Isotopic reaction path

One of the possibilities is to study experimentally the coupled system as a whole, at a time when all the reactions concerned are taking place. On the basis of the data obtained it is possible to solve the system of differential equations (1) simultaneously and to determine numerical values of all the parameters unknown (constants). This approach can be refined in that the equations for the stoichiometrically simple reactions can be specified in view of the presumed mechanism and the elementary steps so that one obtains a very complex set of different reaction paths with many unidentifiable intermediates. A number of procedures have been suggested to solve such complicated systems. Some of them start from the assumption of steady-state rates of the individual steps and they were worked out also for stoichiometrically not simple reactions [see, e.g. (8, 9, 5a)]. A concise treatment of the properties of the systems of consecutive processes has been written by Noyes (10). The simplification of the treatment of some complex systems can be achieved by using isotopically labeled compounds (8, 11, 12, 12a, 12b). Even very complicated systems which involve non-... 

The differences in rate for the two positions of naphthalene show clearly that an additional-elimination mechanism may be ruled out. On the other hand, the magnitude of the above isotope effect is smaller than would be expected for a reaction involving rate-determining abstraction of hydrogen, so a mechanism involving significant internal return had been proposed, equilibria (239) and (240), p. 266. In this base-catalysed (B-SE2) reaction both k and k 2 must be fast in view of the reaction path symmetry. If diffusion away of the labelled solvent molecule BH is not rapid compared with the return reaction kLt a considerable fraction of ArLi reacts with BH rather than BH, the former possibility leading to no nett isotope effect. Since the diffusion process is unlikely to have an isotope effect then the overall observed effect will be less than that for the step k. ... 

As originally derived, however, the mass balance model has an important (and well acknowledged) limitation implicit in its formulation is the assumption that fluid and minerals in the modeled system remain in isotopic equilibrium over the reaction path. This assumption is equivalent to assuming that isotope exchange between fluid and minerals occurs rapidly enough to maintain equilibrium compositions. 

Integrating isotope fractionation into the reaction path calculation is a matter of applying the mass balance equations while tracing over the course of the reaction path the system s total isotopic composition. Much of the effort in programming an isotope model consists of devising a careful accounting of the mass of each isotope. 

The model traces the reaction path by taking a series of steps along reaction progress, moving forward each step from i to 2- Over a step, the system s isotopic composition can change in two ways reactants can be added or removed, and segregated minerals can dissolve. 

We can predict the oxygen and carbon isotopic compositions of the dolomite produced by this reaction path, using the techniques described in Chapter 19. Figure 25.4 shows the compositions of calcite and dolomite cements in the Lyons, as determined by Levandowski et al. (1973). The calcite and dolomite show broad ranges in oxygen isotopic content. The dolomite, however, spans a much narrower range in carbon isotopic composition than does the calcite. 

Kelley and co-workers [70, 71] measured the dynamics of the excited-state intramolecular proton transfer in 3-hydroxyflavone and a series of its derivatives as a function of solvent (Scheme 2.9). The energy changes associated with the processes examined are of the order of 3 kcal/mol or less. The model they employed in the analysis of the reaction dynamics was based upon a tunneling reaction path. Interestingly, they find little or no deuterium kinetic isotope effect, which would appear to be inconsistent with tunneling theories. For 3-hydroxy-flavone, they suggest the lack of an isotope effect is due to a very large... 

The alkene loss from ionized cycloalkyl-substituted nitrobenzenes has been studied by isotopic labelling and collision activation mass spectrometry77. The reaction path was found to depend highly on the placement of the nitro group. The ortho nitro-substituted phenylcyclopropane and its isotopomers were studied. 

Kinetic fractionations can occur when there is incomplete isotopic exchange between the different phases present in a system. A thorough introduction to kinetic stable isotope fractionation theory is unfortunately beyond the scope of the present review. Flowever, it is useful to include a brief discussion of some basic aspects, particularly in comparison to equilibrium fractionation theory. A simple example of kinetic fractionation is the evaporation of a liquid water droplet into a vacuum, in this example FljO molecules entering the gas phase are physically removed from the vicinity of the droplet, so there is no chance for isotopic equilibration between vapor-phase molecules and the residual liquid. Isotopic fractionation in this case is determined by a one-way reaction path, and will not, in general, be the same as the fractionation in a system where vapor-phase molecules are able to equilibrate and exchange with the liquid. In other reactions, isotopic exchange is limited by an energy barrier—an... 

