Constant reaction

The term p is a reaction constant and is mathematically evaluated for a particular reaction by plotting log kjkQ against a. The slope of the straight lines is p, and reflects the sensitivity of the reaction under study to effects of substituents. The value of p is obviously affected by temperature, solvent changes, etc. 

Herein is the rate constant for a dienophile with substituent x ko is the corresponding rate constant for unsubstituted 2,4c Ox is the substituent constant for substituent x and p is the reaction constant, defined as the slope of the plot of log (k / ko) versus Ox. The parameter p is a measure of the sensitivity of the reactions towards introduction of substituents. Figure 2.3 and Table 2.4 show the results of correlating the kinetic data for the reaction of 2.4a-e with 2.5 with a. ... 

A plot against Hammett s cr-constants of the logarithms of the rate constants for the solvolysis of a series of Mz-substituted dimethylphenylcarbinyl chlorides, in which compounds direct resonance interaction with the substituent is not possible, yielded a reasonably straight line and gave a value for the reaction constant (p) of — 4 54. Using this value of the reaction constant, and with the data for the rates of solvolysis, a new set of substituent parameters (cr+) was defined. The procedure described above for the definition of cr+, was adopted for... 

The suitability of the model reaction chosen by Brown has been criticised. There are many side-chain reactions in which, during reaction, electron deficiencies arise at the site of reaction. The values of the substituent constants obtainable from these reactions would not agree with the values chosen for cr+. At worst, if the solvolysis of substituted benzyl chlorides in 50% aq. acetone had been chosen as the model reaction, crJ-Me would have been —0-82 instead of the adopted value of —0-28. It is difficult to see how the choice of reaction was defended, save by pointing out that the variation in the values of the substituent constants, derivable from different reactions, were not systematically related to the values of the reaction constants such a relationship would have been expected if the importance of the stabilization of the transition-state by direct resonance increased with increasing values of the reaction constant. 

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 selectivity of an electrophile, measured by the extent to which it discriminated either between benzene and toluene, or between the meta- and ara-positions in toluene, was considered to be related to its reactivity. Thus, powerful electrophiles, of which the species operating in Friedel-Crafts alkylation reactions were considered to be examples, would be less able to distinguish between compounds and positions than a weakly electrophilic reagent. The ultimate electrophilic species would be entirely insensitive to the differences between compounds and positions, and would bring about reaction in the statistical ratio of the various sites for substitution available to it. The idea has gained wide acceptance that the electrophiles operative in reactions which have low selectivity factors Sf) or reaction constants (p+), are intrinsically more reactive than the effective electrophiles in reactions which have higher values of these parameters. However, there are several aspects of this supposed relationship which merit discussion. 

Although the reaction rate of ethylene and various copolymers differs substantially, the reaction constants can be estabUshed by using an arbitrary value of 1 for ethylene (5). Thus, a value of 0.1 would indicate that the comonomer reacts at 10 times the rate of ethylene. However, the wide range of reaction rates can present problems not only in determining the comonomer content of the final product but also in producing a homogeneous product (4,6). 

The reaction constant k was related to a collision number Z, the number of reactant molecules colliding/unit time, and an activation energy E by the Anhenius equation... 

The numerical values of the terms a and p are defined by specifying the ionization of benzoic acids as the standard reaction to which the reaction constant p = 1 is assigned. The substituent constant, a, can then be determined for a series of substituent groups by measurement of the acid dissociation constant of the substituted benzoic acids. The a values so defined are used in the correlation of other reaction series, and the p values of the reactions are thus determined. The relationship between Eqs. (4.12) and (4.14) is evident when the Hammett equation is expressed in terms of fiee energy. For the standard reaction, o%K/Kq = ap. Thus,... 

Match the p values with the appropriate reactions. Explain your reasoning. Reaction constants -h2.45, -hO.75, —2.39, —7.29... 

The proportion factors related to the reaction constants, together with the geometrical factors of the reaction chamber, can be included in one coefficient G, gi ving... 

Table 7-2 lists 15 reactions whose rates are correlated by the Hammett equation. Besides the reaction constant p, the table gives a value for k° (from the fitted line), which provides all the information needed to estimate k for any member of the series, if the corresponding o is available, by means of Eq. (7-24). Note that kP in Table 7-2 is generally not identical to the experimental value of k for the ct = 0 member of the series, because this experimental point may deviate from the regression line. 

The chemical information available through LFER is primarily the reaction constant p. but this value depends upon the substituent constants selected for the construction of the LFER. The o values available are cr, cr, , a" or ct , and Oi ... 

The reaction constant p is a quantitative measure of the sensitivity of the reaction to the influence of substituents. Three factors combine to determine the value of p ... 

Equation (7-51), the Taft equation, provides good correlations for many aliphatic reactions. The scope of this relationship is illustrated by Table 7-10. The reaction constant p has been interpreted along the lines described for the Hammett p values. 

