Unimolecular reactions, conditions

The introductory remarks about unimolecular reactions apply equivalently to bunolecular reactions in condensed phase. An essential additional phenomenon is the effect the solvent has on the rate of approach of reactants and the lifetime of the collision complex. In a dense fluid the rate of approach evidently is detennined by the mutual difhision coefficient of reactants under the given physical conditions. Once reactants have met, they are temporarily trapped in a solvent cage until they either difhisively separate again or react. It is conmron to refer to the pair of reactants trapped in the solvent cage as an encounter complex. If the unimolecular reaction of this encounter complex is much faster than diffiisive separation i.e., if the effective reaction barrier is sufficiently small or negligible, tlie rate of the overall bimolecular reaction is difhision controlled. 

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. 

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 results obtained for kq are, within the experimental error, in accordance with the values obtained in reaction conditions where the main decomposition path is the unimolecular decarboxylation. 

In general, intramolecular isomerization in coordinatively unsaturated species would be expected to occur much faster than bimolecular processes. Some isomerizations, like those occurring with W(CO)4CS (47) are anticipated to be very fast, because they are associated with electronic relaxation. Assuming reasonable values for activation energies and A-factors, one predicts that, in solution, many isomerizations will have half-lives at room temperature in the range 10 7 to 10 6 seconds. The principal means of identifying transients in uv-visible flash photolysis is decay kinetics and their variation with reaction conditions. Such identification will be difficult if not impossible with unimolecular isomerization, particularly since uv-visible absorptions are not very sensitive to structural changes (see Section I,B). These restrictions do not apply to time-resolved IR measurements, which should have wide applications in this area. 

It has been generally accepted that the thermal decomposition of paraffinic hydrocarbons proceeds via a free radical chain mechanism [2], In order to explain the different product distributions obtained in terms of experimental conditions (temperature, pressure), two mechanisms were proposed. The first one was by Kossiakoff and Rice [3], This R-K model comes from the studies of low molecular weight alkanes at high temperature (> 600 °C) and atmospheric pressure. In these conditions, the unimolecular reactions are favoured. The alkyl radicals undergo successive decomposition by [3-scission, the main primary products are methane, ethane and 1-alkenes [4], The second one was proposed by Fabuss, Smith and Satterfield [5]. It is adapted to low temperature (< 450 °C) but high pressure (> 100 bar). In this case, the bimolecular reactions are favoured (radical addition, hydrogen abstraction). Thus, an equimolar distribution ofn-alkanes and 1-alkenes is obtained. 

In the unimolecular reactions which are also of the first order, only one molecule takes part in the reaction. The process of activation in unimolecular reactions, if caused by collisions should ordinarily lead to second order reactions. How then the observed rate of reaction could be of first order. If however, the activation is by absorption of the radiant energy, this problem can be avoided. But many unimolecular reactions take place under conditions where there is no absorption of radiant energy. For example... 

Much of the recent work on the cyclopropane-propylene isomerization has had one of two objectives, either to try and determine which of the two reaction paths suggested by the early workers is involved, or to test the various theories of unimolecular reactions. Comer and Pease (1945), using catalytic hydrogenation to analyse their reaction product, but otherwise working under similar conditions to Chambers and Kistiakow-sky, suggested that all the results obtained could be represented just as well by the reaction scheme... 

The quasi-equilibrium theory (QET) of mass spectra is a theoretical approach to describe the unimolecular decompositions of ions and hence their mass spectra. [12-14,14] QET has been developed as an adaptation of Rice-Ramsperger-Marcus-Kassel (RRKM) theory to fit the conditions of mass spectrometry and it represents a landmark in the theory of mass spectra. [11] In the mass spectrometer almost all processes occur under high vacuum conditions, i.e., in the highly diluted gas phase, and one has to become aware of the differences to chemical reactions in the condensed phase as they are usually carried out in the laboratory. [15,16] Consequently, bimolecular reactions are rare and the chemistry in a mass spectrometer is rather the chemistry of isolated ions in the gas phase. Isolated ions are not in thermal equilibrium with their surroundings as assumed by RRKM theory. Instead, to be isolated in the gas phase means for an ion that it may only internally redistribute energy and that it may only undergo unimolecular reactions such as isomerization or dissociation. This is why the theory of unimolecular reactions plays an important role in mass spectrometry. 

The reaction has also been extended to the analogous vinyl bromides [30]. Indeed, the alkenyl bromide 77 under normal reduction conditions gave the bicyclic compound 78 in good yield by an Sni reaction given by the vinyl radical (Reaction 6.17). Under these conditions, the reduction products could not be observed which suggests a very fast unimolecular reaction. 

At high temperatures and low pressures, the unimolecular reactions of interest may not be at their high-pressure limits, and observed rates may become influenced by rates of energy transfer. Under these conditions, the rate constant for unimolecular decomposition becomes pressure- (density)-dependent, and the canonical transition state theory would no longer be applicable. We shall discuss energy transfer limitations in detail later. 

The previous derivations describe what must be expected in the simplest catalytic reactions Orders of reaction and rate coefficients change strongly with conditions. For a unimolecular reaction A —> 5 on a surface we expect the rate expression of the form... 

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 ... 

