Hammett plots/equations reactions

Reactions that occur with the development of an electron deficiency, such as aromatic electrophilic substitutions, are best correlated by substituent constants based on a more appropriate defining reaction than the ionization of benzoic acids. Brown and Okamoto adopted the rates of solvolysis of substituted phenyldimeth-ylcarbinyl chlorides (r-cumyl chlorides) in 90% aqueous acetone at 25°C to define electrophilic substituent constants symbolized o-. Their procedure was to establish a conventional Hammett plot of log (.k/k°) against (t for 16 /wcra-substituted r-cumyl chlorides, because meta substituents cannot undergo significant direct resonance interaction with the reaction site. The resulting p value of —4.54 was then used in a modified Hammett equation. 

Miller226 applied the Hammett equation to the rate constants for the reaction of 4-substituted l-chloro-2-nitrobenzenes with OMe in methanol at 50°C. a values (denoted ct in accordance with the practice briefly in vogue at that time, 1956) were used for + R substituents, and S02Me conformed well at a a value of 1.04952. Act value of 1.117 for S02Ph was derived from the Hammett plot, intermediate between the values based on phenol and anilinium ionizations by Szmant and Suld88 at about the same time. 

Waters61 have measured relative rates of p-toluenesulfonyl radical addition to substituted styrenes, deducing from the value of p + = — 0.50 in the Hammett plot that the sulfonyl radical has an electrophilic character (equation 21). Further indications that sulfonyl radicals are strongly electrophilic have been obtained by Takahara and coworkers62, who measured relative reactivities for the addition reactions of benzenesulfonyl radicals to various vinyl monomers and plotted rate constants versus Hammett s Alfrey-Price s e values these relative rates are spread over a wide range, for example, acrylonitrile (0.006), methyl methacrylate (0.08), styrene (1.00) and a-methylstyrene (3.21). The relative rates for the addition reaction of p-methylstyrene to styrene towards methane- and p-substituted benzenesulfonyl radicals are almost the same in accord with their type structure discussed earlier in this chapter. 

It is, however, important to resist the temptation to introduce new parameters into the Hammett equation merely to achieve a better fit with the experimental data. This is particularly true where, as in some cases, it may be difficult to ascribe real significance, in physical terms, to the new parameter anyway. It is in fact possible, as we shall see, to obtain much highly relevant information about reaction pathways using simple Hammett plots only. 

The processes depicted in Equation 5 all involve bond formation, while the reaction in Equation 6 requires cleavage of a carbon-manganese bond and, consequently, it is this step that is most likely to be rate limiting. Since the Hammett plots show that the reaction is accelerated by both electron donating and electron withdrawing substituents, it appears that the reaction can take place via tv/o different transition states, one electron rich and the other electron poor. 

A plot of the logarithm of a rate constant (or an equilibrium constant) for one series of reactions versus the logarithm of the rate constant (or the equilibrium constant) for a related series of reactions. (Recall that at constant temperature and pressure the logarithm of an equilibrium constant is proportional to AG°, and the logarithm of a rate constant is proportional to AG ). An example of a linear free energy relationship is provided by the Hammett crp-equation. With equilibrium constants, this relationship is given by the expression ... 

Haloform reaction, 237, 296 Halogenation alkanes, 300, 323 alkenes, 179,186, 313 benzene, 138,316 ketones, 295 Hammett equation, 362 additional parameters, 374, 388, 395 derivation of, 362 deviations from, 375 empirical nature of, 395 implications of, 394 reaction pathway, and, 375 solvent effects and, 388 spectroscopic correlations, 392 standard reaction for, 362, 395 steric effects and, 361, 383 thermodynamic implications of, 394 Hammett plots, 359 change in rate-limiting step and, 383 change in reaction pathway and, 378... 

The rate of reaction of disubstituted 1,1 diphenylethylenes with lithium, potassium and cesium polystyryl were found by Busson and van Beylen 272) to yield linear Hammett plots corresponding to q values of 1.8, 2.2 and 2.4 respectively, in benzene at 24 °C. The value of q for the reactions involving poly(styryl)lithium in cyclohexane was also 1.8. The active center concentration range studied was small. These authors interpreted their results on the basis of the equation ... 

