Limiting isotope effect determination

Hence, Eq. (17.41), describing the limiting isotope effect on V/K, is independent of the concentration of A. In practice, what we do is to vary [B] at different levels of labeled or unlabeled [A] and determine (V/JCb) from the slope ratio this minimizes any external commitment factors. 

The efficiency of oxidation of open-chain alkyl, cycloalkyl, and unsaturated alcohols in acetonitrile by 9-phenylxanthylium ion (PhXn+) was dependent on the alcohol stmc-tures. Structure-reactivity relationship was discussed with relation to formation of a carbocationic transition state (C +-OH). Kinetic isotope effects determined at a-D, p-D3, and OD positions for the reaction of 1-phenylethanol suggested a hydride-proton sequential transfer mechanism that involved a rate-limiting formation of the a-hydroxy carbocation intermediate. Unhindered secondary alkyl alcohols were selectively oxidized in the presence of primary and hindered secondary alkyl alcohols. Strained C(7)-C(ll) cycloalkyl alcohols reacted faster than cyclohexyl alcohol, whereas the strained C(5) and C(12) alcohols reacted slower. Aromatic alcohols were oxidized efficiently and selectively in the presence of aliphatic alcohols of comparable steric requirements. ... 

It is claimed that the limiting value of k bs, 2.81 x 10" sec-1, represents the rate coefficient for the rearrangement reaction above (k,). The ring deuterium isotope effect kH kD was re-determined for this individual rate coefficient for rearrangement by finding the limiting value in the presence of added N-methylaniline and was found to be 2.4 at two different acidities, as compared with 1.7 for the ratio of the observed composite rate coefficients, as expected, since no isotope effect would be predicted for the de-nitrosation step. 

Figures 7-9 show the fractional conversion of methanol in the pulse as a function of temperature for the three catalysts and the three methanol feeds. Evidently the kinetic isotope effect is present on all three catalysts and over the complete temperature range, indicating that the rate limiting step is the breaking of a carbon-hydrogen bond under all conditions. From these experiments, the effect cannot be determined quantitatively as in the case of the continuous flow experiments, but to obtain the same conversion of CD,0D, the temperature needs to be 50-60° higher. This corresponds to a factor of about three in reaction rate. The difference in activity between PfoCL and Fe.(MoO.), is larger in the pulse experiments compared to tHe steady stateJ results.

Because solvent viscosity experiments indicated that the rate-determining step in the PLCBc reaction was likely to be a chemical one, deuterium isotope effects were measured to probe whether proton transfer might be occurring in this step. Toward this end, the kinetic parameters for the PLCBc catalyzed hydrolysis of the soluble substrate C6PC were determined in D20, and a normal primary deuterium isotope effect of 1.9 on kcat/Km was observed for the reaction [34]. A primary isotope effect of magnitude of 1.9 is commonly seen in enzymatic reactions in which proton transfer is rate-limiting, although effects of up to 4.0 have been recorded [107-110]. 

A mechanistic study of acid and metal ion (Ni2+, Cu2+, Zn2+) promoted hydrolysis of [N-(2-carboxyphenyl)iminodiacetate](picolinato)chromate (III) indicated parallel H+- or M2+-dependent and -independent pathways. Solvent isotope effects indicate that the H+-dependent path involves rapid pre-equilibrium protonation followed by rate-limiting ring opening. Similarly, the M2+-dependent path involves rate-determining Cr-0 bond breaking in a rapidly formed binuclear intermediate. The relative catalytic efficiencies of the three metal ions reflect the Irving-Williams stability order (88). 

Since the kinetic constant is independent of the reagent concentration and of the extent of proton loss from the intermediate, the last step is surely not rate limiting and the formation of the intermediate is for this olefin completely rate determining. (20) Consistent with this hypothesis is the lack of a large primary kinetic isotope effect (KIE), kH/kD = 0.97 (0.01), expected for a slow L+ loss when the vinyl bromide is the main product. Taking into account that the rate determining step is the formation of a bromocarbenium-tribromide (bromide) ion pair and that the transition state should be closely related to the intermediate,... 

