Isotope effects fraction factors

Figure 7. Mo concentotions (o) and isotopic compositions ( ) from reducing pore fluids in Santa Monica Basin (McManus et al. 2002). Dotted line indicates seawater values for both variables. The data can be fit by a 1-D reaction-diffusion model wifli a fractionation factor of —1.005. The effective fractionation factor for Mo removal across tiie sediment-water interface is smaller, <1.0025 (see text).

An important consequence of such a model is that the effect of such sedimentary systems on the ocean Mo isotope budget is not represented by a, but rather by the relative fluxes of the isotopes across the sediment-water interface. This effective fractionation factor, is likely to be smaller than a (Bender 1990 Braudes and Devol 1997) because the diffusive zone acts as a barrier to isotope exchange with overlying waters, approximating a closed system. 

Sulfur isotope relative fractionation factors between various minerals and py-rite are shown in figure 11.40. As we can see, the isotopic compositions of sulfates reflect the relative fractionation effects induced by the 804 groups (compare figures 11.40 and 11.39). 

Although isotope exchange occurs among all the species in the gas and liquid phase, it has been shown previously (29, 30 31) that the effective fractionation factor can be evaluated in terms of three independent exchange reactions ... 

This formulation assumes negligible isotope effect between the same species in the gas and liquid phase and between N2O3 and N2O4 which are assumed to be the principal species in the liquid phase. Further, if the concentration of is small compared with that of the effective fractionation factor a can be expressed in terms of i3, 2.s, and 43 as follows (30, 31)... 

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. 

It is interesting to note that these data (amply confirmed with many additional experiments on uranium and other systems) show that the temperature dependence and the odd-even mass ratios of isotope-exchange fractionation factors of uranium and other metals differ significantly from the predictions of the well-established theory of isotope effects based on vibrational properties (Bigeleisen and Mayer 1947). That observation, one of theoretical importance, has been shown to be a consequence of the large nuclear isotope field shifts found in the heavy elements. The field shifts introduce new mechanisms for understanding the... 

Fig. 3. Operational equation of radioactive deoxyglucose method in comparison to the general equation for measurement of the reaction rates with tracers. T represents the time at the termination of the experimental period X equals the ratio of the distribution space of deoxyglucose in the tissue to that of glucose equals the fraction of glucose which, once phosphorylated, continues down the glycolytic pathway Km, Vm and Km, Vm represent the familiar Michaelis-Menten kinetic constants of hexokinase for deoxyglucose and glucose, respectively. These six constants collectively constitute the lumped constant (equivalent to the isotope-effect correction factor of the general equation). The other symbols are the same as those defined in Fig. 2. (Reproduced with permission from Sokoloff, 1978.)...

Kinetic isotope effects are an important factor in the biology of deuterium. Isotopic fractionation of hydrogen and deuterium in plants occurs in photosynthesis. The lighter isotope is preferentially incorporated from water into carbohydrates and tipids formed by photosynthesis. Hydrogen isotopic fractionation has thus become a valuable tool in the elucidation of plant biosynthetic pathways (42,43). 

Isotope ratios for and Cl were measured for the aerobic degradation of dichlorometh-ane by a methanotroph MC8b (Heraty et al. 1999). Values of the fractionation factor (a) were 0.9586 for carbon and 0.9962 for chlorine, and kinetic isotope effects were 1.0424 for carbon and 1.0038 for chlorine. 

Figures 7-9 show the fractional conversion of methanol in the pulse as a function of temperature for the three catalysts and the three methanol feeds. Evidently the kinetic isotope effect is present on all three catalysts and over the complete temperature range, indicating that the rate limiting step is the breaking of a carbon-hydrogen bond under all conditions. From these experiments, the effect cannot be determined quantitatively as in the case of the continuous flow experiments, but to obtain the same conversion of CD,0D, the temperature needs to be 50-60° higher. This corresponds to a factor of about three in reaction rate. The difference in activity between PfoCL and Fe.(MoO.), is larger in the pulse experiments compared to tHe steady stateJ results.

Further evidence for the Aa11 mechanism was obtained from a solvent kinetic isotope study. The theoretical kinetic isotope effects for intermediates in the three reaction pathways as derived from fractionation factors are indicated in parentheses in Scheme 6.143,144 For the Aa11 mechanism (pathway (iii)) a solvent KIE (/ch2o A d2o) between 0.48 and 0.33 is predicted while both bimolecular processes (pathways (i) and (ii)) would have greater values of between 0.48 and 0.69. Acid-catalysed hydrolysis of ethylene oxide derivatives and acetals, which follow an A1 mechanism, display KIEs in the region of 0.5 or less while normal acid-catalysed ester hydrolyses (AAc2 mechanism) have values between 0.6 and 0.7.145,146... 