Isotope studies also provide some intriguing hints at the mechanism. As seen in Fig. 7.7, when isotopically labeled H2I80 is used at concentrations at or above 5 X 103 ppm, Hl8ONO is formed initially (Sakamaki et al., 1983). Below this concentration, both Hl8ONO and HON18 O are formed, suggesting that there may be more than one reaction path (Svensson et al., 1987). 

The precise nature of the reaction path is ambiguous, because the same products would be obtained regardless of whether an oxygen atom or a chlorine atom were transferred. As they pointed out in their paper, this ambiguity can be resolved by using nitryl chloride with isotopically labeled nitrogen. Pertinent to this question are the calculations of Herschbach, Johnston, Pitzer, and Powell,199 who computed pre-exponential factors based on two alternative activated complexes... 

Chemical isotope effects are divided into two classes—those affecting the position of the equilibrium in a chemical reaction and those affecting the rate of a chemical reaction. Equilibrium isotope effects have their origin in the fact that the extent to which any chemical reaction goes is governed by the number of possible ways it can proceed (the phase space available). The more equally probable reaction paths available, the more likely the reaction will go. To illustrate this point, consider the exchange reaction... 

The comparison of the catalytic performances of metals and their alloys is sometimes hampered by the different degree of deactivation by carbonaceous residues (107, 67). Therefore, it seems appropriate to start with a discussion of the exchange reactions of the hydrogen isotopes protium and deuterium on platinum and Pt-Au films (31). A comparison of this reaction on platinum and its alloy shows that of the two reaction paths possible on platinum in the temperature region studied, one remains unchanged on the alloy but the other, which prevails on platinum except at very low temperatures, seems... 

The use of isotopic tracers has demonstrated that the selective oxidation of propylene proceeds via the formation of a symmetrical allyl species. Probably the most convincing evidence is presented by the isotopic tracer studies utilizing, 4C-labeled propylene and deuterated propylene. Adams and Jennings 14, 15) studied the oxidation of propylene at 450°C over bismuth molybdate and cuprous oxide catalysts. The reactant propylene was labeled with deuterium in various positions. They analyzed their results in terms of a kinetic isotope effect, which is defined by the probability of a deuterium atom being abstracted relative to that of a hydrogen atom. Letting z = kD/kH represent this relative discrimination probability, the reaction paths shown in Fig. 1 were found to be applicable to the oxidation of 1—C3He—3d and 1—QH —1 d. 

VRI, the actual reaction path bifurcates into two products before reaching TS7. The rate is determined by TS6, whereas the product ratio is controlled by the shape of the PES near the VRI point and TS7. Thus, a question arises how the product selection occurs when a subtle perturbation, such as isotopic substitution, is introduced and two symmetrical products become asymmetric ... 

A number of mechanistic problems remain, after accepting that the encounter pair ArNH2.NO is formed by pre-association. One such problem concerns whether the rate-determining step is the proton transfer or the reaction of the nitronium ion with the free amine formed within the encounter pair. It seems likely that the latter view is true from consideration of the rate profile, the very short half-life of the free amine, and the fact that these reactions do not show a marked primary hydrogen isotope effect when the rates in H2S04 and D2S04 are compared the reduction in rate by a factor of 2-3 in the deuterated solvent (Hartshorn and Ridd, 1968) is consistent with the lower concentration of the free amine. The reaction path can then be written as shown in Scheme 7 where NOJ. ArNHJ. B is an encounter triplet . 

Isotopic analysis of the L q] P. obtained from the reaction of PC1 with H 0 shows that the label is incorporated quantitatively into the P, and confirms the assumption that the incorporation is a random process. This assumption furnishes the basis for translating t g isotopic composition of the P. obtained from hydrolysis of Ly- 0]ATP into the isotopic composition of the ATP and the contributions of the various reaction paths that participate in the hydrolysis. Thusjgwe have typically obtained an isotopic enrichment of 96 atom %. -0 in the Y-phosphoryl group of the[y- Ql ATP synthesized from [ 0]P of 99 atom %... 

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