Kinetic orders

A large number of observations on the decay of enzyme activity after prevention of enzyme synthesis suggests simple first-order kinet- 

Although experiments showing enzyme degradation to be a first-order process are based on data from many different enzymes measured under a variety of conditions, it is not entirely clear why first-order kinetics are found. Thus, if an enzyme acts as a high-affinity substrate for a degrading system responsible for breakdown of the enzyme, a low 

The pattern of activity loss shown in Fig. Id is really a special case of the previous example. Here an enzyme is fully active for a period and is then rapidly degraded. These lifetime kinetics will be foimd in all cases where the intracellular enzyme is stable while the cell itself has a fixed life. The best example of this type of kinetic behavior occurs with erythrocytes—cells which have a definite life in the blood. In erythrocytes, all enzymes are required to be stable because the cell does not have the capacity to replenish them. 

---

Nitration in aqueous solutions of nitric acid Added water retards nitration in concentrated nitric acid without disturbing the kinetic order of the reaction. The rate of nitration of nitrobenzene was depressed sixfold by the addition of 5 % of water, (c. 3 2 mol 1 ), but because of the complexity of the equilibria involving water, which exist in these media, no simple relationship could be found between the concentration of water and its effect on the rate. 

A simple kinetic order for the nitration of aromatic compounds was first established by Martinsen for nitration in sulphuric acid (Martin-sen also first observed the occurrence of a maximum in the rate of nitration, occurrii for nitration in sulphuric acid of 89-90 % concentration). The rate of nitration of nitrobenzene was found to obey a second-order rate law, first order in the concentration of the aromatic and of nitric acid. The same law certainly holds (and in many cases was explicitly demonstrated) for the compounds listed in table 2.3. 

More typically its reactions showed an intermediacy of kinetic order like that observed with fluorobenzene or iodobenzene in nitromethane. 

The anticatalytic effect of nitrous acid in nitration The effect of nitrous acid was first observed for zeroth-order nitrations in nitromethane ( 3.2). The effect was a true negative catalysis the kinetic order was not affected, and nitrous acid was neither consumed nor produced by the nitration. The same was true for nitration in acetic acid. In the zeroth-order nitrations the rate depended on the reciprocal of the square root of the concentration of nitrous acid =... 

The effect of nitrous acid on the nitration of mesitylene in acetic acid was also investigated. In solutions containing 5-7 mol 1 of nitric acid and < c. 0-014 mol of nitrous acid, the rate was independent of the concentration of the aromatic. As the concentration of nitrous acid was increased, the catalysed reaction intervened, and superimposed a first-order reaction on the zeroth-order one. The catalysed reaction could not be made sufficiently dominant to impose a truly first-order rate. Because the kinetic order was intermediate the importance of the catalysed reaction was gauged by following initial rates, and it was shown that in a solution containing 5-7 mol 1 of nitric acid and 0-5 mol 1 of nitrous acid, the catalysed reaction was initially twice as important as the general nitronium ion mechanism. 

Table 2. Association Numbers and Fractional Kinetic Orders for Alkyllithium Initiators...

The kinetics of initiation reactions of alkyllithium compounds often exhibit fractional kinetic order dependence on the total concentration of initiator as shown in Table 2. For example, the kinetics of the initiation reaction of //-butyUithium with styrene monomer in benzene exhibit a first-order dependence on styrene concentration and a one-sixth order dependence on //-butyUithium concentration as shown in equation 13, where is the rate constant for... 

The kinetics of this process is strongly affected by an association phenomenon. It has been known that the active center is the silanolate ion pair, which is in equUibrium with dormant ion pair complexes (99,100). The polymerization of cyclosiloxanes in the presence of potassium silanolate shows the kinetic order 0.5 with respect to the initiator, which suggests the principal role of dimer complexes (101). 

The goal of a kinetic study is to establish the quantitative relationship between the concentration of reactants and catalysts and the rate of the reaction. Typically, such a study involves rate measurements at enough different concentrations of each reactant so that the kinetic order with respect to each reactant can be assessed. A complete investigation allows the reaction to be described by a rate law, which is an algebraic expression containing one or more rate constants as well as the concentrations of all reactants that are involved in the rate-determining step and steps prior to the rate-determining step. Each concentration has an exponent, which is the order of the reaction with respect to that component. The overall kinetic order of the reaction is the sum of all the exponents in the... 

