First-Order, Unimolecular Reactions

Since S/t has units of moles per volume per time and a has units of moles per volume, the rate constant for a first-order reaction has units of reciprocal time e.g., s. The best example of a truly first-order reaction is radioactive decay for example, 

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The simplest case of reaction kinetics occurs when the excitation and emission occur in the same atom, molecule, or luminescence center. The recombination can then be treated as a first-order unimolecular reaction. The decay time is independent of the number of other similarly excited atoms or molecules. 

Pyrolytic degradation of esters in the vapour phase [36] occurs by a first-order unimolecular reaction... 

The thermal and photochemical activations of EDA complexes by electron transfer are both enhanced when the radical ions D+- or A--(either paired or free) undergo a facile first-order (unimolecular) transformation such as fragmentation, rearrangement, bond-formation, etc., which pulls the redox equilibrium and thus renders the competition from the energy-wasting back electron transfer less effective (compare Scheme 5). Critical to the quantitative evaluation of the reaction dynamics is the understanding that the typical [D+% A--] intermediates, as described in... 

First-Order Unimolecular Surface Reaction For the reaction... 

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... 

The NH acidities of some sterically hindered ureas, namely the ureido esters (93), have been reported.81 The kinetics and mechanism of the alkaline hydrolysis of urea and sodium cyanate, NaCNO, have been studied at a number of temperatures.82 Urea hydrolysis follows an irreversible first-order consecutive reaction path. Tetrahedral intermediates are not involved and an elimination-addition mechanism operates. Sodium cyanate follows irreversible pseudo-first-order kinetics. The decomposition of the carcinogen /V-mcthyl-/V-nitrosourca (19) was dealt with earlier.19 The pyrolysis of /V-acctylurca goes by a unimolecular first-order elimination reaction.83... 

Reactivities and activation parameters for pyrolytic unimolecular first-order elimination reactions of A -acetylurea, A -acetylthiourca, /V,7V -diacetylthiourea and N-acetylthiobenzamide have been interpreted with reference to those for other amide derivatives.55 The first-order rate constants for pyrolysis of RCONHCSNHCe R (R = Me, R = H R = Ph, R = H, 4-N02, 3-C1, 4-C1, 4-Me) have also been measured at 423-500 K and correlated with Hammett [Pg.378]

First-order unimolecular fission reactions in which the products are stable molecules have been compiled in Table XI.4. As can be seen, the frequency factors all fall in the range between 3 X 10 to about 10 sec with most of them very close to the value of 10 sec b... 

A different model [11] that can be used to obtain the kinetics equation for a pyrolytic reaction is adapted from the theory developed for the kinetics of heterogeneous catalytic reactions. This theory is described in literature for various cases regarding the determining step of the reaction rate. The case that can be adapted for a pyrolytic process in solid state is that of a heterogeneous catalytic reaction with the ratedetermining step consisting of a first-order unimolecular surface reaction. For the catalytic reaction of a gas, this case can be written as follows ... 

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-... 

We conclude that the order for each reactant in a single-step (elementary) process is equal to the coefficient of that reactant in the chemical equation for that process, and, for an elementary process, the overall order is the same as the molecularity (i.e., a unimolecular process is first order, a bimolecular process is second order, etc.) The converse does not hold that is, not all first-order chemical reactions are unimolecular elementary processes, etc. 

Stochastic analysis and modeling of chemical reactions have been accomplished in a closed system or batch reactors. A review of such a formulation has been given by McQuarrie [4]. First-order chemical reactions of the unimolecular type, each involving two or three chemical species, have been considered by McQuarrie [5] and Fredrickson [6]. Cases of first-order reactions among multitype molecules have been treated by Darvey and Staff [7]. 

In true first-order reactions the rate is directly proportional to the concentration or volume of the remaining unreacted material, as defined by Eq. (1). Homogeneous first-order gas reactions—namely, decompositions—are well-known and are usually unimolecular. The present system is considerably more complex. 

