True unimolecular reaction

An Arrhenius expression, k = 1012 exp(—24,300/Hr) sec-1, was quoted for the coefficient of the rate-determining step. It is doubtful whether this step is a true unimolecular reaction. The effect of pressures has not been studied. The range of temperatures used appears to be too narrow to discuss the temperature dependence... 

When a molecule is supplied with an amount of energy that exceeds some threshold energy, a unimolecular reaction can take place, that is, a dissociation or an isomerization. We distinguish between a true unimolecular reaction that can be initiated by absorption of electromagnetic radiation (photo-activation) and an apparent unimolecular reaction initiated by bimolecular collisions (thermal activation). For the apparent unimolecular reaction, the time scales for the activation and the subsequent reaction are well separated. When such a separation is possible, for true or apparent unimolecular reactions, the reaction is also referred to as an indirect reaction. We will discuss the following. 

In a true unimolecular reaction, the activation is done by exposing the molecules to electromagnetic radiation, whereas activation is accomplished by inelastic collisions with other molecules in an apparent unimolecular reaction. The condition for the latter process to be unimolecular is that the time scales of the activation process and the chemical reaction are very different, so that the chemical reaction is much slower than the activation process. 

A true unimolecular reaction is induced by electromagnetic radiation. That is, only one molecule takes part in the reaction and the energy is provided by the electromagnetic field. In fact, chemical reactions induced by electromagnetic radiation form such an important subfield of chemistry that it has its own designation photochemistry. 

In dynamical theories, one solves the equation of motion for the individual nuclei, subject to the potential energy surface. This is the exact approach, provided one starts with the Schrodinger equation. The aim is to calculate k(E) and kn(hi/), the microcanonical rate constants associated with, respectively, indirect (apparent or true) unimolecular reactions and true (photo-activated) unimolecular reactions. 

Fig. 7.2.3 A true unimolecular reaction here photodissociation of a diatomic molecule.

In a true unimolecular reaction, the energized molecules are formed by absorption of electromagnetic radiation see Section 7.2.2. In an apparent unimolecular reaction, the first step is the formation of the energized molecules by collisions with other molecules. We consider in the following subsection the interplay between the formation of energized molecules—by bimolecular collision—and their subsequent reaction. 

Since an elementary reaction occurs on a molecular level exactly as it is written, its rate expression can be determined by inspection. A unimolecular reaction is first-order process, bimolecular reactions are second-order, and termolecular processes are third-order. However, the converse statement is not true. Second-order rate expressions are not necessarily the result of an elementary bimolecular reaction. While a... 

The unusual rate enhancement of nucleophiles in micelles is a function of two interdependent effects, the enhanced nucleophilicity of the bound anion and the concentration of the reactants. In bimolecular reactions, it is not always easy to estimate the true reactivity of the bound anion separately. Unimolecular reactions would be better probes of the environmental effect on the anionic reactivity than bimolecular reactions, since one need not take the proximity term into account. The decarboxylation of carboxylic acids would meet this requirement, for it is unimolecular, almost free from acid and base catalysis, and the rate constants are extremely solvent dependent (Straub and Bender, 1972). 

The self-phosphorylation process catalyzed by many protein kinases as part of the regulatory mechanism for their own activation. Because true autophosphorylation is a unimolecular reaction involving enzyme both as catalyst and phosphoryl acceptor, the fraction of autophosphory-lated enzyme at any time after addition of ATP (or another phosphoryl donor) will be independent of the initial concentration of the enzyme. This criterion was first applied to the autophosphorylation of cardiac muscle cyclic AMP-stimulated protein kinase, now designated protein kinase A (PKA). At a fixed concentration of MgATP , the fraction of autophosphorylated protein will follow the first-order rate laws, [A]/[A ] where k is a first-order rate constant. 

As mentioned in Section 4, the analysis of rate data resulting from unimolecular reactions is considerably easier than the analysis of such data for bimolecular reactions, and the same is true for pseudounimolecular reactions. Kinetic probes currently used to study the micellar pseudophase showing first-order reaction kinetics are almost exclusively compounds undergoing hydrolysis reactions showing in fact pseudofirst-order kinetics. In these cases, water is the second reactant and it is therefore anticipated that these kinetic probes report at least the reduced water concentration (or better water activity in the micellar pseudophase. As for solvatochromic probes, the sensitivity to different aspects of the micellar pseudophase can be different for different hydrolytic probes and as a result, different probes may report different characteristics. Hence, as for solvatochromic probes, the use of a series of hydrolytic probes may provide additional insight. 

Note that the mean value of the stochastic representation is the deterministic result, showing that the two representations are consistent in the mean. We shall see later that this is true only for unimolecular reactions. The stochastic model, however, also gives higher moments and so fluctuations can now be included in chemical kinetics. One sees that the stochastic approach is to chemical kinetics as statistical thermody-... 

