Stable isotopes difference fractionation factor

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).

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. 

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 ... 

The above example is easily generalized to more complicated systems involving more than two fluid species and several mineral phases and different stable isotopes. In each case, care should be taken to evaluate the fractionation factor. For some isotopes. 

The subject of isotope effects in H2O-D2O mixtures has been treated in some detail because kinetic studies in these solvents have been recently used extensively to obtain detailed information about the nature of transition states in proton-transfer reactions. The problems involved are essentially the same as arise for equilibria, in particular with respect to transfer effects, and there is the added difficulty that fractionation factors and transfer activity coefficients for the transition state must either be guessed at by analogy with stable species, or derived from the kinetic measurements themselves. On the other hand, the numerical value of /c /k is often more favourable for distinguishing between different possibilities than are the values of K /K commonly met with in equilibrium systems, and there is also another piece of experimental information, the so-called product isotope effect, which is sometimes helpful. These kinetic problems will be discussed briefly in the next chapter. 

As light stable isotopes with signiflcant relative mass differences (e.g., 2 1 for D and H or 18 16 for oxygen isotopes), there are measmable differences in the physical properties of end member hght stable isotopic compoimds (e g., D2O and H2O or H2 0 and H2 0). These differences in physical properties manifest themselves in their thermodynamic properties so that the ratios of isotopically substituted compounds represent chemical activity products (a s) that have temperature signiflcance. Exchange reactions are the special class of chemical reactions where the only difference between the reactants and the products is in the isotopically substituted species. The compoimds are otherwise identical. In general, the fractionation factor a is the ratio of isotopes of two substances. Phases 1 and 2 ... 

At equilibrium, the fractionation factor is related to the temperature of exchange. Measured fractionations (differences in delta values) are therefore proportional to temperature of exchange. Harold Urey s recognition of these properties led to the application of stable isotopic measurements to fossils containing carbonate to infer the temperature of the ancient oceans. 

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