Radioactive exchange, equations

The equations of heterogeneous isotope exchange are simpler than ion-exchange equations because the two ions are chemically the same. In the treatment by the law of mass action, it means that the equilibrium constant is equal to 1. The selectivity coefficients at X = 0 and X = 1 can be determined by measuring heterogeneous isotope exchange in which the concentration of the radioactive isotopes is very low and approaches zero (carrier-free radioactive isotope). 

D can be regarded as a constant of the system in this experiment since drere is no change of chemical composition involved in tire exchange of radioactive and stable isotopes between the sample and the deposited layer. The solution of this equation with these boundaty conditions is... 

Solving the forward problem of the isotopic and chemical evolution of n reservoir exchanging a radioactive and its daughter isotope requires the solution of 3n— 1 differential equations (the minus one stems from the closure condition). The parameters are n (n — 1) independent flux factors k for the stable isotope N and n (n — 1) independent M/N fractionation factors D. In addition, the n values of R y the n values of Rh and the n—1 allotments x of the stable isotope among the reservoirs must be assumed at some time, preferably at the beginning of the evolution (e.g., 4.5 Ga ago), or in the modern times, in which case integration is carried out backwards in time. 

Alkali metals form porphyrin complexes of the type M2(Por) when their alkoxides are heated with porphyrin in dry pyridine, but are readily hydrolyzed.17 The transmetallation experiments indicate the stability of M2(Por) in the order K < Na < Li (Using radioactive sodium. Na2(TPP) is shown to undergo rapid metal exchange with Nal in pyridine (equation 2). 

These workers studied the exchange reaction of optically active j-octyl iodide with radioactive iodide ion in acetone (Equation 4.8) and found that (1) the kinetics are second-order, first-order each in octyl iodide and in iodide ion,... 

Let us now turn to whether the transition state is open (S 2) or cyclic (S i). The exchange of radioactive mercury shown in Equation 4.53 is a second-... 

In the late 1940s, the 1950s and later, radioactive isotopic tracers were used extensively to study the mechanistic paths of chemical reactions. One such use was in isotopic exchange reactions [19], such as the reaction, equation (1.5), in an aqueous medium,... 

Equations 2.25-2.34 represent the reactions between solid and liquid (Boxes 3 and 4). Among them, Equations 2.25-2.28 represent the dynamic heterogeneous exchange of ions between montmorillonite and solution if the ions are labeled by radioactive isotopes, they also include heterogeneous isotope exchange ... 

Both adsorption and ion exchange can be treated by isothermal equations Equations 1.73, 1.74, 1.94, and 1.95 in Chapter 1 can be used for the competitive adsorption or cation exchange. Radioactive ions are usually present in extremely low concentrations in the geological environment. In Chapter 1, Equations 1.73 and 1.94, c, = 0. So, Equations 1.73 and 1.94 can be simplified as follows ... 

When a radioactive ion is sorbed both by adsorption and ion exchange on a given mineral, it has two members for different sorption mechanisms in Equation 3.9. 

Formation of the enediol(ate) of RuBP is readily assayed on the basis of exchange of solvent protons with the C3 proton of substrate (20-22). The six-carbon intermediate of the carboxylation pathway (II in Fig. 1) can be prepared by rapid quench after mixing equimolar amounts of RuBP and the carboxylase in the presence of 14CO2 (23). Availability of this labeled intermediate allows determination of an enzyme s commitment to forward processing in the carboxylation step. Decomposition, via decarboxylation, is observed as a decrease in radioactivity that can be stabilized by borohydride, whereas forward catalysis is equated with an increase in acid-stable radioactivity. 

The study of electron transfer reactions began in earnest when radioactive isotopes, produced for nuclear research and the atom bomb program during World War II, became accessible. Glen Seaborg, in a 1940 review of artificial radioactivity, noted the first attempt to measure the self-exchange reaction between aqueous iron(III) and iron(II), equation (1.9).1"... 

Experimental data indicated that the isotope exchange process is described by first order equations, and in most cases, e.g., on supported C0M0/AI2O3 catalysts by a superposition of two curves representing two types of sulfur mobility, the more and the less mobile i.e., rapidly and slowly exchangeable sulfur. In general, the H2S molar radioactivity a (in percent of the initial molar radioactivity of catalyst sulfide sulfur), as a function of the produced H2S-[X(cm )], is given (Fig. 7) as a superposition of curves... 

Experiments indicatedthat the molar radioactivity function of H2S production on M0S2 can be described by one equation (A = 100, i= 1) biexponential equations were required for promoted catalysts with different Aj and Aj. This indicates that the catalyst sulfur was not bonded homogenously, like that of the observations with H2 S or H2 S exchange.An important difference from those observations is that, in this case, we deal with H2 S, replaced by sulfur, formed in HDS, so that the H2S molar radioactivity represents sulfur formed on the (or via) cat-al Tically active sites. Consequently, the fact that function (7) is described by a biexponential equation with two A-s and A-s, indicates that there exist two types of catalytic sites, active in HDS on promoted Mo-based catalysts. 

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