With bimolecular gas reactions, as we have seen, it is plausible to assume that the kinetic energy of the impact between the two molecules provides the energy of activation, and on this assumption we find for the number of molecules reacting number of collisions x e ElRT. This equation in six out of seven known examples is as nearly true as experiment can decide. Thus there is no absolute necessity to look any further for the interpretation of bimolecular reactions. At first it seemed natural to apply an analogous method of calculation to determine the maximum possible rate of activation in unimolecular reactions this led to the result that unimolecular reactions in general proceed at a rate many times greater than the expression Ze ElRT requires, e. g. about 105 times as many molecules of acetone decompose at 800° abs. in unit time as this method of calculation would admit to be possible, f... 

The first term, representing acid-"catalyzed" hydrolysis, is important in reactions of carboxylic acid esters but is relatively unimportant in loss of phosphate triesters and is totally absent for the halogenated alkanes and alkenes. Alkaline hydrolysis, the mechanism indicated by the third term in Equation (2), dominates degradation of pentachloroethane and 1,1,2,2-tetrachloroethane, even at pH 7. Carbon tetrachloride, TCA, 2,2-dichloropropane, and other "gem" haloalkanes hydrolyze only by the neutral mechanism (Fells and Molewyn-Hughes, 1958 Molewyn-Hughes, 1953). Monohaloalkanes show alkaline hydrolysis only in basic solutions as concentrated as 0.01-1.0 molar OH- (Mabey and Mill, 1978). In fact, the terms in Equation(2) can be even more complex both elimination and substitution pathways can operate, leading to different products, and a true unimolecular process can result from initial bond breaking in the reactant molecule. 

Equation (2.67) would enable the calculation of ASf because the following relationship for a unimolecular reaction is true ... 

Fig. 5.31 Graph of log ly2 = 0.175AG1 — 13.0. If this equation for the halflife of a unimolecular reaction were strictly true, then the threshold value of AG1 for ready observability at room temperature would be about 85 kJ mol-1, corresponding to iy2 = 75 s. Actually, a rough rule of thumb is that the threshold barrier for observability at room temperature is about 100 kJ mol 1...

A unimolecular reaction is first-order in the species that undergoes the spontaneous rearrangement or decomposition. This is true because there is a natural probability that a molecule will undergo the reaction in a specific time interval. Also, the overall rate per unit volume is the product of this probability per unit time and the total number of molecules per unit volume (which in turn is proportional to concentration). 

Fig. 7.1.1 Photodissociation (at a fixed bending angle) for a symmetric triatomic molecule like ozone. The vibrational ground state is superimposed on the potential energy surface of the electronic ground state an illustration of a true (direct) unimolecular reaction. (Note that in this figure all potential energies above a fixed cut-off value Amax have been replaced by Bmax, in the electronic ground state as well as in the excited electronic state.)...

The basic assumption in statistical theories is that the initially prepared state, in an indirect (true or apparent) unimolecular reaction A (E) —> products, prior to reaction has relaxed (via IVR) such that any distribution of the energy E over the internal degrees of freedom occurs with the same probability. This is illustrated in Fig. 7.3.1, where we have shown a constant energy surface in the phase space of a molecule. Note that the assumption is equivalent to the basic equal a priori probabilities postulate of statistical mechanics, for a microcanonical ensemble where every state within a narrow energy range is populated with the same probability. This uniform population of states describes the system regardless of where it is on the potential energy surface associated with the reaction. 

Gas phase kinetic results (Table 64) on hydroperoxide decompositions (methyl, ethyl, isopropyl and t-butyl hydroperoxide) are very poor. Since the thermochemistry is fairly well established for these reactions, and since observed activation energies are as much as 6 kcal.mole lower than the reaction enthalpies, it is apparent that the reported parameters cannot be those for the unimolecular hydro-peroxy bond fission processes. Surface catalysis was considerable in all experimental systems. It therefore seems likely that the true homogeneous reactions were never completely isolated. 

In the final subsection we shall look in more detail at one of the crucial aspects of decomposition reactions, the true unimolecular and energy dependent dissociation of an activated molecule. Exciting new developments, both theoretical and experimental, are taking place in this area confirming and interpreting some of the proposed theories of unimolecular reactions. 

Most synthetically useful reactions involve the interaction of two substrates on a catalytically active site to give the reaction product or products. Such systems are more complex than the simple unimolecular reaction but resemble somewhat the inhibited unimolecular processes just described. There are, however, some significant differences in that the two adsorbed substrates must interact to form products and not give a non-productive species. Thus, for two reactants, A and B, it is necessary to look at the initial rate data for a series of reactions that are run keeping the concentration of A constant while varying the concentration of B as well as a reaction series in which [B] is kept constant while [A] changes. The K, which is the dissociation constant for A at a fixed value of [B] may not be the true... 

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