Pseudo-unimolecular

Pseudo-unimolecular rate constants measured at various temperatures, one of which is tabulated. 

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. 

Pseudo-unimolecular rate constant in sec. f Water was added to absolute ethanol to make 99.8% ethanol. 

Plots of the concentration of carboxylate formed vs. time were drawn for each copolymer, and the initial rates of hydrolysis were determined by measurement of the slope of the tangent to the curve at zero time. The pseudo-unimolecular rate constant (K) is given by ... 

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. 

The first indication that A-acyloxy-A-alkoxyamidcs reacted by an acid-catalysed process came from preliminary H NMR investigations in a homogeneous D20/ CD3CN mixture, which indicated that A-acetoxy-A-butoxybenzamide 25c reacted slowly in aqueous acetonitrile by an autocatalytic process according to Scheme 4 (.k is the unimolecular or pseudo unimolecular rate constant, K the dissociation constant of acetic acid and K the pre-equilibrium constant for protonation of 25c).38... 

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 ... 

Pseudo unimolecular rate constants k for sulfuric acid-catalysed solvolysis of 25c in CD3CN/D20 (adjusted to a constant ratio of 3.8 1) were found to be linearly dependent upon the acid concentration (Fig. 11) and the gradient afforded a composite rate constant of (2.41+0.10) x 10 2lmol 1 s-1 at 308K. From the intercept, ka, the rate constant for uncatalysed solvolysis, was at least three orders smaller and zero within experimental error. A similar linear dependence and near-zero uncatalysed rate constant was demonstrated for other /V-acetoxy-TV-alkoxybenzamides given in Table 3. 

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. 

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). 

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. 

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. ... 

Two points should be noted (1) Because the rate constants are pseudo-unimolecular, there is a concentration dependence, so ka and koff may be resolved without the amplitude factor. (2) There is a lower limit to 1/r that is, 1/t cannot be less than koS. This sets a limit on the measurement of these rate constants. A good stopped-flow spectrophotometer can cope only with rate constants of 1000 s 1 or less, and many enzyme-substrate dissociation constants are faster than this. 

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. 

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... 

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

The lifetime of the excited state (i°) is equal to the reciprocal of the sum of the (pseudo)unimolecular rate constants of all processes that cause the decay ... 

The results of the kinetic studies have been summarized (85H1765) they are usually conducted in chlorobenzene at 100°C under pseudo-unimolecular conditions (Scheme 117). 

Lifetime (t) The lifetime of a molecular entity which decays in a first-order process is the time needed for a concentration of the entity to decrease to 1/e of its original value. Statistically, it represents the life expectation of the entity. It is equal to the reciprocal of the sum of the (pseudo)unimolecular rate constants of all processes which cause the decay. Lifetime is used sometimes for processes which are not first order. However, in such cases, the lifetime depends on the initial concentration of the entity, or of a quencher and therefore only an initial or a mean lifetime can be defined. In this case it should be called apparent lifetime, instead. Occasionally, the term half-life (T1/2) is used, representing the time needed for the concentration of an entity to decrease to one half of its original val-... 

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)... 

For example, if kplk, = 103 mol L, the ultimate conversion will be 1%, 10%, 63%, and 99.9% for [I] = 10 5 mol/L, I0 4 mol/L, 10 3 mol/L, and 10 2 mol/L, respectively. Thus, the ratio kp/k, can be obtained by determining the monomer conversion as a function of the concentration of initiator, assuming that initiation is quantitative. The same equation can be applied when termination is pseudo-unimolecular, and excess terminating agent, T, reacts slowly with active species. In this case, k, should be substituted with /t,-[T]0. If transfer is a prerequisite for termination, it may become the rate-determining step, and the actual termination may not be kinetically measurable. 

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