The secondary deuterium KIEs obtained by converting the secondary tritium KIEs found for the E2 reactions of several different 2-arylethyl substrates into secondary deuterium KIEs with the Swain-Schaad equation (Swain et al., 1958) are in Table 36. As discussed above, one would expect the secondary deuterium isotope effect to reflect the extent to which rehybridization of the /3-carbon from sp3 of the reactant to sp2 in the product has taken place in the transition state. According to this reasoning, the secondary tritium EIE should be a good estimate of the maximum secondary tritium KIE. Because these reactions were not reversible, the EIE could not be measured. However, one can estimate the EIE (the maximum expected secondary KIE) using Hartshorn and Shiner s (1972) fractionation factors. The predicted EIE (Kh/Kd) values were 1.117 at 40°C and 1.113 at 50°C. Seven of the reactions... 

These equations are important. They connect VPIE and ln(a"), both measurable properties, with basic theoretical ideas. The last two terms in Equation 5.10 and the last term in Equation 5.18 are generally small compared to the leading term. They are often neglected. The ratio of Q s in the leading term expresses VPIE or fractionation factor as the isotope effect on the equilibrium constant for the process condensed = ideal vapor- It remains true, of course, that condensed phase Q s are complicated and difficult to evaluate. Except for especially simple systems (e.g. monatomic isotopomers) approximations are required for further progress. 

The products of Rayleigh fractionation are effectively isolated from isotopic exchange with the rest of the system immediately upon formation. If the process occurs slowly, such that each increment of product B forms in isotopic equilibrium with the reactant A prior to isolation of B from the system, then would be an equilibrium isotope fractionation factor. However, if the process of formation of B is rapid, incremental formation of B may be out of isotopic equilibrium withH. In this case, would be a kinetic isotope fractionation factor, which may be a function of reaction rates or other system-specihc conditions. 

A good example of translational fractionation is one-way diffusion through an orifice that is smaller than the mean-free path of the gas. Related, but somewhat more complex velocity-dependent fractionations occur during diffusion through a host gas, liquid, or solid. In these fractionations the isotopic masses in the translational fractionation factor are often replaced by some kind of effective reduced mass. For instance, in diffusion of a trace gas JiR through a medium, Y, consisting of molecules with mass ttiy. 

In the earliest work, Krouse and Thode (1962) found the Se isotope fractionation factor Sse(iv)-se(o) to bc 10%o ( l%o) with hydroxylamine (NH2OH) as the reductant. Rees and Thode (1966) obtained a larger value, 12.8%o, for reduction by ascorbic acid. Webster (1972) later obtained 10%o for NHjOH reduction. Rashid and Krouse (1985) completed a more detailed study, and found that the fractionation factor varied with time over the course of the experiments. They explained the variations observed among the experiments in all four studies using a model in which reduction consists of two steps. With the rate constant of the second step two orders of magnitude smaller than the first, and kinetic isotope effects of 4.8%o and 13.2%o for the hrst and second steps, respectively, all the data (Table 3) were fit. Thus, kinetic isotope effects of apparently simple abiotic reactions can depend on reaction conditions. 

Equation (16) notes that the difference in measured 5 Fe values for Fe(II)aq and ferrihydrite precipitate is equal to difference in the Fe(III)aq-ferrihydrite and Fe(III)aq-Fe(II)aq fractionation factors, assuming that the proportion of Fe(III)aq is very small (<5%). In cases where the proportion of Fe(III)aq ratio is significant (>5%), the isotopic effects of combined oxidation and precipitation may still be calculated using an incremental approach and Equation (12), along with the pertinent fractionations between components (Eqns. 14 and 17). 

In complex systems that involve multiple Fe-bearing species and phases, such as those that are typical of biologic systems (Tables 1 and 2), it is often difficult or impossible to identify and separate all components for isotopic analysis. Commonly only the initial starting materials and one or more products may be analyzed for practical reasons, and this approach may not provide isotope fractionation factors between intermediate components but only assess a net overall isotopic effect. In the discussions that follow on biologic reduction and oxidation, we will conclude that significant isotopic fractionations are likely to occur among intermediate components. 

We wish to stress that comparison of the isotopic effects in biologic and abiologic systems will be most meaningful if experimental conditions are identical, where the only difference is the presence or absence of bacteria. The wide variety of buffers, growth media, and others conditions that are involved in biological experiments raise the possibihty that spurious results may be obtained if these factors are not carefully controlled. Because speciation may exert a strong control on Fe isotope fractionations (Schauble et al. 2001), even small differences across experimental studies may be significant. 

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