Isotopes’ transfer rate

Besides the isotopes transfer rate also the reaction rate r = r+ - r can be measured... 

Cant, N.W., Lukey, C.A. and Nelson, P.F. (1990), Oxygen Isotop Transfer Rates during the Oxydative Coupling of Methane over a Li/MgO Catalyst, J. Catal. 124, 336. Peil, K.P., Goodwin, J.G. Jr. and Marcelin, G. (1989), An Examination of the Oxygen Pathway during Methane Oxidation over a Li/MgO Catalyst, J. Phys. Chem. 93, 5977. Wanzek, A. (1991), Ph.D. Thesis, Ruhr-University Bochum. 

The electronic, rotational and translational properties of the H, D and T atoms are identical. However, by virtue of the larger mass of T compared with D and H, the vibrational energy of C-H> C-D > C-T. In the transition state, one vibrational degree of freedom is lost, which leads to differences between isotopes in activation energy. This leads in turn to an isotope-dependent difference in rate - the lower the mass of the isotope, the lower the activation energy and thus the faster the rate. The kinetic isotope effects therefore have different values depending on the isotopes being compared - (rate of H-transfer) (rate of D-transfer) = 7 1 (rate of H-transfer) (rate of T-transfer) 15 1 at 25 °C. 

Unidirectional, first-order transfer rates (day1) between compartments were developed for 6 age groups, and intermediate age-specific values are obtained by linear interpolation. The range of age-specific transfer rate values are given in Table 2-8. The total transfer rate from diffusible plasma to all destinations combined is assumed to be 2,000 day"1, based on isotope tracer studies in humans receiving lead via injection or inhalation. Values for transfer rates in various tissues and tissue compartments are based on measured deposition fractions, or instantaneous fractional outflows of lead between tissue compartments (Leggett 1993). 

Fig. 17. Biological model recommended for describing the uptake and retention of cerium by humans after inhalation or ingestion. Numbers in parentheses give the fractions of the material in the originating compartments which are cleared to the indicated sites of deposition. Clearance from the pulmonary region results from competition between mechanical clearances to the lymph nodes and gastrointestinal tract and absorption of soluble material into the systemic circulation. The fractions included in parentheses by the pulmonary compartment indicate the distribution of material subject to the two clearance rates however, these amounts will not be cleared in this manner if the material is previously absorbed into blood. Transfer rate constants or functions, S(t), are given in fractions per unit time. Dashed lines indicate clearance pathways which exist but occur at such slow rates as to be considered insignificant compared to radioactive decay of the cerium isotopes.

Finally, in many cases the acidity equilibria cannot be measured but the rate of proton transfer or transmetallation can be measured to give an ionic or ion pair kinetic acidity. Studies using the rates of proton transfer have included the use of isotopes such as tritium and deuterium5,6. The rate is then used to calculate the Brpnsted slope, a, by plotting the logarithm of the proton transfer rate against the pK, as determined by the equilibrium acidity, for a series of compounds. From this plot, the approximate pKa of an unknown compound can be determined by comparison of the same type of compounds. 

In the aldol-Tishchenko reaction, a lithium enolate reacts with 2 mol of aldehyde, ultimately giving, via an intramolecular hydride transfer, a hydroxy ester (51) with up to three chiral centres (R, derived from rYhIO). The kinetics of the reaction of the lithium enolate of p-(phenylsulfonyl)isobutyrophenone with benzaldehyde have been measured in THF. ° A kinetic isotope effect of fee/ o = 2.0 was found, using benzaldehyde-fil. The results and proposed mechanism, with hydride transfer rate limiting, are supported by ab initio MO calculations. 

Information on the steps in a reaction mechanism can be extended significantly by isotopic tracer measurements, especially by transient tracing [see Happel et al. (54,55)]. Studies by Temkin and Horiuti previously referenced here have been confined to steady-state isotopic transfer techniques. Modeling with transient isotope data is often more useful since it enables direct determination of concentrations of intermediates as well as elementary step velocities. When kinetic rate equations alone are used for modeling, determination of these parameters is more indirect. 