Dissociative ionization of [l,2,5]thiadiazolo[3,4-f][ l,2,5]thiadiazole 6 was found to be an efficient preparative route to in j// -generated thionitrosyl cyanide and its radical cation, both of which are stable and did not undergo unimolecular rearrangement under the reaction conditions. The [C,N2,S] ions were characterized by mass spectrometry (ml% 72) (see Section 10.05.3.2.2) <1997JST(418)209>. 

This approach applies only when we are certain that the substrate is mainly in the form of the free ion at the lowest anion concentrations. This is true in the chloride exchange of cw-[Co en2 Cl2]+ in methanol and we can safely conclude that the mechanism is unimolecular (8, 9. 10, 11, 26, 27). This condition did not exist when we studied the displacement of water in trans-[Co en2N02H20]+2 by anions where, because of the large ion association constants, none of the substrate was in the free ion form under reaction conditions. However, in the reaction between trans-[Co en2N02Br]+ and thiocyanate in sulfolane, the substrate was mainly in the free ion form. The observed second-order kinetic form was fully consistent with assigning a bimolecular mechanism to the rearrangement of the ion pair. 

In every mol. of iodine (I2) at 1043°, 0-25 mol. will be dissociated hence, a 2=0-0625 1— =0 75 and K=0 0833/v. To evaluate v, remember that one mol. of iodine vapour at 0° and 760 mm. occupies 22 3 litres and at 1043°, 107-5 litres. This quantity of gas contains 0 25 more molecules of iodine because of dissociation, and hence its volume is 107 5+J of 107-5=134-4 litres. Hence A=0 0833 -134-4 =0-00062 oi k A =0-00062 1 or 1 1600 (nearly). Otherwise expressed, Ct2=1600 Ci2, that is, the atoms of iodine will unite 1600 times as fast as the molecules dissociate under such conditions that unit concentration of each is present. The dissociation of iodine molecules is a unimolecular reaction because one molecule is concerned in the reaction and the formation of the two-atom molecule by the union of two one-atom molecules is a bimolecular reaction because two molecules are concerned in the process. 

Under ordinary mass spcctrometric conditions only unimolecular reactions of excited ions occur, but at higher ionization chamber pressures bimolecular ion molecule reactions are observed in which both the parent ions and their unimolecular dissociation product ions are reactants. Since it requires a time of 10 5 sec. to analyze and collect the ions after their formation all of the ions in the complete mass spectrum of the parent molecule are possible reactants. However, in radiation chemistry we are concerned with the ion distribution at the time between molecular collisions which is much shorter than 10 5 sec. For example, in the gas phase at 1 atm. the time between collisions is 10 10 sec. and in considering the ion molecule reactions that can occur one must know the amount of unimolecular decomposition within that time. By utilizing the quasi-equilibrium theory of mass spectra6 it is possible to calculate the ion distribution at any time. This has been done for propane at a time of 10 10 sec.,24 and although the parent ion is increased by a factor of 2 the relative ratios of the other ions are about the same as in the mass spectrum observed in 10 r> sec. Thus for gas phase radiolysis the observed mass spectrum is a fair first approximation to the ion distribution. In... 

A unimolecular reaction is one in which the absolute rate of change is proportional to the first power of the concentration of the reacting substance. The fraction of the total number of the molecules in the system which change in unit time is therefore independent of the concentration, and thus, in gaseous systems, cannot be proportional to the nuinber of collisions undergone in unit time by the molecules. It must therefore be concluded that, whether or not previously received collisions have done anything to put the molecule into an abnormal condition, the actual chemical transformation is an event happening to the isolated molecule. 

For some time the thermal decomposition of phosphine at high temperatures was believed to be a homogeneous unimolecular reaction. It was studied by Trautz and Bhandarkar, who concluded that under the conditions of their experiments, namely in a 3-litre porcelain bulb, the reaction on the walls of the vessel was negligible above 945° abs., in comparison with the homogeneous reaction. 

Under these conditions the rate varies as the first power of n, although the reaction really depends upon collisions, a result which we have already derived from a more general argument in dealing with unimolecular reactions. 

The lifetimes of the BRs are of critical importance to any attempt at quantitative analysis of the factors which will determine quantum yields and product distributions (E/C and t/c ratios) in Type II reactions of ketones under various reaction conditions. Virtually all information about lifetimes is derived from study of triplet BRs and much of it has been provided, and reviewed, by Scaiano [261]. There are many interesting reactions, both bimolecular and unimolecular, which occur at only one of the radical centers but they have little relevance to this chapter and are not discussed here. BR triplets derived from alkanophenones have lifetimes of 25-50 ns in hydrocarbon solvents. They are lengthened several fold in t-butyl alcohol and other Lewis bases capable of hydrogen bonding to the OH groups of the BRs. The rates of decay are virtually temperature independent but are shortened by paramagnetic cosolutes such as 02 or NO. The quenchers react with the BRs... 

The transient nature of the cavitation event precludes conventional measurement of the conditions generated during bubble collapse. Chemical reactions themselves, however, can be used to probe reaction conditions. The effective temperature realized by the collapse of clouds of cavitating bubbles can be determined by the use of competing unimolecular reactions whose rate dependencies on temperature have already been measured. The sonochemical ligand substitutions of volatile metal carbonyls were used as... 

---