The effective rate law correctly describes the pressure dependence of unimolecular reaction rates at least qualitatively. This is illustrated in figure A3,4,9. In the lunit of high pressures, i.e. large [M], becomes independent of [M] yielding the high-pressure rate constant of an effective first-order rate law. At very low pressures, product fonnation becomes much faster than deactivation. A j now depends linearly on [M]. This corresponds to an effective second-order rate law with the pseudo first-order rate constant Aq ... 

The individual reactions need not be unimolecular. It can be shown that the relaxation kinetics after small perturbations of the equilibrium can always be reduced to the fomi of (A3.4.138t in temis of extension variables from equilibrium, even if the underlying reaction system is not of first order [51, fil, fiL, 58]. 

An important example for the application of general first-order kinetics in gas-phase reactions is the master equation treatment of the fall-off range of themial unimolecular reactions to describe non-equilibrium effects in the weak collision limit when activation and deactivation cross sections (equation (A3.4.125)) are to be retained in detail [ ]. 

There is one special class of reaction systems in which a simplification occurs. If collisional energy redistribution of some reactant occurs by collisions with an excess of heat bath atoms or molecules that are considered kinetically structureless, and if fiirthennore the reaction is either unimolecular or occurs again with a reaction partner M having an excess concentration, dien one will have generalized first-order kinetics for populations Pj of the energy levels of the reactant, i.e. with... 

Fast transient studies are largely focused on elementary kinetic processes in atoms and molecules, i.e., on unimolecular and bimolecular reactions with first and second order kinetics, respectively (although confonnational heterogeneity in macromolecules may lead to the observation of more complicated unimolecular kinetics). Examples of fast thennally activated unimolecular processes include dissociation reactions in molecules as simple as diatomics, and isomerization and tautomerization reactions in polyatomic molecules. A very rough estimate of the minimum time scale required for an elementary unimolecular reaction may be obtained from the Arrhenius expression for the reaction rate constant, k = A. The quantity /cg T//i from transition state theory provides... 

When a unimolecular reaction occurs with an initial product partial pressure of the reactant A, to yield an amount of die product, jc, the first-order reaction rate equation reads... 

The thermal decompositions described above are unimolecular reactions that should exhibit first-order kinetics. Under many conditions, peroxides decompose at rates faster than expected for unimolecular thermal decomposition and with more complicated kinetics. This behavior is known as induced decomposition and occurs when part of the peroxide decomposition is the result of bimolecular reactions with radicals present in solution, as illustrated below specifically for diethyl peroxide. 

The first step, which is rate determining, is an ionization to a carbocation (carbonium ion in earlier terminology) intermediate, which reacts with the nucleophile in the second step. Because the transition state for the rate-determining step includes R-X but not Y , the reaction is unimolecular and is labeled S l. First-order kinetics are involved, with the rate being independent of the nucleophile identity and concentration. 

From this expression, it is obvious that the rate is proportional to the concentration of A, and k is the proportionality constant, or rate constant, k has the units of (time) usually sec is a function of [A] to the first power, or, in the terminology of kinetics, v is first-order with respect to A. For an elementary reaction, the order for any reactant is given by its exponent in the rate equation. The number of molecules that must simultaneously interact is defined as the molecularity of the reaction. Thus, the simple elementary reaction of A P is a first-order reaction. Figure 14.4 portrays the course of a first-order reaction as a function of time. The rate of decay of a radioactive isotope, like or is a first-order reaction, as is an intramolecular rearrangement, such as A P. Both are unimolecular reactions (the molecularity equals 1). 

First-order reaction (Section 11.4) A reaction whose rate-limiting step is unimolecular and whose kinetics therefore depend on the concentration of only one reactant. 

This reaction follows first-order kinetics. It is not unimolecular, however, and occurs by a chain mechanism. Table 9-1 summarizes the activation parameters. The rate constant is nearly the same in the gas phase as in solution, and from one solvent to the next. 

As in a unimolecular chemical reaction, the rate law for nuclear decay is first order. That is, the relation between the rate of decay and the number N of radioactive nuclei present is given by the law of radioactive decay ... 

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