Mass balance equations isotopic

If no KIE is present, the contribution of the derivative atom to the measured 8 value of the derivatised compound can be calculated using a simple mass balance equation (14.2), where n is number of moles of the isotope of interest, F is the fractional abundance of the isotope of interest, c refers to the compound of interest, d refers to the derivative group and... 

Bowers and Taylor (1985) were the first to incorporate isotope fractionation into a reaction model. They used a modified version of EQ3/EQ6 (Wolery, 1979) to study the convection of hydrothermal fluids through the oceanic crust, along midocean ridges. Their calculation method is based on evaluating mass balance equations, as described in this chapter. 

Lee and Bethke (1996) presented an alternative technique, also based on mass balance equations, in which the reaction modeler can segregate minerals from isotopic exchange. By segregating the minerals, the model traces the effects of the isotope fractionation that would result from dissolution and precipitation reactions alone. Not unexpectedly, segregated models differ broadly in their results from reaction models that assume isotopic equilibrium. 

Integrating isotope fractionation into the reaction path calculation is a matter of applying the mass balance equations while tracing over the course of the reaction path the system s total isotopic composition. Much of the effort in programming an isotope model consists of devising a careful accounting of the mass of each isotope. 

Once we have computed the total isotopic compositions, we calculate the compositions of the reference species using the mass balance equations (Eqns. 19.13, 19.20, 19.21, 19.22). We can then use the isotopic compositions of the reference species to calculate the compositions of the other species (Eqns. 19.10, 19.14, 19.15, 19.16) and the unsegregated minerals (Eqns. 19.11,19.17,19.18, 19.19). 

The combined effects of a +2.9%o equilibrium fractionation between Fe(III)aq and Fe(II)jq, and a +2.0%o fractionation between Fe(Ill)aq and ferrihydrite upon precipitation is illustrated in Figure 10. Although a k ki ratio of 5 appears to fit the fractionations measured by Bullen et al. (2001) (Fig. 10), we note that at these relatively low kjk ratios. Equation (16) cannot be used, but instead the calculations are made using an incremental approach and simple isotope mass-balance equations (e.g., Eqn. 12). As the kjki ratio increases to 20, Equation (16) may... 

When a diet consists of two isotopically distinct food sources for which the 6 C values are known, it becomes possible to estimate the relative proportions of each by applying an isotopic mass balance equation ... 

The calculation of past CO2 levels using GEOCARB begins with the iterative solution of equations (11) and (12) and a parallel mass balance equation for carbon isotopes to yield fluxes that are consistent with the carbonate... 

The mass balance equation for stable isotope transport... 

The change of mass (or moles) of oxygen isotope within the small cube with volume dV can alternatively be calculated from the change of mass, dm, of the system. Mass gain or loss of can be calculated by multiplying the concentration of by the volume of the system, dV. Hence we obtain for the basic mass balance equation ... 

Note that the concentration gain of an isotope in the system is equal to the negative of the change in flux of this isotope. The dV terms can be dropped to yield the basic mass balance equation for stable isotope transport (or any other element) ... 

The general continuum mechanics equation of stable isotope transport can now be assembled. All individual mass transport fluxes need to be summed in the mass balance Equation (13) ... 

In a similar way the isotopic composition of crust and mantle reservoirs have been interpreted by means of a series of mass balance equations between crust, mantle and the original composition of the bulk silicate Earth. This has allowed us to explore the interrelationships between different reservoirs, set limits on the proportion of mande involved in the formation of the continental crust and offer insights into the nature of mantle convection (AUegre et a/., 1983a,b AUegre, 1987 ... 

We analyzed the desert dust samples (yellow sand samples) for carbon and nitrogen isotopic composition with and without HCl treatment (Table 2). Using isotopic mass balance equations as below, carbon isotopic ratios of removed carbon from the Chinese loess samples (S CRemoved c)... 

Equation (18) illustrates that the measured 5 Fe value for Fe(ll)jq is dependent not only on t Fe(iii)L-Fe(ii)Lj but On the proportion of Fe(III)-LFe(in) in the components that are open to isotopic exchange, which additionally includes Fe(II)-LFe(n) and Fe(ll)a, we will refer to these three components as the exchangeable pool of Fe in the system. We stress that the isotopic mass balance described by Equation (18) assumes that the ligand-bound Fe(lll) component is not sampled in the aqueous phase component, but instead exists as a component that is bormd to the cells. 

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