Reversible unimolecular first-order reactions

This could be considered as a particular case of Equation 4.1 above when A = C, and we re-label k2 as k as in Equation 4.4  

Equation 4.5 shows that, for this kind of reversible reaction, a plot of ln([A]f - [A]eq) against time is linear with the gradient — (k + k- ), i.e. the reaction approaches equilibrium as a typical first-order reaction with an observed constant k0bs = k + k.  

A particular case of this kinetic system is the racemisation of an enantiomeric compound, i.e. Equation 4.4 where A and B are enantiomers, and k = k 1( the rate constant for enan-tiomerisation. The rate constant for the approach to equilibrium, measurable by polarimetry, is the rate constant for racemisation, which is twice the rate constant for enantiomerisation, kmc = 2h [11]. 

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The thermal cis-trans isomerization of crotonitrile has been studied in the gas phase at pressures from 0.2 to 20 torr and temperatures from 300° to 560° C . The isomerization is a homogeneous unimolecular reversible first order reaction, the rate coefficient for the direction cis trans being given by exp((-51.3 3.7)//i7 ) sec. Calculated thermodynamic parameters are = 0.17 + 0.12 kcal.mole and AS = —0.39+0.19 eu. The only side reaction with an appreciable rate was a surface polymerization. 

Elementary uni- and bimolecular reactions will necessarily show first- and second-order kinetic behaviour, but the reverse is not necessarily true a first-order reaction may not be unimolecular and a second-order reaction may not be bimolecular. For example, we considered the decomposition of dibenzylmercury in Chapter 1, in which the mechanism could either be elementary, giving a mercury atom and a 1,2-diphenylethane molecule directly (reaction 2.13a), or the reaction could be complex, with a slow initial homolysis of a carbon-mercury bond, followed by rapid further reactions to give the products (reaction 2.13b). Similarly for the Cope rearrangement of diene 2 to diene 4, the reaction could be elementary, with a concerted cyclic movement of electrons (reaction 2.14a), or might involve a di-radical intermediate 3 which rapidly reacted further to give the observed product 4 (reaction 2.14b). Both these mechanisms would lead to first-order kinetics, so the establishment of first-order kinetic behaviour for both these reaction schemes does not establish the... 

The cis-trans isomerization of cyclopropanes is not restricted to the deuterium-substituted molecules, cis- and traws-l,2-Dimethylcyclo-propane have been shown to imdergo reversible geometrical isomerization as well as slower structural isomerization. All the processes are homogeneous and kinetically first order, and almost certainly unimolecular. The reaction scheme is shown below. 

First-Order Reversible Reactions. Though no reaction ever goes to completion, we can consider many reactions to be essentially irreversible because of the large value of the equilibrium constant. These are the situations we have examined up to this point. Let us now consider reactions for which complete conversion cannot be assumed. The simplest case is the opposed unimolecular-type reaction... 

Consider the simple unimolecular reaction of Eq. (15.3), where the objective is to compute the forward rate constant. Transition-state theory supposes that the nature of the activated complex. A, is such that it represents a population of molecules in equilibrium with one another, and also in equilibrium with the reactant, A. That population partitions between an irreversible forward reaction to produce B, with an associated rate constant k, and deactivation back to A, with a (reverse) rate constant of kdeact- The rate at which molecules of A are activated to A is kact- This situation is illustrated schematically in Figure 15.1. Using the usual first-order kinetic equations for the rate at which B is produced, we see that... 

This mechanism has a reversible unimolecular decomposition as a first step. As will be shown later, when unimolecular steps are involved in chain reactions, this can cause a change in order or a change in the value of the rate constant if the pressure is lowered. 

Answer. When the unimolecular reaction is in the first order region the ratedetermining step is reaction, rather than activation. The reverse reaction must also have reaction as rate determining and this corresponds to the second order region of the recombination. Recombination and decomposition will be in the high pressure region. 

Rates of thermal cracking are first-order in good approximation for propane, butane and still higher hydrocarbons [21], This is remarkable because chain mechanisms with initiation by break-up of a reactant normally result in reaction orders of one half or one-and-a-half, depending on which radical is consumed by termination. First-order behavior can result from "mixed" termination, which, however, can in most cases be ruled out as dominant mechanism (see Section 9.3). A more probable explanation is a combination of effects that key hydrocarbon radicals participate in several steps of different molecularities, that some steps are reversible, and that some unimolecular ones require collision partners. 

Amide CTI is a first-order reversible reaction (unimolecular process) characterized by a kinetic constant kobs = k( >c + kr >(. In secondary amides, kobs is entirely determined by kc >(, suggesting that a stabilized cis isomer corresponds to a decelerated cis —r trans isomerization rather than an accelerated trans —> cis reaction, whereas both rate constants usually contribute in a similar way for tertiary amides. The kinetic constant kc >( was determined for a set of Gly- and Ala-con-... 

Although the explicit solution is not possible, several limiting cases provide solutions that are capable of simple interpretation. If 3 is much smaller than k, the rate of the product formation, dD/dt, is governed by the unimolecular breakdown of C, which in turn is formed rapidly and reversibly from A plus B kmeticahy the reaction is first order in either reactant ... 

Besides undergoing reversible, thermal, geometrical isomerization, cyclopropane also undergoes a slower, irreversible structural isomerization. The kinetics of both reactions of trans-C Hj] cyclopropane at 480 °C in the 10 Torr pressure range have been reported, as well as the kinetics of the structural isomerization of cyclopropane between 454 and 538 °C in the pressure range 0.4—137 atm. First-order kinetics for the gas-phase isomerization of 1,1,2-trimethylcyclopropane between 427 and 481°C have been established. The kinetic data and the formation of the complex mixture of products were interpreted in terms of a unimolecular, biradical-intermediate mechanism, in line with precedent. 

Denaturation of LDH-H4 was induced by various methods including 6 M GuHCl, 6 M urea, and low pH. An irreversible unimolecular-bimolecular kinetic mechanism correctly describes refolding and reactivation (Fig. 11.5), with only a first-order rate constant kj = (1.45 0.45) x 10" sec" and a second-order reaction rate constant 2 = (5 1) mM sec" These two constants are identical regardless of the denaturant employed. Irreversible steps in the kinetic mechanism are only operational that means rate constants of the reversible process are very small under the experimental... 

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