Pseudo-unimolecular reactions

The most straightforward of the various models describing micellar kinetics is the Menger-Portnoy model for (pseudo) unimolecular reactions.The Menger-Portnoy model assumes rapid equilibration of the reactant of interest over bulk water and the micellar pseudophase with equilibrium constant K. The reaction then proceeds in both pseudophases with rate constants and in bulk water and the micellar pseudophase, respectively (Scheme 4). 

The effect of charge delocalization en route to the activated complex is the result of the relatively nonpolar micellar environment compared to bulk water, charges in the micellar pseudophase are less stabilized by interactions with their environment (cf. stabilization of developing charges by the electrostatically non-neutral environment for (pseudo) unimolecular reactions). This effect was found for the dehydro-bromination reaction of 2-(p-nitrophenyl) ethyl bromide and the dehydrochlorination of 1,1,1 -trichloro-2,2-bis(p-chlorophenyl)ethane. ... 

Problem 5 (a) What are pseudo-unimolecular reactions (Meerut 2000)... 

Reactions which are not unimolecular, but obey the first order rate expression are known as pseudo-unimolecular reactions. For example, hydrolysis of methyl acetate, inversion of cane sugar etc. are pseudo-unimolecular reactions. In general, when the order of reaction is generally less than the molecularity of a reaction, it is said to be a pseudo order reaction. 

Show that the hydrolysis of methyl acetate is a pseudo unimolecular reaction. 

SoL The reaction will be of the first order or pseudo unimolecular reaction if the data conforms to the first order rate expression... 

The decompositions of complex materials are treated as combinations of a series of parallel and/or consecutive pseudo-unimolecular reactions representing the rates of formation of the individual products. Detail is given [99,100] for pseudo-nth order and autocatalytic reaction types. 

The direction of radical reactions that involve competitive, mixed-order kinetics could be changed as dose rate is increased. Bimolecular reactions would be favored in competition with unimolecular (or pseudo-unimolecular) reactions, because of the higher instantaneous radical concentrations. This effect could be encountered in lipids and in polymers. It is responsible for the greater retention of vitamin B] (thiamin) in pork when irradiated with electron beams than when irradiated with gamma rays (Figure 1) [6]. 

At low pH values, when additional protons are present, the separation step becomes reversible and one observes homogeneous proton recombination. The reaction under these conditions undergoes a transition from unimolecular (correlated pairs) to a bimolecular (or pseudo-unimolecular) reaction. The rate of this recombination reaction is expected to diminish with increasing concentration of inert salt, which screens the Coulombic attraction between the proton and the anion. In fact, the classical Bronsted-Bjerrum theory of salt effects puts all of the effect in the recombination reaction while predicting zero salt effect on the dissociation direction [7]. 

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 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. 

The calculated pseudo-unimolecular rate constants (k) for the hydrolysis reaction [Fig. 3], clearly show the inhibiting effect of AMPS, relative to sodium acrylate at all three temperatures. 

Upon addition of a solution of sulfuric acid in D20 the reaction of A-acetoxy-A-alkoxyamides obeys pseudo-unimolecular kinetics consistent with a rapid reversible protonation of the substrate followed by a slow decomposition to acetic acid and products according to Scheme 5. Here k is the unimolecular or pseudo unimolecular rate constant and K the pre-equilibrium constant for protonation of 25c. Since under these conditions water (D20) was in a relatively small excess compared with dilute aqueous solutions, the rate expression could be represented by the following equation ... 

A distinction between "molecularity" and "kinetic order" was deliberately made, "Mechanism" of reaction was said to be a matter at the molecular level. In contrast, kinetic order is calculated from macroscopic quantities "which depend in part on mechanism and in part on circumstances other than mechanism."81 The kinetic rate of a first-order reaction is proportional to the concentration of just one reactant the rate of a second-order reaction is proportional to the product of two concentrations. In a substitution of RY by X, if the reagent X is in constant excess, the reaction is (pseudo) unimolecular with respect to its kinetic order but bimolecular with respect to mechanism, since two distinct chemical entities form new bonds or break old bonds during the rate-determining step. 

As pointed out before kuni is a pseudo first order rate constant. Since kuni/[M] is independent of [M], kuni/[M] is a second order rate constant at low pressure. It is significant and important for consideration of isotope effects that this second order rate constant for unimolecular reactions depends only on the energy levels of reactant molecules A and excited molecules A, and on the minimum energy Eo required for reaction. It does not depend on the energy levels of the transition state. There will be further discussion of this point in the following section. 

If reactions are not (pseudo) unimolecular but bimolecular, data analysis becomes considerably more complicated (higher order reactions will not be discussed here, but kinetic schemes can be derived following similar approaches). Two limiting cases can be discerned (1) the second reactant is a counterion to the surfactant or (2) the second reactant is a neutral molecule. 

Note that all the rate constants are unimolecular or pseudo-unimolecular (in the case of bimolecular processes like quenching or chemical reaction M + N-+P). 

This effect of N08 ion is quantitatively consistent with a reaction mechanism (43) in which N08 interacts with an electronically excited water molecule before it undergoes collisional deactivation by a pseudo-unimolecular process (the NOs effect is temperature independent (45) and not proportional to T/tj (37)). Equation 1, according to this mechanism, yields a lifetime for H20 of 4 X 10 10 sec., based on a diffusion-controlled rate constant of 6 X 109 for reaction with N08 Dependence of Gh, on Solute Concentration. Another effect of NOa in aqueous solutions is a decrease in GH, with increase in N08 concentration (5, 25, 26, 38, 39). This decrease in Gh, is generally believed to result from reaction of N08 with reducing species before they combine to form H2. These effects of N08 on G(Ce+3) and Gh, raise the question as to whether or not they are both caused by reaction of N08 with the same intermediate. 

As the values of k are nearly constant, the reaction is pseudo unimolecular. 

If the majority of reactions occur in the solid at 77°K and it is assumed that the energy flows into and out of the radical-molecule cage with a frequency, v, similar to that of the lattice vibrations (v = 10 sec ) then the extent of reaction at any time, t, is given by the first-order rate equation (pseudo-unimolecular)... 

Using the above equation, we can calculate the rate constant k for various values of AG, shown in Table 2.2. The half-life of a unimolecular reaction is equal to (In 2) k or 0.693/, and a reaction is 97% complete after five half-lives. Table 2.2 uses the formula ln(c7c) = kt to relate the rate constant, k, and the original concentration, c°, to the concentration, c, at time t seconds for a unimolecular reaction. Reactant concentrations are very important in a bimolecular reaction. If reactant B in a bimolecular reaction is in large excess, then its concentration will not change significantly over the course of the reaction and can be considered a constant, making the reaction pseudo-first order. We can then use the above formula to calculate the concentration of A at time t by substituting the pseudo-first-order rate constant, k = [B]. 

For Eq. (3.10) and Eq. (3.12) the bimolecular rate constants can be replaced with pseudo unimolecular rate constants within the limits of either fractional electron capture or constant positive ion concentration. All the above reactions take place on a time scale that is fast relative to the time required for transport through the detector. Under steady state conditions the electron capture coefficient K (see Eq. 3.7) is given by... 

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