Kinetically equivalent terms

Kilocalories, 14 conversion of, 246 Kilojoules, 14 conversion of, 246 Kinetically equivalent terms, 123 Kinetically indistinguishable terms, 123 Kinetic equivalence, 123, 136, 217, 349 in intramolecular catalysis, 267 salt effect and, 411 Kinetic isctdpe effects, 292 primaiy, 293 secondary, 298 solvent, 300... 

The rate terms A [HA] and A [H ][A ] are said to be kinetically equivalent or kinetically indistinguishable. There is no purely kinetic basis upon which to make a choice between them in Chapter 5 we will see why this is so, but a simple interpretation is that the two terms describe equivalent chemical compositions of atoms and charges. 

In these circumstances a decision must be made which of two (or more) kinet-ically equivalent rate terms should be included in the rate equation and the kinetic scheme (It will seldom be justified to include both terms, certainly not on kinetic grounds.) A useful procedure is to evaluate the rate constant using both of the kinetically equivalent forms. Now if one of these constants (for a second-order reaction) is greater than about 10 ° M s-, the corresponding rate term can be rejected. This criterion is based on the theoretical estimate of a diffusion-controlled reaction rate (this is described in Chapter 4). It is not physically reasonable that a chemical rate constant can be larger than the diffusion rate limit. 

In Section 3-3 we discussed the problem of kinetically equivalent rate terms. Suppose one of the rate constants evaluated for such a rate equation were larger than the diffusion-limited value this is a reasonable basis upon which to reject the formulation of the rate equation leading to this result. Jencks has given examples of this argument. 

Three kinetically equivalent rate terms involving intramolecular participation are shown in Table 6-3 with representations of appropriate transition states (mechanisms). Differentiation among these possibilities can be difficult. 

Finally we should note that the demonstration of a Br nsted relationship does not constitute proof that general acid or general base catalysis is occurring. Because of the problem of kinetic equivalence of rate terms, we may not be able unequivocally to distinguish between these possibilities ... 

The mechanisms available to intramolecular reactions are the same as those of intermolecular reactions. The same problems of kinetic equivalence of rate terms may arise, and Table 6-3 shows some kinetically equivalent mechanisms for intramolecular reactions of the acyl function. The efficiency of intramolecular reactivity may be difficult to assess. One technique, described above as a method for the detection of an intramolecular reaction, is to make a comparison with an analog incapable of the intramolecular process. Thus p-nitrophenyl 5-nitrosalicylate, 17, hydrolyzes about 2500 times faster than p-nitrophenyl 2-methoxy-5-nitrobenzoate, 18. 

An important cautionary note must be inserted here. It may seem that the study of the salt effect on the reaction rate might provide a means for distinguishing between two kinetically equivalent rate terms such as k[HA][B] and k [A ][BH ], for, according to the preceding development, the slope of log k vs. V7 should be 0, whereas that of log k vs. V7 should be — 1. This is completely illusory. These two rate terms are kinetically equivalent, which means that no kinetic experiment can distinguish between them. To show this, we write the rate equation in the two equivalent forms, making use of Eq. (8-26) ... 

Although their results for uncatalyzed oxidation agree with those of other workers, the results in the presence of N02 do not. Furthermore, the proposed mechanism leads to a rate law with an additional factor of two in the far right-hand term. The combination of rate constants kBK2,-2 41,-41 is kinetically equivalent to k.1<, which leads to a value of 2k i6 = 1.28 x 104 AT-2 sec 1 from their data. This value is 100 times as large as the value found by Ray and Ogg357 and 64 times as large as the value deduced by Ashmore and Burnett.8... 

Under what conditions will these mechanisms fit the experimental data and be kinetically equivalent Hint consider the denominator and the mathematical and chemical significance of each term. 

Base hydrolysis of an ester in presence of metal ions, metal ion catalysis - analysis in terms of kinetically equivalent mechanisms, 330-331 Acid hydrolysis of a charged ester in the presence of SC>4 (aq) anion catalysis - analysis in terms of kinetically equivalent mechanisms, 332-336 Decarboxylation of /3-ketomonocarboxylic acids - formulation of the rate expression from the mechanism, 339-341... 

The mechanistic significance of the terms in Eq. (27) for pseudobase decomposition must, of course, be the microscopic reverse of the interpretations given for the pseudobase formation reactions. Thus, k,[H+] is the microscopic reverse of the kHl0 term, and may be formally interpreted as either the spontaneous loss of a molecule of water from the O-protonated pseudobase (i.e., specific-acid catalysis transition state C) or alternatively as elimination of hydroxide ion from the neutral pseudobase molecule with the aid of H30+ as a general-acid catalyst (transition state D). The k2 term is the microscopic reverse of fc0H[OH ], and so formally represents either the spontaneous decomposition of the pseudobase to heterocyclic cation and hydroxide ion (transition state A) or the kinetically equivalent general-acid catalysis of this reaction by a water molecule (transition state B). 

An important cautionary note must be inserted here. It may seem that the study of the salt effect on the reaction rate might provide a means for distinguishing between two kinetically equivalent rate terms such as and [A"][BH ],... 

The correction term r accommodates the fact, as yet unexplained, that extrapolation at constant pH to zero [phosphate] gives a rate higher than in the actual absence of phosphate. With carbonate at pH greater than 10 there are considerable deviations from second-order kinetics. They need more study. In almost all cases EDTA was present at low concentration. It appears to have been effective in suppressing side reactions. The mechanism of the uncatalysed reaction is likely to involve (7) and (8) or their kinetic equivalents... 

There are several possible approaches to simplifying the vibrational Hamiltonian given by Eq. (3.13). Some of these will be outlined here. The first approach consists of removing the harmonic potential energy cross terms and the kinetic energy terms by the equivalent of a normal coordinate transformation. We define a new set of coordinates Q... 

Eq. (5.A37) is equivalent to supposing that the motion in Q is sufficiently slow that its kinetic energy term P cannot induce transitions between various levels n) of the rapid motion. Mathematically it means that all matrix elements of P of the form m P n are zero, unless m = n, in which case it is then equal to P (it still acts on a wavefunction of the slow motion on its right hand). This is the basis of the Bom-Oppenheimer separation between electrons and nuclei in molecules. We may then write, supposing that the electric dipole moment ju(0) displays a linear dependence on normal mode q, an approximation called electrical harmonicity that reveals excellent for most molecular systems... 

When performing calculations or an experiment, it is the total pressure drop that is calculated or measured. When the analytic expressions for pressure drop in both tubes are subtracted, what remains is the excess pressure drop due to the contraction. The change of kinetic energy can be calculated so that the remaining term, viscous dissipation, is readily available. As seen in Fig. 8.4, the viscous term predominates at low Reynolds numbers (i.e., in microfluidics) whereas the kinetic energy term predominates at high Reynolds number (> 100). The equivalent expressions for other geometries are ... 

An asterisk is applied in order to distinguish this collision term from the original coagulation function. In addition, r2 is replaced by r. The diffusion coefficient can also be replaced by the gas kinetic equivalent expression... 

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