To compare these two mechanisms, an NADH model without the recognition site was synthesised. The contribution of the flavin binding to the rate constant was thus evaluated and it was shown that the proximity of flavin and NADH model influenced the electron transfer rate. Mechanistic computations helped to show that with the appropriate NADH model system, both components were optimally arranged for the electron transfer. Although the exact mechanism of the reaction is still under debate, the kinetic isotope effect experiment indicated that in this case, the hydrogen at 4-position was transferred in the rate determining step which supported the hydride mechanism. 

When the equilibrium partitioning or transfer rate of a given element between two reservoirs depends on atomic mass, isotopic fractionation may arise. For elements... 

The essential features of the results and the mechanistic model can be summarized as follows (1) proton transfer occurs for n = 3 and 4 clusters in the state and is suggested to occur in the S0 state for n > 5, (2) no transfer is found for n < 3 clusters, (3) substitution of deuterium for hydrogen in these clusters [i.e., l-naphthol-d1(ND3)3] has dramatic effects on the observed transfer rates, (4) at the origin of the St - S0 transition the kinetic isotope effect is at least a factor of 20 (D+ transfer is slower than H+ transfer) but at an energy of 1400 cm -1 the kinetic isotope effect is about a factor of 6, (5) the proposed model for proton transfer in these clusters equates proton transfer with a simple barrier penetration... 

By 1950, such isotopic tracer methods began to revolutionize the study of redox reactions as color alone could not always be used to distinguish product formation see equation (1.9). The importance of H+ and other ions on electron transfer rates was soon discovered. A symposium on electron transfer took place in 1951 at the University of Notre Dame, during which a distinction between outer- and inner-sphere electron transfer was made. 

For the case of degenerate HH-transfers, the following isotopic reaction rate constants have been derived [18a-c, 26]... 

Figure 6.15 Degenerate triple-barrier triple hydron transfer involving two z A/itterionic intermediates. A complete transfer consists of a d issociation step, one or more cation or anion propagation steps, characterized by the forward and backward rate constants kf = kb, and a neutralization step. These isotope dependent rate constants depend on whether a cation or an anion is propagated.

The reaction rates observed are substantially increased as compared to TPP the increase is larger for the /1-form as compared to the a- form (Fig. 6.22(b)). Kinetic H/D isotope effects have not yet been studied. The difference in the reaction kinetics of the two forms has been explained as follows. The observed tautomerism in the a- form was interpreted with a circular tautomerism as illustrated in Fig. 6.21(a), with similar transfer rates for the formation of all intermediates. However, the observed transfer in the /1-form was assigned to a local HH-transfer within the two intramolecular hydrogen bonds which led to an extra increase in the rate constants. 

This generalized model yielded satisfactory descriptions of the temperature and isotope dependence of some reported transfer rate constants [9]. The calculated rate constants, plotted as an exponential function of Trather than 1/T, show a constant part at low temperatures followed by a quasi-linear part at higher temperatures. Siebrand et al. [9] applied their procedure to a number of intramolecular H- and D-atom transfers for which some experimental data were available. This included the isomerizations of the tri-terl-butylphenyl radicals, 1J and IJ,. The curves obtained [9] using an anharmonic low frequency motion (which was superior to the harmonic version) are shown in Fig. 28.2. These curves give very satisfactory fits to the experimental rate constants. The calculated, limiting, low temperature QMT-only, OKIE is 50000 It appears to be worthy of the Guinness Book of Records [28]. 

The kinetics of reaction (29) have been investigated by rapid-scan i.r. spectroscopy. The experimental rate constant is in reasonable agreement with an earlier calorimetric value, but the use of isotopic NO has now established the reaction mechanism to be a Cl atom transfer. Rate constants for the nitrogen isotope exchange reactions (30) and (31) have also been determined. ... 

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