium (iia) and 2-methylisoquinolinium (iii)... 

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