Unimolecular reactions that produce

One important point to remember when using kinetics to study soil-water processes is that the apparatus chosen for the study is capable of removing or isolating the end product as fast as it is produced. A second point is that unimolecular reactions always produce first-order plots, but fit of kinetic data (representing a process not well understood) to a first-order plot is no proof that the process is unimolecular. Complementary data (e.g., spectroscopic data) are needed to support such a conclusion, On the other hand, rate-law differences between any two reaction systems suggest that the mechanisms involved may represent different elementary reactions. 

Table XI.5. Unimolecular Gas-phase Reactions That Produce Radicals...

Detailed reaction dynamics not only require that reagents be simple but also that these remain isolated from random external perturbations. Theory can accommodate that condition easily. Experiments have used one of three strategies. (/) Molecules ia a gas at low pressure can be taken to be isolated for the short time between coUisions. Unimolecular reactions such as photodissociation or isomerization iaduced by photon absorption can sometimes be studied between coUisions. (2) Molecular beams can be produced so that motion is not random. Molecules have a nonzero velocity ia one direction and almost zero velocity ia perpendicular directions. Not only does this reduce coUisions, it also aUows bimolecular iateractions to be studied ia intersecting beams and iacreases the detail with which unimolecular processes that can be studied, because beams facUitate dozens of refined measurement techniques. (J) Means have been found to trap molecules, isolate them, and keep them motionless at a predetermined position ia space (11). Thus far, effort has been directed toward just manipulating the molecules, but the future is bright for exploiting the isolated molecules for kinetic and dynamic studies. 

In this part of the chapter, we will briefly outline the main types of CL reactions which can be functionally classified by the nature of the excitation process that leads to the formation of the electronically excited state of the light-emitting species. Direct chemiluminescence is the term employed for a reaction in which the excited product is formed directly from the unimolecular reaction of a high-energy intermediate that has been formed in prior reaction steps. The simplest example of this type of CL is the unimolecular decomposition of 1,2-dioxetanes, which are isolated HEI. Thermal decomposition of 1,2-dioxetanes leads mainly to the formation of triplet-excited carbonyl compounds. Although singlet-excited carbonyl compounds are produced in much lower yields, their fluorescence emission constitutes the direct chemiluminescence emission observed in these transformations under normal conditions in aerated solutions ... 

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... 

The only example of all the unimolecular reactions known where such a difficulty has actually arisen in an acute form is the decomposition of nitrogen pentoxide. It appears that at low pressures nitrogen pentoxide reacts at a rate which is considerably greater than the maximum possible rate of activation by collision, however great a value of n be assumed. There is a limit to the maximum rate theoretically possible, since, when n is increased beyond a certain point, the increase in the term E — EArrhenius + n- )RT produces a decrease in the calculated rate which more than compensates for the increase due to the term (E/RT)1l2n 1 multiplying the exponential term. 

This equation tells us what happens to an individual 03 molecule. It is an example of a unimolecular reaction, because only one reactant molecule is involved. We can picture an ozone molecule acquiring energy from sunlight and vibrating so vigorously that it shakes itself apart. If we believe that an O atom produced by the dissociation of 03 goes on to attack another 03 molecule, we write for that step... 

The field of unimolecular reaction rates had an interesting history beginning around 1920, when chemists attempted to understand how a unimolecular decomposition N2Os could occur thermally and still be first-order, A — products, even though the collisions which cause the reaction are second-order (A + A— products). The explanation, one may recall, was given by Lindemann [59], i.e., that collisions can produce a vibrationally excited molecule A, which has a finite lifetime and can form either products (A — products), or be deactivated by a collision (A + A— A + A). At sufficiently high pressures of A, such a scheme involving a finite lifetime produces a thermal equilibrium population of this A. The reaction rate is proportional to A, which would then be proportional to A and so the reaction would be first-order. At low pressures, the collisions of A to form A are inadequate to maintain an equilibrium population of A, because of the losses due to reaction. Ultimately, the reaction rate at low pressures was predicted to become the bimolecular collisional rate for formation of A and, hence, second-order. 

Although the theory was initially developed in 1952 and had been partly prompted by my prior experimental work, there were very few experimental data to which it could be applied. Around 1959 and subsequent years, B.S. Rabinovitch and coworkers used this theory to interpret their data on chemical activation [62, 69]. It may be recalled that chemical activation produced a narrower energy distribution of dissociating molecules than that in thermal unimolecular reactions and, hence, is better for testing the theory. 

