Unimolecular reaction, rate constants

Scheme 1 illustrates the design of an experiment that could be used to determine the rate constant for H-atom abstraction from a group 14 hydride. Radical A- reacts with the hydride to give product A-H. In competition with this reaction, radical A- gives radical B- in a unimolecular or bimolecular reaction with a known rate constant, and product radical B- also reacts with the hydride, giving B-H. The rate constant for reaction of A- with the metal hydride can be determined from the product distribution, the known rate constant for conversion of A- to B-, and the concentrations... 

In these equations, [A] and [R]0 are the respective initial concentrations of polymer (or olefin) and rubrene, K and kd are the respective rate constants for reaction of rubrene with singlet molecular oxygen and for the unimolecular decay of the latter to triplet oxygen. The quantities m and mA are the initial rates of rubrene consumption in the absence and presence of A, respectively. Under our experimental conditions the first term in the denominator is small, so we have ... 

Therefore, provided that there is an equilibrium between the micellar and aqueous pseudophases, the problem resolves itself into estimation of the distribution of reactants between aqueous and micellar pseudophase and calculation of the rate constants of reaction in each pseudophase. Menger and Portnoy [70] developed an equation which successfully accounted for micellar inhibited saponification of 4-nitrophenyl alkanoates. This model was also applied to spontaneous, unimolecular, hydrolyses of dinitrophenyl sulfate monoanions [66] and phosphate dianions [68] which are speeded by cationic micelles in water. 

The Epithermal Nonequilibrium Model. The MNR thermalization tests may be conceptualized in terms of an epithermal steady-state hot atom collision energy probability density distribution 4,20,21 22,41 43,63,64,65). In epithermal terminology, high-pressure unimolecular rate constants for Reaction 13 can reveal temperature changes for the reacting C1 atoms. Based on the reported energy dependence for this system (40), experiments with 20% sensitivity could detect temperature variations of about 100 35 K. 

Rate constants for unimolecular homogeneous PH3 decomposition were calculated by the Rice-Ramsperger-Kassel-Marcus (RRKM) theory and by the use of estimated values for the activation energies. Rate constants at the high-pressure limit for reaction (5), log(k/s)= 14.18-11 610/T [5] or 14.00-12610/T [4], include activation energies of 222 or 241 kJ/mol, respectively. Calculated rate constants for reaction (6) are log(k/s)=15.74-18 040/T with an activation energy of 345 kJ/mol. At 900 K PH formation is thus predicted to exceed PH2 formation by a factor -10. Calculated fall-off pressures for both reactions which indicate the onset of second-order decomposition, are quite high, about 10 Torr in an H2 bath gas [5]. 

The pyrolysis mechanism of PPE and its derivatives given in Scheme 7.2 consist of bimolecular and unimolecular reactions. Applying transition state theory, we calculate the rate constants for the hydrogen abstraction reactions using Eq. (7.19) and the rate constants for reactions 1 and 3-5 using Eq. (7.21). The Wigner correction (Eq. (7.20)) is utilized to approximate quantum effects and the molecular partition functions are defined through Eqs (7.14), (7.15), (7.17), (7.18), and (7.28). 

A recurring theme in this article has been the close links between the reaction and nonreactive relaxation of excited species. For the interpretation of competitive experiments, such as bulk photochemical studies on hot atom reactions, as well as chemical and photochemical activation experiments on unimolecular reactions, more accurate and detailed information about the energy-transfer processes are required. In other more direct experiments, for example, those in which fluorescence or chemiluminescence is observed, it is often difficult to determine whether it is reaction or relaxation by the active species which predominates. As we have seen, a powerful method of obtaining detailed rate constants is to apply the equations derived from the principle of microscopic reversibility to the results of experiments on exothermic processes. In favorable, nearly thermoneutral, cases, a detailed rate constant for reaction can then be compared with the rate constant for total removal obtained directly. 

This yields die qiiasi-stationaty reaction rate with an effective unimolecular rate constant... 

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 ... 

Gilbert R G, Luther K and Troe J 1983 Theory of thermal unimolecular reactions in the fall-off range. II. Weak collision rate constants Ber. Bunsenges. Phys. Chem. 87 169-77... 

A situation that arises from the intramolecular dynamics of A and completely distinct from apparent non-RRKM behaviour is intrinsic non-RRKM behaviour [9], By this, it is meant that A has a non-random P(t) even if the internal vibrational states of A are prepared randomly. This situation arises when transitions between individual molecular vibrational/rotational states are slower than transitions leading to products. As a result, the vibrational states do not have equal dissociation probabilities. In tenns of classical phase space dynamics, slow transitions between the states occur when the reactant phase space is metrically decomposable [13,14] on the timescale of the imimolecular reaction and there is at least one bottleneck [9] in the molecular phase space other than the one defining the transition state. An intrinsic non-RRKM molecule decays non-exponentially with a time-dependent unimolecular rate constant or exponentially with a rate constant different from that of RRKM theory. 

Green W H, Moore C B and Polik W F 1992 Transition states and rate constants for unimolecular reactions Ann. Rev. Phys. Chem. 43 591-626... 

Miller W H 1988 Effect of fluctuations in state-specific unimolecular rate constants on the pressure dependence of the average unimolecular reaction rated. Phys. Chem. 92 4261-3... 

Thus, this eigenvalue detenuines the unimolecular steady-state reaction rate constant. 

Note that in the low pressure limit of iinimolecular reactions (chapter A3,4). the unimolecular rate constant /fu is entirely dominated by energy transfer processes, even though the relaxation and incubation rates... 

Troe J 1977 Theory of thermal unimolecular reactions at low pressures. II. Strong collision rate constants. Applications J. Chem. Phys. 66 4758... 

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... 

The catalytic effect on unimolecular reactions can be attributed exclusively to the local medium effect. For more complicated bimolecular or higher-order reactions, the rate of the reaction is affected by an additional parameter the local concentration of the reacting species in or at the micelle. Also for higher-order reactions the pseudophase model is usually adopted (Figure 5.2). However, in these systems the dependence of the rate on the concentration of surfactant does not allow direct estimation of all of the rate constants and partition coefficients involved. Generally independent assessment of at least one of the partition coefficients is required before the other relevant parameters can be accessed. 

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). 

The rate constants (in absolute solvents unless otherwise specified) are measured at a temperature giving a convenient reaction rate and calculated for a reference temperature used for comparison. These constants have all been converted to the same units and tabulated as 10 A . Where comparisons could otherwise not be made, pseudo-unimolecular constants (Tables IX and XIII, and as footnoted in Tables X to XIV) are used. The reader is referred to the original articles for the specific limits of error and the rate equations used in the calculations. The usual limits of error were for k, 1-2% or or 2-5% and logio A, 5%, with errors up to double these figures for some of the high-temperature reactions. 

A fast, unimolecular reaction can be used to excellent advantage. The rm-butoxyl radical offers the advantage that /3-scission occurs with a known rate constant. For Eq. (5-31), ki = 1.4 X 106 s-1 in water.8 In the presence of a hydrogen donor, AH, the competition is... 

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. 

Rate constants that are near the diffusion-controlled limit may need to have a correction applied, if they are to be compared with others that are slower. To see this, consider a two-step scheme. In the first, diffusion together and apart occur the second step is the unimolecular reaction within the solvent cage. We represent this as... 

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