Usually the most convenient way to use Hammett s equation is to plot log k/k0 or just log k of the reaction of interest on the vertical axis and o values for the substituents on the horizontal axis. The slope of the plot of log k vs. o may change as a result of changes in the mechanism and in response to the variable electron demand of each substituent. It is anticipated that the various substituents will exert the same kinds of effects on the rate constants as they do on the benzoic acid rate constants, but the greater separation between substitution site and reaction site in the same chemical family makes the reaction less sensitive to the substituent effects. Many different oxidation reactions have been treated using Hammett s equation. The consistent trend of linear relationship with all of the Hammett s constants holds for all chemical classes except halogenated phenols. 

When r) values are plotted against the g values, Hammett s equation is satisfied for all the substituents except for bromine and iodine, as shown in Figure 12.2. The p value is 4.8, which is within the range of p values reported for a variety of substituted reactions such as nitration, bromination, and hydrolysis (Stock and Brown, 1956). Therefore, Hammett s equation for substituted benzenes reaction with e can be expressed as ... 

A Hammett plot of the rate data according to equation 83, where kx is the absolute rate constant for reaction of the X-substituted phenol and k is that for reaction of the parent phenol (Figure 13), shows clear evidence for different addition mechanisms depending on whether the phenol is substituted with electron-donating or electron-withdrawing substituents. 

For the compounds obeying the Hammett equation, the distribution pattern for the OH attack can be estimated by assuming that the position on the ring with the maximum C7 value has the least probability, while the one with the minimum has the greatest probability. In our recent work > on cinnamate derivatives where the addition of the OH radical to the olefmic double bond is an additional pathway, a value of-0.3 was estimated from the Hammett plot (Fig. 5). This value is in agreement with those reported earlier for several substituted benzenes (p" = -0.52 to -0.4). However, the Hammett treatment for reactions with rate constants close to diffusion-controlled ones may not be satisfactory due to limited variation in kinetic data and large experimental uncertainty. In contrast, better correlation is expected in the corresponding gas phase reactions. 

For neutral nucleophiles, we have utilized a series of ring-substituted N,N-dimethylanilines. The second-order rate coefficients should now be independent of nucleophile concentration, and this was confirmed by showing that log (k/k0 obtained from the product ratios, was independent of the amine concentration for 0.008 to 0.08 M N,N-dimethyl-p-toluidine. The log (k/k0) values could also be conveniently determined for m-CH3-, H-, p-Br-, and m-Cl-substituted derivatives (equation 13). For the m-N02 derivative, even at 0.32 M, the dominant reaction is solvolysis and only an approximate value for log (k/k0) could be obtained. A Hammett plot against the tabulated a values (43) (omitting the approximate m-N02 data) led to a linear plot and a slope (p value) of —2.77 0.15 (r = —0.996). This value is similar to values for reaction with other ethyl derivatives, derived from kinetically determined k values —3.60 for reaction with ethyl iodide in nitrobenzene at... 

Prepare a second Hammett plot using the values of the apparent rate constant for the catalytic reaction. Use the Hammett relation to estimate the apparent rate constant for esterification of m-bromobenzoic acid over AIPO4 and compare this value with the experimental value of (7.6 0.6) X 10" [mol/(atm-g-s)]. Consider two ways to generate the equation of the line that best represents the data. 

Waltman et al. [325] found a linear correlation when the peak oxidation potentials, py, of 3-substituted thiophene monomers were plotted versus their Hammett substituent constants, o-" [324], as shown in Fig. 15. values, which are normally plotted versus cr", were not available in this case because these reactions were irreversible in nature. Regardless, the values should be similar to the values as determined for other families of polymers, such as substituted fluorenes [325]. Three parameters—polar, steric, and mesomeric effects—control the change in the Ep values [326]. The Hammett-Taft equation describes the behavior as... 

This potential diagram can explain the Hammett plots for both sides of the reaction equation examples are shown in Figure 12 for the addition reactions of p-X-Cf l4-S with the substituted phenylacetylenes (CH=C-Cf,H4-Y-/7) [11]. If the stabilities of P-X-C6H4-S are not much influenced by the substituent X, the slopes (p kJx) the Hammett plots in Figure 12(a) should be almost mirror images of the slopes p k.Jy) in Figure 12(b). However, the observed slopes indicate that p (fca)xl>lP ( a)Yl which implies contribution of the y term to the variations of k., and k, . 

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