Isotopic equilibrium

A special case of opposing reactions is the one in which chemical equilibrium has been attained, but not isotopic equilibrium. Isotopic equilibration reactions are termed exchange reactions. They occur with virtually no net driving force i.e., AG 4 is very nearly zero, save for that provided by the entropy of isotopic mixing. 

At isotopic equilibrium, the tracer will be distributed statistically ... 

Gross-Butler equation is that the reactant is in isotopic equilibrium with the solvent. Given that the process under consideration occurs on an exceptionally short time scale, the assumption is not necessarily valid. A very thorough analysis of the isotopic possibilities was used to show that the interpretation presented here is nonetheless correct.25... 

As for carbonate measurements, the model confirms that bioapatite-carbonate should exhibit a 8 C value offset from the average-ingested-diet by an amount equal to the isotopic equilibrium fractionation between carbonate and gaseous CO2. 

If sulfur isotopic equilibrium between coexisting sulfates and sulfides was attained, using average values of sulfates and sulfides, -i-22%c and +5%c, respectively, we could estimate temperature using the equation by Ohmoto and Rye (1979). This temperature seems too high compared with temperature estimated from fluid inclusions and mineral assemblages (section 1.3.3). That means that sulfates and sulfides precipitated under the condition far from equilibrium. 

There is another explanation for the variations in values of sulfide sulfur. It was cited that oxidation state (/02) od pH of ore fluids are important factor controlling values of ore fluids (e.g., Kajiwara, 1971). According to the sulfur isotopic equilibrium model (Kajiwara, 1971 Ohmoto, 1972), of sulfides in predominance... 

They calculated the change in 8 0 values of hydrothermally altered volcanic rocks as a function of water to rock ratio by weight and temperature, assuming that oxygen isotopic equilibrium is attained in a closed system, and demonstrated that the increase in 8 0 values of altered andesitic rocks from the veins towards peripheral zones can be interpreted as a decrease in temperature from the vein system (Fig. 1.135). In their calculations, the effect of mixing of hydrothermal solution with groundwater was not considered. 

Oxygen isotopic equilibrium between mixed fluid and alteration minerals is attained. 

Minerals in oxygen isotopic equilibrium with mixed fluid are feldspar for ore deposit/zone IV, and zone III/II, montmorillonite, and kaolinite for zone II/I, and montmorillonite for zone I/fresh rocks. 

An important aspect in the preceding discussion is the need to separate the fluid and sediment components spatially and (as we will see) also temporally. Quantitative mass balance estimates (e g., McCulloch and Gamble 1991 Stolper and Newman 1994 Ayers 1998) often conclude that there is as much, or even more, Th and U in the bulk slab componenf (i.e., sediment plus fluid from the altered oceanic crust). However, if the sediment component added is in U-Th isotope equilibrium (or returns to this state prior to fluid addition see Section 5.3), then addition of only 0.02 ppm U in the fluid will result in significant U-excesss in the composite source (e.g., Condomines and Sigmarsson 1993 Turner et al. 1997). 

For destructive measuring methods, a CRM would serve as a reference to check the recovery of a particular matrix removal procedure. This is especially important for open destructions at atmospheric pressure. Alternatively, isotope dilution methods may be used once isotopic equilibrium is established, loss of analyte does not affect the analysis result. Isotope dilution techniques are only available in a few specialised laboratories. Another type of problem is encountered in pressurised methods oxidising the matrix in a closed vessel or bomb. Due to the large amounts of gas (CO2, NO, SO2) evolving from samples with a high organic matrix content, an excessive pressure build-up occurs that prohibits the use... 

One of the advantages of the isotope dilution technique is that the quantitative recovery of the analytes is not required. Since it is only their isotope ratios that are being measured, it is necessary only to recover sufficient analyte to make an adequate measurement. Therefore, when this technique is used in conjunction with graphite furnace atomic absorption spectrometry, it is possible to determine the efficiency of the preconcentration step. This is particularly important in the analysis of seawater, where the recovery is very difficult to determine by other techniques, since the concentration of the unrecovered analyte is so low. In using this technique, one must assume that isotopic equilibrium has been achieved with the analyte, regardless of the species in which it may exist. 

Whether the oxygen in tree rings comes from water or from C02 is a non-question, because Cohn and Urey [34] showed that isotopic equilibrium between the two substances is obtained in a damp atmosphere within a few hours at room temperature. 

As originally derived, however, the mass balance model has an important (and well acknowledged) limitation implicit in its formulation is the assumption that fluid and minerals in the modeled system remain in isotopic equilibrium over the reaction path. This assumption is equivalent to assuming that isotope exchange between fluid and minerals occurs rapidly enough to maintain equilibrium compositions. 

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. 

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. 19.2. Isotopic composition (bold lines) of dolomite formed by reaction between a limestone and migrating groundwater, assuming that minerals maintain isotopic equilibrium over the simulation. Fine lines show results of simulation holding minerals segregated from isotopic exchange, as already presented (Fig. 19.1).

How would the results differ if we had assumed isotopic equilibrium among minerals instead of holding them segregated from isotopic exchange To find out, we enter the commands... 

To set up the calculation, we specify initial isotopic compositions for the fluid and calcite. We choose a value of —13 %c for r) 18 Os mow of the Lyons fluid, reflecting Tertiary rainfall in the region, and set the calcite composition to +11 %o, the mean of the measured values (Fig. 25.4). We further set S13C pi)B for the fluid to — 12 %o. We do not specify an initial carbon composition for the calcite, so the model sets this value to — 11 %c, in isotopic equilibrium with the fluid. Again, this value is near the mean of the measurements. 

Fig. 25.4. Oxygen and carbon stable isotopic compositions of calcite ( ) and dolomite ( ) cements from Lyons sandstone (Levandowski et al., 1973), and isotopic trends (bold arrows) predicted for dolomite cements produced by the mixing reaction shown in Figure 25.3, assuming differing CO2 fugacities (25, 50, and 100) for the Fountain brine. Fine arrows, for comparison, show isotopic trends predicted in calculations which assume (improperly) that fluid and minerals maintain isotopic equilibrium over the course of the simulation. Figure after Lee and Bethke (1996).

Hofmann, A. W. Hart, S. R. (1978). An assesment of local and regional isotopic equilibrium in the mantle. Earth Planet. Sci. Letters, 38, 44-62. 

The protocol described in Section 7.1.2 involves isotopic competition, but with the different isotopomers held in separate containers. Equations 7.10 to 7.13 apply equally well to a type of competition experiment known in biochemistry as the perturbation method for determining KIE s of reversible enzyme catalyzed reactions. The perturbation method differs from simultaneous non-competitive measurements in several important ways. One begins by mixing equilibrium concentrations of substrate and product but with one component (substrate or product) at a different isotopic composition than the other. Thus, the mixture is in chemical, but not isotopic equilibrium. At this stage no enzyme is present and the interconversion is... 

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