The basic NR mass spectrum contains information on the fraction of undissociated (survivor) ions and also allows one to identify dissociation products that are formed by purely unimolecular reactions. NRMS thus provides information on the intrinsic properties of isolated transient molecules that are not affected by interactions with solvent, matrix, surfaces, trace impurities, radical quenchers, etc. However, because collisional ionization is accompanied by ion excitation and dissociation, the products of neutral and post-reionization dissociations overlap in the NR mass spectra. Several methods have been developed to distinguish neutral and ion dissociations and to characterize further short lived neutral intermediates in the fast beam. Moreover, collisionally activated dissociation (CAD) spectra have been used to characterize the ions produced by collisional reionization of transient neutral intermediates [51]. This NR-CAD analysis adds another dimension to the characterization of neutral intermediates, because it allows one to uncover isomerizations that do not result in a change of mass and thus are not apparent from NR mass spectra alone. 

Recent years have also witnessed exciting developments in the active control of unimolecular reactions [30,31]. Reactants can be prepared and their evolution interfered with on very short time scales, and coherent hght sources can be used to imprint information on molecular systems so as to produce more or less of specified products. Because a well-controlled unimolecular reaction is highly nonstatistical and presents an excellent example in which any statistical theory of the reaction dynamics would terribly fail, it is instmctive to comment on how to view the vast control possibihties, on the one hand, and various statistical theories of reaction rate, on the other hand. Note first that a controlled unimolecular reaction, most often subject to one or more external fields and manipulated within a very short time scale, undergoes nonequilibrium processes and is therefore not expected to be describable by any unimolecular reaction rate theory that assumes the existence of an equilibrium distribution of the internal energy of the molecule. Second, strong deviations Ifom statistical behavior in an uncontrolled unimolecular reaction can imply the existence of order in chaos and thus more possibilities for inexpensive active control of product formation. Third, most control scenarios rely on quantum interference effects that are neglected in classical reaction rate theory. Clearly, then, studies of controlled reaction dynamics and studies of statistical reaction rate theory complement each other. 

E2 elimination reactions occur preferentially when the leaving groups are in an anti copla-nar arrangement in the transition state. However, there are a few thermal, unimolecular sy -eliminations that produce alkenes. For example, pyrolysis of several closely related amine oxides, sulfoxides, selenoxides, acetates, benzoates, carbonates, carbamates and thio-carbamates gives alkenes on heating (Scheme 4.10). The syn character of these eliminations is enforced by a five- or six-membered cyclic transition states by which they take place. 

Uncatalyzed hydrocarbon oxidations can give high yields of peroxides under certain conditions. The conditions required are those that favor long chain lengths with little decomposition of the hydroperoxide. Relatively low temperatures favor survival of the hydroperoxide and low rates favor unimolecular reaction (eq. (2)) (which produces hydroperoxide) over bimolecular reaction (eq. (5)) (which consumes ROO radicals without producing hydroperoxide). Of course, enough hydroperoxide must decompose to provide new radicals to the system at the rate at which they are removed by chain termination. 

The efficient decomposition of hydroperoxides by a non-radical pathway can greatly increase the stabilizing efficiency of a chain-breaking antioxidant. This generally occurs by an ionic reaction mechanism. Typical additives are sulfur compounds and phosphite esters. These are able to compete with the decomposition reactions (either unimolecular or bimolecular) that produce the reactive alkoxy, hydroxy and peroxy radicals and reduce the peroxide to the alcohol. This is shown in the first reaction in Scheme 1.69 for the behaviour of a triaryl phosphite, P(OAr)3 in reducing ROOH to ROH while itself being oxidized to the phosphate. 

Kinetic theory tells us that reactions take place because random collisions between molecules produce a small number of molecules with an energy greater than the minimum (the activation energy) for reaction to occur. For unimolecular reactions at a particular temperature, this number (and thus the rate of reaction) will be proportional to the number of molecules present in a particular space (volume), i.e. the concentration. Thus for a reaction... 

The energy imparted in species such as M- however, is much larger than that imparted in its positive counterpart, M+-. The cascade of unimolecular dissociations that follows is so important that it produces mass spectra that usually are devoid of molecular ion information (i.e. no M-- is observed) and gives rise to rather unorthodox reactions that can hardly be related to conventional chemistry principles (e.. benzene, CgHg, under electron impact conditions and recorded in the negative ion mode, exhibits a large ion at m/z 72 that corresponds to Ccr ). As a result of the limited structural information that... 

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