Kinetic Equivalence of Rate Terms

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. 

Another example is a second-order term containing the concentration of an acid and a base, say 

When the elements of the solvent are involved, as in hydrolysis reactions in 

The elements of water are omitted because the concentration of water cannot be varied and, therefore, is not explicitly included in the rate equation. A complete kinetic scheme requires only reactions 1, 2, 4, 7, and 9 the other reactions are superfluous. For example, the rate term k3[H2A][OH ] is equivalent to k4[HA-], as is the term kg[H ][A -]. 

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. 

---

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. 

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. 

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) ... 

Thus the observed rate coefficient is equivalent to feiA 2/fc i. Because of the limitations of the kinetic procedure, there is some small doubt over the inclusion of a term in Ce(IV) concentration in the denominator of (12.4). However, the relative insignificance of this term means that A i[Ce(III)] > A 2[Ce(IV)]. Also, the inequality A 3[Ce(rV)] 2[Ce(Iir)] is a consequence of the observed kinetics. As in the Cr(VI)-l-Fe(II) system , the slow stage involves the inter-... 

In turbulent flow, there is direct viscous dissipation due to the mean flow this is given by the equivalent of equation 1.98 in terms of the mean values of the shear stress and the velocity gradient. Similarly, the Reynolds stresses do work but this represents the extraction of kinetic energy from the mean flow and its conversion into turbulent kinetic energy. Consequently this is known as the rate of turbulent energy production ... 

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... 

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... 

A manometric technique was used to measure the rate of pressure rise which in turn is a measure of the rate of formation of volatile products produced during the thermal decomposition of hydrazinium monoperchlorate and hydrazinium diperchlorate. Kinetic expressions were developed, temperature coefficients were determined, and an attempt was made to interpret these in terms of current theories of reaction kinetics. The common rate-controlling step in each case appears to be the decomposition of perchloric acid into active oxidizing species. The reaction rate is proportional to the amount of free perchloric acid or its decomposition products which are present. In addition the temperature coefficients are similar for each oxidizer and are equivalent to that of anhydrous perchloric acid. 

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... 

The absolute value of the first term on the right-hand side of Eq. (156) is at maximum equal to (DA/V)C /5conv where C is the bulk concentration of the electroactive reactant (Sec. IV.B). The electrode consumption or production is then equivalent to pseudo-first-order kinetics whose apparent rate constant is at maximum equal to... 

---