Changes in Rate Limiting Step

Evidence for a shift in the rate limiting step at low H2 partial pressure [508,652], at high temperatures [664], at low temperatures [663, 666] and far from equilibrium [652] has been reported. Transients in the rate during NH3 cracking suggest that the rate limiting step for NH3 decomposition is different on iron surfaces than on iron nitride surfaces [595, 665]. 

The synthesis of ammonia under transient [682, 683] or cyclic [684] operation has been studied. The rate of the catalytic reaction has been found to exhibit hysteresis during changes in the H2 NH3 ratio [665] and with changes in temperature [685]. The occurrence of hysteresis has been assigned to a recrystallisation of the surface [685]. 

Transients in the rate of ammonia synthesis have been observed when the flow is changed [418, 536, 686, 687], when the reaction mixture is changed from N2 + 3H2 to pure H2 or to pure N2 [536, 687, 688], and when the temperature is changed [686]. The behavior under transient operation has been taken as evidence for auto catalysis [686, 536, 689] or for the existence of parallel reaction pathways [682, 683]. By modelling the situation of a reactor under transient operation it has been concluded [690] that limited information can be derived from such experiments. 

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This approximation will in most cases provide a very significant simplification in particular for large reaction mechanisms. In the quasi-equilibrium approximation the transient behavior is eliminated. Further, the description of changes in rate-limiting step has been lost. 

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... 

A kinetic study9 of the mechanism of acid-catalysed chlorination of a range of substituted phenols by A-chlorobenzenesulfonamide has suggested a common mechanism for the compounds studied, with a change in rate-limiting step with the varying nature of the substituents. The formation of some novel addition products on bromination of some bicyclic aromatics has been reported.10 Bromination of 1-methoxynaphthalene... 

This observation is compatible with either a change in rate limiting step with temperature or with two competing mechanisms for retention of configuration (the inversion mechanism is always zero order in NMI). Both of these possibilities are expressed in Scheme 8. 

It is essential to demonstrate that both the measured forward and reverse rate constants refer to the same rate-limiting step and that there is no change in rate-limiting step in the extrapolated range. Consider the quasi-symmetrical reaction of phenolate ions with 4-nitrophenyl acetate (Equation 13). 

The Hammond postulate is often accepted as a general principle an increase in reactivity is accompanied by a decrease in selectivity because the transition structure becomes closer to that of the reactant state as the energy barrier decreases. This idea has some truth for a hypothetical A to B reaction model where it is implicit that only a single bond change occurs moreover the Hammond postulate is predicted by the Marcus theory (above). The postulate often breaks down for reactions where more than one major bond change results in product formation. It should be emphasised that any discussion of the reactivity-selectivity relationship has to be confined to those reactions where there is no change in rate-limiting step or mechanism. 

Figure 3 Hydrolysis of 2-methyl-4,6-dipheny I pyrylium salt over a pH-range exhibiting a change in rate-limiting step and mechanism. The line is calculated from k, = kfH OJKl + [H.ajkjk, + koHK7/ //3<97...

The substituent parameters for the condition k, = 2 be predicted for quasi-symmetrical reactions. The decomposition steps of a quasi-symmetrical intermediate to reactants (, ) and to products therefore obey identical linear free energy relationships. A change in rate-limiting step will occur when the intermediate is perfectly symmetrical (and k. In the addition-elimination mechanisms of Scheme 9 the ratio k Jk2 becomes unity when entering and leaving groups are identical. 

Figure 24 illustrates the three cases of non-linear free energy correlations for a change in rate-limiting step. The break-points occur at k x - k when... 

Figure 24 Three non-linear free energy correlations indicating changes in rate-limiting step...

Figure 26 Brensted plot for the hydroxide ion catalysed elimination reaction of N(2-cyanoethyl)pyridinium ions (Scheme 26). Line is theoretical for a change in rate limiting step...

The free energy relationship is diagnostic of a change in rate-limiting step (near pX = 2 and the simplest mechanism fitting these results is the Elcb mechanism of Scheme 26. 

Figure 11.6. Influence of temperature-induced changes in rate-limiting steps on observed S A/ain-Schaad exponents, / HD)obs nd observed H/D isotope effects. Sho A/n above each curve are variables a and (kj moh ) for the ratio of rate constants ka/k (defined in Fig. 11.4) expressed as The curves...

If a change in rate-limiting step occurs during variation of a substituent then a non-linear free-energy relationship will occur the separate limbs of the correlation will obey equations of the type (Eqn. 128)... 

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