Difference fractionation factor

The fractionation factor and difference fractionation factor are related by the approximation that... 

For a derivation of the numeric relationships between K, a, 5, and e for the exchange of 0 between water and carbonate ion, see Appendix 5.1. Difference fractionation factors for many of the important reactions among molecules containing the elements H, C, N, and 0 are presented in Table 5.3. 

Table 5.3. 1 Difference fractionation factors, e= product- Sre ctant, for important equilibrium (equations with two-way arrows) and kinetic (one-way arrows) reactions among the elements H, C, 0, and N Equilibrium fractionation factors are for 20 °C. Kinetic fractionation factors are approximate as they vary in the marine environment. ...

Schematic diagram of the stable nitrogen isotope ratios of different nitrogen reservoirs in the sea. The general range of stable isotope ratios (with respect to the atmosphere) found in nature is given in the boxes and the difference fractionation factors e (in %o) accompany arrows between the boxes. Many of the values are approximations because of the wide variations of observations. See Table 5.3 for more details of some of the reactions and the text for explanation. Values are based on data presented by Altabet and Small (1990), Altabet and Francois (1994) and Sigman and Casciotti (2001).

The main processes involved in the biologieal utilization of nitrogen are all associated with kinetic fractionation effects, nevertheless they exhibit different fractionation factors. The isotope effect of nitrogen fixation (a = 1.000 to 1.004) is small relative to the effects of bacterial nitrification, denitrification, or anammox (a = 1.02 to 1.04) (see Montoya et al. 1994 Table 1). The results by Miyake and Wada (1971) indicate that little overall isotope fractionation occurs in the... 

As also shown in Figures lla/b, elemental abundance ratios in P3 may be related to those in the solar wind in a similar fashion as those in Q, with slightly different fractionation factors. Furthermore, for Kr and Xe (although definitely not for Ne), the... 

In this case, mechanistic information suggests that the reactant and the transition state have one and the same exchangeable position for hydrogen or deuterium, which is a hydroxyl group in ethanol (Fig. 9). The rate of reaction was faster in DOD, and an inverse solvent effect on fccat of 2.0 was observed the data in Fig. 10 were fitted with Eq. (17.72), assuming one protonic site having different fractionation factors in reactant and transition states. 

To emphasize small variations in fractionation factors (a), a new term (5) is introduced, which accentuates small differences. Since the latter are very small, they are usually multiplied by 1000 (mil). 

The difference in 5 values for two substances (P,Q) measured against a standard substance is approximately equal to 1000 times the natural logarithm of their fractionation factor (app). 

Instead of the fractionation factor (apQ) for two substances (P,Q), a slightly different fractional abundance (/pq) may be defined ... 

Distillation. Vacuum distUlation (qv) of water, which contains the three molecular species H2O, HDO, and D2O, was the first method used for the large-scale extraction of deuterium (10,58) (Fig. 2). From the equHibrium constant in the Hquid phase it is evident that the distribution of H and D is not statistical. The differences in vapor pressure between H2O and D2O are significant, and a fractionation factor (see Table 7) of 1.05 can be obtained at... 

FIGURE 2.11 Receptor-occupancy curves for activation of human calcitonin type 2 receptors by the agonist human calcitonin. Ordinates (response as a fraction of the maximal response to human calcitonin). Abscissae (fractional receptor occupancy by human calcitonin). Curves shown for receptors transfected into three cell types human embryonic kidney cells (HEK), Chinese hamster ovary cells (CHO), and Xenopus laevis melanophores. It can be seen that the different cell types lead to differing amplification factors for the conversion from agonist receptor occupancy to tissue response. 

Otherwise, i f j / k and after rearrangement and introduction of different fractional scaling factors the following equation results ... 

When species or phases are in isotopic equilibrium, their isotopic ratios differ from one another by predictable amounts. The segregation of heavier isotopes into one species and light isotopes into the other is called isotope fractionation. The fractionation among species is represented by a fractionation factor a, which is determined empirically. The fractionation factor between species A and B is the ratio... 

Fig. 9 Predicted fractionation factors (tpA HA- ) for protons in different potential wells 1 2...

Since M and N are different chemical species, we make fractionation factors apparent in the form... 

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... 

The isotopic abundance of deuterium in the L30+ ion will differ from that in the water with which it is equilibrated. This is expressed in terms of the fractionation factor / which is the ratio of D/H ratios in the lyonium ion and the mixed solvent (water)... 

Figure 4. Illustration of mass-dependent fractionation of Mg isotopes, cast in terms of 5 values. 5 Mg and 5 Mg values based on Mg/ Mg and Mg/ Mg ratios, respectively. A common equilibrium fractionation model, as defined by exponential relations between a values (fractionation factors) for different isotope ratios, is shown in the gray line. A simple linear relation, where the slope is proportional to the mass difference of the isotope pair, is shown in the black line. Additional mass-dependent fractionation laws may be defined, and all are closely convergent over small ranges (a few per mil) in isotope compositions at 5 values that are close to zero.

Fractionations are typically very small, on the order of parts per thousand or parts per ten thousand, so it is common to see expressions like 1000 ln(a) or 1000 (a-l) that magnify the difference between a and 1. a =1.001(1000 [a-l] = 1) is equivalent to a 1 per mil (%o) fractionation. Readers of the primary theoretical literature on stable isotope fractionations will frequently encounter results tabulated in terms of P-factors or equilibrium constants. For present purposes, we can think of Pjjh as simply a theoretical fractionation calculated between some substance JiR containing the elementX, and dissociated, non-interacting atoms ofX. In the present review the synonymous term Uxr-x is used. This type of fractionation factor is a convenient way to tabulate theoretical fractionations relative to a common exchange partner (dissociated, isolated atoms), and can easily be converted into fractionation factors for any exchange reaction ... 

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