Stable isotopes equilibrium isotope effects

A related approach is to study complexes formed with normal NAD+ but with an unreactive second substrate. An example is oxamate, which binds well to lactate dehydrogenase to form stable ternary complexes for which equilibrium isotope effects have been studied.39... 

A classic example of the application of an equilibrium isotope effect in oceanographic research is the use of stable oxygen isotope methods to estimate the temperature of an ancient environment in which a carbonate shell formed. The reaction on which this application is based is the equilibrium exchange of between CaC03(s) and water ... 

Equilibrium isotope effects The distribution of pairs of stable isotopes between reacting substances in accordance with the principles of chemical equilibria. 

One possibility for separating the contributions of primary sources with the same mass composition is to include stable isotope measurements. Isotope balances in addition to mass balances have been used with some success in areas where local sources dominate long-range transport effects(30). For isotope balances, fractionation factors cannot be considered unity. There is a fractionation effect between light and heavy isotopes for each physical-chemical change. For equilibrium between gas and liquid species and species of different oxidation states, the fractionation factors are fixed. 

The symbol MMI has exactly the same meaning as in expression for the equilibrium isotope effect (Eq. (17.4)), but the symbols ZPE and EXC are different. Without engaging in detailed derivation and development of Eq. (17.8), we can state that the contribution of ZPE and EXC are different in the transition state compared to product state, because the transition-state quantity contains contributions from only 3N-7 stable vibrations of the transition-stale and not from the single unstable (barrier-crossing) quasi-vibration (Stihnel Schowen, 1991). 

Saunders and coworkers have applied the isotopic perturbation technique to a number of persistent carbocations and have demonstrated that C—H hyperconjugation is a principal cause of P-secondary deuterium equilibrium isotope effects in stable carbocations. The results fully support the interpretation of secondary kinetic isotope effects in solvolytic substitution reactions. 

Equations (8) and (10) are applicable to stable isotope systems where isotopic fractionation occurs through mass-dependent processes which comprise the majority of cases described in this volume. These relations may also be used to identify mass-independent fractionation processes, as discussed in Chapter 2 (Birck 2004). Mass-dependent fractionation laws other than those given above distinguish equilibrium from kinetic fractionation effects, and these are discussed in detail in Chapters 3 and 6 (Schauble 2004 Yormg and Galy 2004). Note that distinction between different mass-dependent fractionation laws will generally require very... 

Figure 1. Translation, rotation, and vibration of a diatomic molecule. Every molecule has three translational degrees of freedom corresponding to motion of the center of mass of the molecule in the three Cartesian directions (left side). Diatomic and linear molecules also have two rotational degrees of freedom, about rotational axes perpendicular to the bond (center). Non-linear molecules have three rotational degrees of freedom. Vibrations involve no net momentum or angular momentum, instead corresponding to distortions of the internal structure of the molecule (right side). Diatomic molecules have one vibration, polyatomic linear molecules have 3V-5 vibrations, and nonlinear molecules have 3V-6 vibrations. Equilibrium stable isotope fractionations are driven mainly by the effects of isotopic substitution on vibrational frequencies.

The importance of equilibrium versus kinetic effects has yet to be addressed in any coherent way by the limited laboratory experiments conducted for Li isotope study. It is clear from the study of other stable isotope systems that kinetic effects may dominate the fractionation pathways under many circumstances (e.g., Johnson and Bullen 2004), especially in laboratory simulations of low-temperature natural phenomena (Beard and Johnson 2004). The clarification of how kinetic effects on Li isotopic compositions are manifested remains a major area for future study in natural, synthetic and theoretical systems. 

In Guo, after the very fast protonation of the electron adduct by water at the heteroatom [k > 107 s 1, von Sonntag 1991 Candeias et al. 1992 at 0(6), N(3) or N(7), cf. reaction (180)], a rapid transformation occurs [reaction (181) k in H20) = 1.2 x 106 s k(in D20) = 1.5 x 10s s 1] which is also catalyzed by phosphate buffer (k = 5.9 x 107 dm3 mol-1 s 1) which has been attributed to a protonation at C(8) (Candeias et al. 1992). This assignment is based upon solid-state EPR data, where C(8)-H--adduct is the thermodynamically most stable H -adducl radical (Rakvin et al. 1987 for DFT calculations see Naumov and von Sonntag, unpubl. results). The high solvent kinetic isotope effect of ku/ko = 8 is a strong indication that a proton is transferred in the rate-determining step. The magnitude of the rate of phosphate buffer catalysis points to a protonation at carbon (for a similar reaction observed with the Thy radical anion see Table 10.20). The C(8)-H -ad-duct has a pKa value of 5.4 [equilibrium (182)]. 

Isotopic fractionation selective removal of the lighter or heavier stable isotope in a sample due to both kinetic and equilibrium effects. 

Stable isotope fractionation was predicted and calculated by Urey and coworkers as early as 1932. Bigeleisen (1961) dealt with the statistical mechanics of isotope effects. Hydrogen isotope fractionation is mainly connected with the processes in the hydrosphere, but its equilibrium and kinetic effects were also studied for water of crystallization, ore-forming fluids, as represented by liquid inclusions, and biological cycles. 

In the case of the stable isotopes of carbon, and C, two isotope effects are noticeable the kinetic isotope effect in photosynthesis, leading to an enrichment of in plants, and the equilibrium isotope effect in the exchange reaction... 

There were several key observations, which were made almost around the same time, that led to studies in the fields of stable isotope geochemistry and cosmochemistry. First, it was the physicochemical formalism for isotope effects, particularly the determination of the position of equilibrium in isotopic exchange reactions. Urey (1947) and Bigeleisen and Mayer (1947) demonstrated that the position of isotope exchange in a chemical reaction may be calculated with high precision. The difference in chemical behavior for... 

Much of what is currently understood about the Cenozoic history, of deep-sea temperature, carbon chemistry, and global ice volume, has been gleaned from the stable isotope ratios of benthic foraminifera. Benthic foraminifera extract carbonate and other ions from seawater to construct their tests. In many species, this is achieved near carbon and oxygen isotopic equilibrium. Kinetic fractionation effects tend to be small and constant (Grossman, 1984, 1987). As a result, shell fi C and strongly covary with the isotopic... 

Mickler, P.J., Banner, J.L., Stem, L., Asmerom, Y., Edwards, R.L. Ito, E. (2004) Stable isotope variations in modem tropical speleothems evaluating equilibrium vs. kinetic effects. Geochimica et Cosmochimica Acta 68, 4381-4393. 

In Table 12 the distribution of sodium ions between water and chloroform (referred to g HjO/g CHCI3) is presented in dependence on the different polyethers. All results were obtained under analogous conditions with 0.1 mmol Na and 0.1 mmol polyether in the system where the pH-value was established to be 8 by adding 10 mmol of tetraethylammonium chloride. The establishment of the equilibrium requires less than 60 min in all systems and was followed by the y-activity of the sodium isotopes and the P-activity of C-labeled polyethers. The enrichment of one of the sodium isotopes in a practical scale from a Na/ Na-mixture can only be achieved in a system where the distribution ratio (Na ),/(Na ) g is not too high. However, in contrast to the enrichment of stable isotopes from a sample with natural isotope abundance, the enrichment of Na or of Na from an isotopic mixture is not of great importance because these two isotopes can be produced by nuclear reactions. On the other hand, the investigations on sodium isotopic separations are of common interest in respect to further knowledge about isotopic effects. 

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