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 nucleation rate is plotted versus the supersaturation for different stirrer speeds in a log-log diagram (Figure 6.21). The kinetic order n in the correlating equation... 

The kinetic order of the copolymerization reaction with respect to the initiator is equal to 0,5, and the total activation energy amounts to 14,4 kcal/mol (60,3 kJ/mol). 

Table I. Kinetic orders of various non-catalyzed polyesterifications of adipic acid with aliphatic primary diols. The first figure in the 3rd column is the overall order and figures in brackets denote orders with respect to acid and alcohol. 2 + 3 means that kinetics has been treated as resulting from the superposition of two reactions with orders 2 and 3, respectively. The range of conversion which has been studied is given in the 2nd column for instance, 80-100 means that kinetics has been studied between 80 and 100% conversion...

Acetoxylation is found to accompany nitration of fairly reactive aromatics by nitric acid in acetic anhydride and gives rise to zeroth-order kinetics76. The electrophile is believed to be protonated acetyl nitrate the formation of which is rate-determining, hence the kinetic order (see p. 37). Acetoxylation can also accompany halogenation by positive halogenating agents in acetic acid solvent, especially in the presence of sodium acetate137, but no kinetic studies have been carried out. 

Kinetic studies using acidified hypochlorous acid are rather more complicated than these with hypobromous acid. Much higher concentrations of mineral acid are necessary so that the activities of the reacting entities do not correspond closely to their molecular concentrations, and the kinetic order of reaction varies according to the acid concentration and the reactivity of the aromatic. 

With 77 % aqueous acetic acid, the rates were found to be more affected by added perchloric acid than by sodium perchlorate (but only at higher concentrations than those used by Stanley and Shorter207, which accounts for the failure of these workers to observe acid catalysis, but their observation of kinetic orders in hypochlorous acid of less than one remains unaccounted for). The difference in the effect of the added electrolyte increased with concentration, and the rates of the acid-catalysed reaction reached a maximum in ca. 50 % aqueous acetic acid, passed through a minimum at ca. 90 % aqueous acetic acid and rose very rapidly thereafter. The faster chlorination in 50% acid than in water was, therefore, considered consistent with chlorination by AcOHCl+, which is subject to an increasing solvent effect in the direction of less aqueous media (hence the minimum in 90 % acid), and a third factor operates, viz. that in pure acetic acid the bulk source of chlorine ischlorineacetate rather than HOC1 and causes the rapid rise in rate towards the anhydrous medium. The relative rates of the acid-catalysed (acidity > 0.49 M) chlorination of some aromatics in 76 % aqueous acetic acid at 25 °C were found to be toluene, 69 benzene, 1 chlorobenzene, 0.097 benzoic acid, 0.004. Some of these kinetic observations were confirmed in a study of the chlorination of diphenylmethane in the presence of 0.030 M perchloric acid, second-order rate coefficients were obtained at 25 °C as follows209 0.161 (98 vol. % aqueous acetic acid) ca. 0.078 (75 vol. % acid), and, in the latter solvent in the presence of 0.50 M perchloric acid, diphenylmethane was approximately 30 times more reactive than benzene. 

RELATIVE RATES (AND KINETIC ORDERS) FOR BROMINATION IN HOAC-CHCI3 (OR... 

It then follows that at low bromine concentrations this latter process is less likely, consequently the kinetic order is reduced. More ionic media will facilitate equilibrium (137) without the need for intervention of equilibrium (139) and vice versa, so that the observed variation in the kinetic order with this condition then follows. The absence of high kinetic orders in molecular chlorination also becomes rationalised since the C1J ion is not as stable as BrJ. 

Berliner et a/.284-8 have examined kinetics of bromination in aqueous acetic acid in an attempt to find the acid concentration at which the change in kinetic order principally occurs, though it follows from the earlier work that this will depend upon the aromatic reactivity. In 50 % acid the bromination of naphthalene was second-order overall284, and at constant ionic strength the rate coefficient showed a dependence on [Br-] according to equation (140)... 

---