Isotope reactions

Janecky, D.R. and Shanks, W.C. Ill (1988) Computational modeling of chemical and sulfur isotopic reaction processes in seafloor hydrothermal systems, chimney, massive sulfides, and subjacent alteration zones. Can. Mineral, 26, 805—826. 

The ratio of the quantum partition functions (Eq. (4-29)) for two different isotopes can be obtained directly through free energy perturbation (FEP) theory by perturbing the mass from the light isotope to the heavy isotope. Consequently, only one simulation of a given isotopic reaction is performed, while the ratio of the partition function, i.e., the KIE, to a different isotopic reaction, is obtained by FEP. This is conceptually and practically an entirely different approach than that used previously [23]. 

Figure Schematic diagram to show the reorganization energy for isotopic reactions for harmonic free energy profiles. Ci i, and Gf, represent the initial (reactant) and the final (product) system free energy respectively.

Figure 3. For the same reaction, different values of reorganization energy are found if the free profile is harmonic (.ipin (a) or Morse type (Ap in (b) where /t] (harmonic) X2 (Morse). Cm, and G( represent the initial (reactant) and the final (product) system free energy, respectively. Fcr the Morse free energy profile, AG A2/4 for the isotopic reaction in (b).

Also, a rigorous treatment of isotope effects within the framework of QET reveals that the assumption /muZ/mD = hZZ d represents a simplification. [69] It is only valid for when the species studied populate a small internal energy distribution, e.g., as metastable ions do, whereas wide internal energy distributions, e.g., those of ions fragmenting in the ion source after 70 eV electron ionization, may cause erroneous results. This is because the fc(E) functions of isotopic reactions are not truly parallel, [76] but they fulfill this requirement over a small range of internal energies (Figs. 2.17 and 2.18)... 

In the homogeneous case, the derivation of an activation-driving force relationship and of an expression of the intrinsic barrier is less straightforward. It is interesting in this connection to relate the kinetics of crossexchange reactions (31) to those of the two self-exchange reactions (also called identity or isotopic reactions) [(32) and (33)]. 

Quantitatively, many observed deviations from simple equilibrium processes can be interpreted as consequences of the various isotopic components having different rates of reaction. Isotope measurements taken during unidirectional chemical reactions always show a preferential emichment of the lighter isotope in the reaction products. The isotope fractionation introduced during the course of an unidirectional reaction may be considered in terms of the ratio of rate constants for the isotopic substances. Thus, for two competing isotopic reactions... 

Comment After you have solved the problem, you should find that ACr° is much smaller for isotopic exchange reactions than for "normal" chemical reactions. Sometimes AC/ for a reaction is called the driving force for the reaction, and the reaction rate is assumed to be proportional to AC/. Because isotopic reactions are not any slower than chemical reactions, you can see that the driving force concept defined this way is not very helpful.)... 

Fig. 7.63. Influence of zero-point energies on isotopic reaction rate.

In some presentations this equation has been applied to isotopic reactions in solution. There is in effect a negligible AG° if the redox ions in equilibrium are isotopes. Thus, one could find in solution "iA2+ + "2A3+ - " A3+ + "lA2 With AG = 0,... 

Marcus stressed that only harmonic modes U = were involved in the ion-solvent interactions and went further than Weiss in formulating a simple equation for the rate of adiabatic electron transfer, taking the case of an isotopic reaction so that the AG° term was eliminated. Under this condition and using Eq. (9.32), the current density (or electrochemical reaction rate) at a given overpotential t], in the cathodic direction (T] is negative) is... 

What conditions would be necessary for (9.38) to give Tafel s law (9.36) and replicate the Butler-Volmer equation (Section 7.2.3) Suppose (as with isotopic reactions) AG° = 0, then,... 

The theory of IEs was formulated by Bigeleisen and Mayer.9 The IE on the acid-base reaction of Equation (1) is defined as the ratio of its acidity constant KA to the acidity constant of the isotopic reaction, Equation (2). The ratio KJ KA is then the equilibrium constant XEIE for the exchange reaction of Equation (3). That equilibrium constant may be expressed in terms of the partition function Q of each of the species, as given in Equation (4), which ignores symmetry numbers. 

It is important to note that these equations are based on the Swain-Schaad relationship, which assumes that there is no tunnelling in any of the isotopic reactions (the KIEs are semiclassical) and that the relationship between the KIEs is determined only by the masses of the hydrogen, deuterium and tritium atoms. The secondary and kfyko KIEs calculated both with and... 

L. Ya. Karpov Physicochemical Institute, Isotope Reaction Laboratory, Moscow, U.S.S.R. 

The present paper is a brief review of investigations concerned with the study of hydrogen exchange in liquid ammonia, which have been carried out by the author in collaboration with Yu. P. Vyrskii, N. M. Dykhno, E. A. Izrailevich, E. A. Yakovleva, E. N. Zvyagintseva, A. V. Vedeneev, Yu. I. Ranneva, and other workers at the Isotope Reaction Laboratory. 

The appearance of methane relatively enriched in 13C during ethane oxidation may seem surprising but can be explained by the isotopic reaction sequence... 

To digress, the method of internal reference is a device for making interpretation of intermolecular isotope effects on ion abundances more sound, even if not watertight. What is done is to use as an internal reference a reaction whose rate coefficient, kREF(E), is not expected to be affected by the isotope substitution. The product abundance for the isotopic reaction of interest in each molecule is divided by the product abundance for the reference reaction in that molecule (intramolecular comparison). These normalised abundances for the different molecules are then compared to give the isotope effects (intermolecular comparison). 

The usual situation, however, is that the log10[fe( )] vs. E curves for the reference reaction and those of the isotopic reactions of interest are not parallel. In this more general case, the abundance ratios 7j/7REF(j) and 7u/7REF(n) will represent some sort of averages of the ratios of rate coefficients ki(E)/kREF(E) and kn(E)/kREF(E) (see Sect. 7.1), but there is no assurance that the averages are comparable. 

The photodissociation rate coefficients are included as source and sink terms in a system of time-dependent continuity equations for the atmosphere. Modem values for vertical (eddy) diffusion and solar photon flux are utilized. The system of 2nd-order ordinary differential equations is solved by integration, and yields chemical species abundances as a function of time and altitude. The isotope atmospheric chemistry includes only SO2 isotopologue photodissociation reactions and production of SO isotopologues. Additional isotopic reactions such as SO2 oxidation by OH, SO photolysis, SO disproportionation during self-reaction, and SO dimmer formation, have been neglected. My objective here is to focus only on SO2 photolysis as a S-MIF mechanism. 

Catalyst Isotope Reaction Temp. C. for Measurable Rates Reference... 

Chemical, physical, and biological processes can be viewed as either reversible equilibrium reactions or irreversible unidirectional kinetic reactions. In systems out of chemical and isotopic equilibrium, forward and backward reaction rates are not identical, and isotope reactions may, in... 

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