Isotopic equilibration reaction

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. 

It can be seen from Fig. 6.63 that the rate of isotopic equilibration reaction is higher than the ammonia synthesis reaction without Sm20s. At the same time, with the addition of Sm203, the rate of isotopic equilibration reaction declines a lot, while the rates of ammonia synthesis reaction are all higher. This indicates that the effect of hydrogen is very evident at this time, which is a problem that cannot be ignored on Ru catalyst. 

For Raney Ru and Raney Ru-CsNOs, Hikita et al. studied the relationship between the rate of isotopic equilibration reaction of nitrogen with the pressure of hydrogen and compared its rate on equilibration and ammonia synthesis reaction, pointed out that the nitrogen dissociative adsorption on Ru catalyst are significantly... 

Pig. 6.63 Relationship of rate and temperature on ammonia synthesis reaction (N2 -H 3H2 = 600 Torr) and isotopic equilibration reaction ( N2 -f N2 = 150 Torr)... 

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. 

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]. 

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). 

Hydrogen spillover can be interestingly investigated with the help of isotopic molecules such as D2 and T2. Exchange reactions between the surface and the gas phase, and equilibration reactions involving hydrogen and deuterium, are easily monitored by IR spectroscopy, chromatography, and mass spectroscopy. 

In the example illustrated in Figure 8 the isotope of interest is concentrated in the liquid phase. A feed solution is introduced at the top of a cold tower where it equilibrates in a multiplate column against a gas stream with which it undergoes an isotopic exchange reaction. The isotope concentration builds up to a maximum at the bottom of the cold tower. The hot tower serves as a refluxer for the cold tower. Its performance and function can be seen by focusing attention on the gas stream which is in a closed loop. At the top of the cold tower the gas stream composition is determined by equilibration against the cold feed liquid... 

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 ... 

An illustration of an isotope exchange reaction is the distribution of stable carbon isotopes between equilibrated C02(g) and aqueous HCO3 species of the carbonate buffer system. The hydration reaction for CO2, Eq. (4.11)... 

Sulfate-sulfide isotopic exchange disequilibrium (where sulfate is reduced to sulfide without isotopic exchange but sulfide minerals and H2S isotopically equilibrate) in closed and open isotopic systems result in significantly smaller shifts in isotopic compositions (Figure 1). In addition, the calculated shifts are to higher sulfide compositions, generally consistent with the measured values for seafloor sulfide minerals. Analyses of the natural samples, however, provide no evidence of systematic isotopic differences between pyrite, sphalerite, and chalcopyrite, as predicted by both standard fractionation approaches and these calculated isotopic reaction pathways, possibly due to dynamic variations of mixing and precipitation on a local scale. 

In this scheme, the initial dissociative adsorption is followed by fast formation of a triatomic 03 intermediate (with equal probability from 1602 or 1802 of the isotopically non-equilibrated 1602 + 1802 gas phase) which serves as the propagator of step (c). The latter has the character of a chain reaction, scrambling the gas phase into isotopic equilibration with reversible second-order kinetics as observed experimentally. Another aspect of experimental observations at 295 K readily accounted for by eqns. (35) was the diminution of activity as successive doses of the isotopically non-equilibrated (1602 4- 1802) were introduced, since step (a) shows destruction of ZnCU8. The alternative weak-activation case is... 

Duprez and al. investigated the first and the second step by means of I q/ISq isotopic exchange [6-8], The rate of step 1 can be deduced from the rate of tlie 1602/ 02 equilibration reaction that occurs on the metal ... 

---