Isotope equilibration

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. 

Isotope dilution mass spectrometry (IDMS) can be applied with most of the ionisation methods used in mass spectrometry to determine isotope ratios with greater or lesser accuracy. For calibration by means of isotope dilution, an exactly known amount of a spike solution, enriched in an isotope of the element(s) to be determined, is added to an exactly known amount of sample. After isotopic equilibration, the isotope ratio for the mixture is determined mass spectrometrically. The attraction of IDMS is its potential simplicity it relies only on the measurement of ratios. The... 

Where interactions between the (supercritical) gas and water are possible, there is rapid isotopic equilibration between the oxygen in C02 and H20. The potential to use this isotopic exchange equilibria as a measure of the extent of C02-water interaction, and thus as an indicator of C02 migration, is discussed in Kharaka etal. (2006). Unlike the results of Kharaka et al. (2006), there are no consistent changes in the oxygen isotopic composition of the fluid samples at the Otway site. 

Kinetic fractionations can occur when there is incomplete isotopic exchange between the different phases present in a system. A thorough introduction to kinetic stable isotope fractionation theory is unfortunately beyond the scope of the present review. Flowever, it is useful to include a brief discussion of some basic aspects, particularly in comparison to equilibrium fractionation theory. A simple example of kinetic fractionation is the evaporation of a liquid water droplet into a vacuum, in this example FljO molecules entering the gas phase are physically removed from the vicinity of the droplet, so there is no chance for isotopic equilibration between vapor-phase molecules and the residual liquid. Isotopic fractionation in this case is determined by a one-way reaction path, and will not, in general, be the same as the fractionation in a system where vapor-phase molecules are able to equilibrate and exchange with the liquid. In other reactions, isotopic exchange is limited by an energy barrier—an... 

Accordingly, isotopic equilibration for Cr and Se species is expected to be much slower than for the aqueous Fe(III)-Fe(II) couple, which reaches equilibrium within minutes in laboratory experiments (Beard and Johnson 2004). Additionally, Cr(III) and Se(0) are highly insoluble and their residence times in solution are small, which further decreases the likelihood of isotopic equilibration. In the synthesis below, isotopic fractionations are assumed to be kinetically controlled unless otherwise stated. However, definitive assessments of this assumption have not been done, and future studies may find that equilibrium fractionation is attained for some reactions or rmder certain conditions. 

A ratio defining the isotopic distribution of two isotopes equilibrated between two different chemical species. If X, followed by a subscript, represents the mole fraction of an isotope (denoted by that same subscript), then the fractionation factor, often symbolized by , with respect to chemical species A and B is (Xi/X2)a/(-X i/-X 2)b- Fractionation factors can also refer to different sites, A and B, within the same chemical species. As an example, the deuterium solvent fractionation factor, used in studying solvent isotope effects, is = (AD/A"H)soiute/(- o/... 

The natural cycles of the bioelements carbon, oxygen, hydrogen, nitrogen and sulphur) are subjected to various discrimination effects, such as thermodynamic isotope effects during water evaporation and condensation or isotope equilibration between water and CO2. On the other hand, the processes of photosynthesis and secondary plant metabolism are characterised by kinetic isotope effects, caused by defined enzyme-catalysed reactions [46]. 

Additional checks were made using a dialysis procedure in which zeolite samples which had been isotopically equilibrated with a 22Na O.OlAf NaCl solution were dialyzed against distilled water. After repeated washings, the sodium loss from NaX reached a steady value of 2.8 ( 0.1) ions/ unit cell at a zeolite content of 0.44 gram/liter, i.e. a value which is nearly identical to the data in Table I for a 10 NaCl concentration. Under similar conditions, the sodium loss from NaY is much less and corresponds to 1.5 ( 0.1) ions/unit cell. These results were confirmed by electrical conductivity measurements on the respective dialysates the conductivity for NaX is about twice as large (7.5 X 10 6 mhos/cm) as for NaY (3.9 X 10 6 mhos/cm). 

The rates of these reactions (R -R2) have been determined by the quantitative analysis of the reduction of H3PM12O40 (M = Mo, W) by a mixture of H2 and D2. With H3PW12O40, the isotopic equilibration of H2 and D2 in the gas phase, as well as the isotopic exchange between the entire solid and the gas phase, is very rapid, so that, to our surprise, the content of H in the gas phase increased rapidly (Fig. 50). The detailed kinetics analysis shows that the reactions of Eqs. (29) and (30) are very rapid and that of Eq. (31) is the slow step, the equilibrium strongly favoring the reactions on the left-hand side of Eq. (29) (Fig. 51, left). 

Usually, this method is applied to enzymatic reactions, and the equilibrium IEs are obtained along with kinetic IEs that are of greater interest. An example is the deuterium IE on the reaction of acetone-c/6 with NADH, to form 2-propanol-fi 6 + NAD+. A mixture of acetone-c/6 and 2-propanol is prepared along with coreactants NADH and NAD+ at concentrations such that the reaction is at chemical equilibrium. Isotopic equilibration is initiated by adding enzyme. In this case the spectral signature lies in the NADH, but the measured maximum or minimum of absorbance provides the right-hand side of Equation (25) or (26) and thus a for each mixture. An estimate of AThh is needed to solve for each R in Equation (23) in order to fit the data to Equation (27), but after successive iterations the values of R and XEIE converge. 