Some authors use O] instead of cr as the substituent constant in such correlations.) An example is provided by the aminolysis of phenyl esters in dioxane the substrates RCOOPh were reacted with -butylamine, and the observed first-order rate constants were related to amine concentration by = k2 [amine] kj [amine]. The rate constants kz and k could be correlated by means of Eq. (7-54), the reaction constants being p = +2.14, b = + 1.03 (for A 2) and p = -1-3.03,8 = -1-1.08 (for ks). Thus, the two reactions are about equally sensitive to steric effects, whereas the amine-catalyzed reaction is more susceptible to electronic effects than is the uncatalyzed reaction. 

Some authors plot log k or AG against 1/e rather than against the Kirkwood function. Since 1/e is nearly linearly related to (e — 1)/(2e + 1), within the assumptions of a theory in which the solvent is treated as a continuum this substitution of variable is not serious. Another approach is to interpret the solvent dependence of the Hammett reaction constant p on a dielectric constant function. ... 

Following the early work by one of the authors and by Sixma on the evaluation of substituent and reaction constants by molecular orbital theory, little more has been done along these hnes. Reaction constants have further been treated theoretically with at least moderate success, and a complete theoretical treatment of the Hammett equation awaits detailed testing. 

A completely different approach has been taken by Hine, who has considered that the substituent and reaction center are not really distinct, both being substituents in a benzene nucleus, and has then related substituent and reaction constants. Although of considerable theoretical interest, Hine s work has little bearing on practical applications of the Hammett equation since he starts from the premise of unique, single-valued substituent constants. This premise is invalid whether we are utilizing the naive approach with three separate, well-defined sets or the more refined methods with a continuous range of para values. 

The difference, ApK = pAgubst. pyridine pApyridine. where both values refer to work by the same authors determined under the same experimental conditions, is given here and is used to plot Fig. 1 and to calculate the reaction constant given in Table V to... 

Reaction Constants for the Reactivity of Substituted Pybidines and Pyridine 1-Oxides... 

Finally, two sets of physical properties have been correlated by the Hammett equation. Sharpe and Walker have shown that changes in dipole moment are approximately linearly correlated with ct-values, and Snyder has recently correlated the free energies of adsorption of a series of substituted pyridines with u-values. All the reaction constants for the series discussed are summarized in Table V. 

The alternate procedure, which has actually been applied, is to define separate reaction constants p, pp, and py), depending on the location of the side-chain relative to the heteroatom, and to make separate correlations. Here, the remaining uncertainty is that for 2-Y there are the two meta-type positions mentioned above. This is the approach which has been used successfully in the few reported correlations to be discussed below. 

A further complication arises out of the fact that of all the orientations discussed only one, 5-R-3-Y, does not involve a vicinal relationship between at least two of the three structural features—substituent, side-chain, and heteroatom. In the cases of 4-R- and 5-R-2-Y the problem of vicinal relations appears not too serious, since this relation is equivalent to the problem of the constant ortho substituent. For this situation it was shown that the constant ort u) substituent, i.e., in this case the heteroatom, may make a contribution to the substituent-independent term (logA °) but generally leaves the reaction constant (p) unaffected. Where the substituent, however, is alpha to the heteroatom it appears likely that its electronic structure, and hence its <7-values, may be substantially affected. This appears particularly likely for large substituents and especially for those which can form a hydrogen bond with the heteroatom, such as CO OH. 

In the manner outlined, a few attempts have been made to apply the Hammett equation to the transmission of substituent effects in the pyridine series. In the alkaline hydrolysis of 5-substituted ethyl picolinates (5-R-2-COOEt) in 85% ethanol at 25, 35, and 45°, the reaction constants are about 60% as large as those in the corresponding benzene series the overall fit to the Hammett equation, however, is at best fair, since out of four points (R = Et, H, I, Ac) one (Ac) deviates widely. 

Imoto and co-workers have also studied the pA values of substituted thiazolecarboxylic acids and the alkaline hydrolysis of their ethyl esters, each in three relative positions (2-B-4-Y, 2-B-5-Y, and 5-II-2-Y). In the case of the pA values, the p-values are far from constant, varying from 0.83 to 2,35, This variation is likely to be due to the intervention of tautomeric equilibria and of hydrogen bonds. The /3-ratios for the three sets of ester hydrolyses are roughly constant (0,61-0.73), and, assuming that the introduction of two heteroatoms leads to cumulative (multiplicative) effects on the transmission, this result is of the same order of magnitude as the product of the and values discussed above, i.e. 1.0 and 0.6, respectively. The lowest value for the pA (0,83) for the 2-R-5-COOH series is also of the same order of magnitude. All the available reaction constants are summarized in Table VI. 

Reaction constant for the transmission of electrical effects through atom X to Y. 

In all cases where a sufficiently large number of substituents has been tested, a linear free-energy correlation is found with Hammett s [Pg.305]

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