It is worth noting that Murr and Donnelly (1970a,b) have demonstrated that the secondary a-deuterium KIE is only approximately 75% of the theoretical maximum kinetic isotope effect when the ionization (ki) step of the reaction (Scheme 1) is fully rate determining, i.e. when the reaction occurs via a limiting SN1 mechanism (Shiner, 1970b Westaway, 1987c). 

This non-competitive method has several practical limitations. Since the ordinary precision of determination of rate constants, (8kL/kL) or (Ske/kn), is on the order of a few percent, the method is limited as a practical matter to large, primary kinetic isotope effects, generally of hydrogen. This, because deuterium, the common heavy isotopomer for hydrogen, is available at 100% abundance at reasonable cost, and for hydrogen KIE s are usually large enough to constrain the relative error, 8(kL/kH)/(kL/kH), to acceptable values. 

The energy level density is not important in determining the magnitude of the isotope effect at high pressure. At the low pressure limit, again for thermal activation,... 

T-secondary isotope effect can be determined. As recounted in the last item of Chart 3, such effects are expected to be measures of transition-state structure. If the transition state closely resembled reactants, then no change in the force field at the isotopic center would occur as the reactant state is converted to the transition state and the -secondary kinetic isotope effect should be 1.00. If the transition state closely resembled products, then the transition-state force field at the isotopic center would be very similar to that in the product state, and the a-secondary kinetic isotope effect should be equal to the equilibrium isotope effect, shown by Cook, Blanchard, and Cleland to be 1.13. Between these limits, the kinetic isotope effect should change monotonically from 1.00 to 1.13. 

Note that the ratios of observable to microscopic rate constants (in square brackets) determine the fractional degree to which the microscopic rate constant determines the rate with protiated substrate (i.e., [(kcat/ M)H/ oiH] = 1 when ioiH = ( cat/ M)H and moiH is fully rate-limiting [(kcat/ M)H/ ioiH] =0 when ioiH ( cat/ M)H and moiH has no effect on the rate). These quantities are weighting factors for the individual isotope effects ... 

Lewis et al. (entry 11 of Table 2) examined the temperature-dependence of isotope effects in the action of both the human enzyme and the soybean enzyme, by measuring the relative amounts of per-protio and per-deuterio-13-hydroperoxy-products by HLPC. The observed effects are, therefore, composed of primary, secondary, and perhaps remote isotope-effect contributions. Isotope effects on fecat/ M for both enzymes (determined by competition between labeled substrates) are increased by high total substrate concentration, an effect previously observed but stiU ill-understood. At 100 /rM substrate, the effects are roughly independent of temperature below about 15 °C, and are about 60 (H/D) for the human enzyme and 100 (H/D) for the soybean enzyme. Above 15 °C, the effects decline to about 50 for the human enzyme and about 60 for the soybean enzyme, perhaps because non-isotope-sensitive steps become more nearly rate-limiting (see Chart 4). 

The mechanism of the aldol-Tishchenko reaction has been probed by determination of kinetics and isotope effects for formation of diol-monoester on reaction between the lithium enolate of p-(phenylsulfonyl)isobutyrophenone (LiSIBP) and two molecules of benzaldehyde. ". The results are consistent with the formation of an initial lithium aldolate (25) followed by reaction with a second aldehyde to form an acetal (26), and finally a rate-limiting intramolecular hydride transfer (Tishchenko... 

A further limitation stems from a detailed examination of the possible reaction coordinate in an Sfjl reaction. Consider a scheme where substrate A may solvolyse to form an intimate ion pair, B, that dissociates and then reacts with solvent. Shiner et al. (1969), Shiner and Dowd (1971) and Shiner and Fisher (1971) have suggested that maximum a-effects will be found where there is a rate-determining conversion of the intimate ion pair into a solvent-separated ion pair, and Murr and Donnelly (1970) have shown how partitioning of the ion pair, B -> A and C, results in an isotope effect in the diphenylmethyl... 

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