The substitution leading from (155) to (156) is a prerequisite to application of the theory for the case of mechanism (153) but it may be noted that equation (157) is itself entirely predictive, since the fractionation factor of the substrate, SL, is in principle amenable to measurement (e.g. by isotopic equilibration in an acidic medium if the reaction is not also subject to acid catalysis). 

The ideal internal standard is the same element as the analyte because it has similar mass, ionization energy, and chemical properties. Therefore, isotope dilution based calibration provides high accuracy as long as isotope equilibration is attained and the measured isotopes are free of spectral overlaps [192,193]. Standards do not need to be matrix-matched. Quadrupole-based ICP-MS instruments can typically provide isotope ratio precision of 0.1% to 0.5%. Much better isotope ratio precision can be obtained by using simultaneous MS detection, such as a multicollector-based instrument or perhaps time-of-flight MS. In comparison to thermal ionization mass spectrometry, ICP-MS provides much higher sample throughput and simpler, faster sample preparation. 

Off-line dicarbamate solvent extraction and ICP-MS analysis [317] provided part-per-trillion detection limits Cd (0.2 ppt), Co (0.3 ppt), Cu (3 ppt), Fe (21 ppt), Ni (2 ppt), Pb (0.5 ppt), and Zn (2 ppt). Off-line matrix removal and preconcentration using cellulose-immobilized ethylenediaminetetraacetic acid (EDTA) have also been reported [318]. Transition metals and rare earth elements were preconcentrated and separated from the matrix using on-line ion chromatography with a NTA chelating resin [319]. Isotope-dilution-based concentration measurement has also been used after matrix separation with a Chelex ion-exchange resin [320]. The pH, flow rate, resin volume, elution volume, and time required for isotope equilibration were optimized. A controlled-pore glass immobilized iminodiacetate based automated on-line matrix separation system has also been described [321]. Recoveries for most metals were between 62% and 113%. 

During metamorphism and recrystallization, oxygen isotopes are redistributed among mineral phases, according to the mass-dependent equilibrium fractionations corresponding to the peak metamorphic temperature. The measured mineral-pair fractionations (usually for major minerals olivine, pyroxene, and feldspar) can then be used for metamorphic thermometry, yielding temperatures of 600 °C for an L4 chondrite, and 850 50 °C for several type-5 and type-6 chondrites (Clayton et al., 1991). Isotopic equilibration, even in type-6 chondrites, involves oxygen atom transport only over distances of a few millimeters (Olsen et al., 1981). 

Lewis S., Holness M., and Graham C. (1998) Ion microprobe study of marble from Naxos Greece grain-scale fluid pathways and stable isotope equilibration during metamorphism. Geology 26, 935-938. 

Rumble D., Ill and Spear F. S. (1983) Oxygen isotope equilibration and permeability enhancement during regional metamorphism. J. Geol. Soc. London 140, 619-628. 

Tie-lines between coexisting garnet and omphacite plotted as 8Nd(0 versus S Osmow are shown in Figure 7 (redrawn from Zheng et al., 2002). In such a plot, values of SNd(0 calculated for the age of UHP metamorphism are expected to be identical for minerals experiencing isotopic equilibration under UHP conditions. The differences between values of for minerals equilibrated... 

Elburg M. A. (1996c) Evidence of isotopic equilibration between microgranitoid enclaves and host granodiorite, Warburton Granodiorite, Eachlan Fold Belt, Australia. Lithos 38, 1-22. 

The primary control on the 5 0 of CO2 is the 5 0 of the liquid water with which it was last in contact. CO2 isotopically equilibrates with water according to the following reaction ... 

Because of this, the time required for chemical equilibration mrns out to be roughly an order of magnitude smaller (i.e., 200/1,800) than that for isotopic equilibration. 

A full account of the problems considered in collecting, storing, and processing marine samples for transuranic analysis is given in the above-mentioned review (4). The specific methods discussed here were foimd effective at least for the transuranic analyses of seawater and sediments contaminated by global fallout, nuclear fuel reprocessing wastes, or nuclear power plant operation waste. In these cases, a preliminary acid treatment of the sample in the presence of suitable yield monitors seems to solubilize the transuranic elements and achieves isotopic equilibration between the yield monitor and sample. The yield monitors used were either Pu or sep qj. 238,239,240,24ip whereas Am was used for Am, 2 Cm, and by inference, Cf. In addition, it was convenient to use 50 mg of a lanthanide (neodymium) as a carrier for americium to purify the separated americium fraction. 

Fig. 6.12 Sample pretreatment and conversion of organic compounds into gases for isotope ratio mass spectrometry (IRMS). The reductive pyrolysis is normally performed on glassy carbon (for a summary see e.g. [ 1291). In case of coupled HPLC-IRMS for determination wet oxidation is used [ 122f In the routine isotope ratio analysis of water often isotope equilibration with gases are used for 0-analysis CO2 [ 130], for S H-analysis H2 gas in the presence of Pt [131]. Recently an on-line method for S O and in water has been described showing dual-inlet like performance [ 132]. Low-temperature pyrolysis in connection with GC is used for compound fragmentation with the aim of partial isotope pattern analysis [133]. TC-EA = thermo conversion elemental analyser...

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