Kinetic isotope effects equilibrium

An isotope effect (either kinetic or equilibrium) resulting from a comparison made between isotopically different reactant molecular entities. See Intramolecular Isotope Effect Kinetic Isotope Effect Equilibrium Isotope Effect lUPAC (1979) Pure and Appl. Chem. 51, 1725. 

KINETIC ISOTOPE EFFECT EQUILIBRIUM PERTURBATION METHOD KINETIC ISOTOPE EFFECT SOLVENT ISOTOPE EFFECT EQUILIBRIUM THERMODYNAMIOS (Measurable Quantities)... 

KINETIC ISOTOPE EFFECT EQUILIBRIUM ISOTOPE EFFECT SOLVENT ISOTOPE EFFECT HEAVY ATOM ISOTOPE EFFECT INTRAMOLECULAR KINETIC ISOTOPE EFFECT... 

Alteration of either the equilibrium constant or the rate constant of a reaction if an atom in a reactant molecule is replaced by one of its isotopes, distinguished are kinetic isotope effect, equilibrium isotope effect, primary isotope effect, secondary isotope effect. 

The details of proton-transfer processes can also be probed by examination of solvent isotope effects, for example, by comparing the rates of a reaction in H2O versus D2O. The solvent isotope effect can be either normal or inverse, depending on the nature of the proton-transfer process in the reaction mechanism. D3O+ is a stronger acid than H3O+. As a result, reactants in D2O solution are somewhat more extensively protonated than in H2O at identical acid concentration. A reaction that involves a rapid equilibrium protonation will proceed faster in D2O than in H2O because of the higher concentration of the protonated reactant. On the other hand, if proton transfer is part of the rate-determining step, the reaction will be faster in H2O than in D2O because of the normal primary kinetic isotope effect of the type considered in Section 4.5. 

Grovenstein and Kilby218 showed that the kinetic isotope effect kH/kD is 3.97 for the iodination 2,4,6-trideuterophenol by iodine in aqueous buffer at 25 °C, and this is in accord with the base catalysis described above. However, this large isotope effect means that the intermediate is in fairly rapid equilibrium with the reactants, so that it is difficult to determine from kinetic studies which iodinating species is involved. Thus it might be positive iodine, equilibria (112), (113), (115)... 

Interest has been shown by several groups on the effect of solvent and of added anions upon the oxidation of alcohols. The oxidation of isopropanol proceeds 2500 times faster in 86.5 % acetic acid than in water at the same hydrogen ion concentration . The kinetics and primary kinetic isotope effect are essentially the same as in water. Addition of chloride ion strongly inhibits the oxidation and the spectrum of chromic acid is modified. The effect of chloride ion was rationalised in terms of the equilibrium,... 

The k pathway is three times faster in D+/D20 than in H+/H20 for la. The reverse kinetic isotope effect suggests that the rate-limiting event for the k pathway could involve protonation of an amido-nitrogen or an N-Fe bond, forming the stronger N-H bond as the weaker N-Fe bond is cleaved. The k 3 pathway is rationalized as involving pre-equilibrium peripheral protonations of the TAML macrocycle (Scheme 1). The dependence of obs on [H + ] is then given by Eq. (4), which corresponds... 

However, the formation of intermediate 14 requires at least two steps, (i) a proton transfer and (ii) the formation of the cyclic intermediate. If formation of the intermediate, 14, is rate-determining, the carboxy hydrogen must be lost in a pre-equilibrium step because no deuterium kinetic isotope effect is observed for this reaction (Scheme 34). Alternatively, the mandelic acid could displace an acetate ligand in a slow step and the proton could be transferred to the acetate ion in a fast, subsequent step (Scheme 35). Unfortunately, the results do not indicate which step in the formation of the cyclic intermediate, 14, is rate-determining. 

The reaction was second order in acid and first order in substrate, so both rearrangements and the disproportionation reaction proceed via the doubly-protonated hydrazobenzene intermediate formed in a rapid pre-equilibrium step. The nitrogen and carbon-13 kinetic isotope effects were measured to learn whether the slow step of each reaction was concerted or stepwise. The nitrogen and carbon-13 kinetic isotope effects were measured using whole-molecule isotope ratio mass spectrometry of the trifluoroacetyl derivatives of the amine products and by isotope ratio mass spectrometry on the nitrogen and carbon dioxide gases produced from the products. The carbon-12/carbon-14 isotope... 

Abstract The statistical thermodynamic theory of isotope effects on chemical equilibrium constants is developed in detail. The extension of the method to treat kinetic isotope effects using the transition state model is briefly described. 

The understanding of isotope effects on chemical equilibria, condensed phase equilibria, isotope separation, rates of reaction, and geochemical and meteorological phenomena, share a common foundation, which is the statistical thermodynamic treatment of isotopic differences on the properties of equilibrating species. For that reason the theory of isotope effects on equilibrium constants will be explored in considerable detail in this chapter. The results will carry over to later chapters which treat kinetic isotope effects, condensed phase phenomena, isotope separation, geochemical and biological fractionation, etc. 

The chapter starts with a brief review of thermodynamic principles as they apply to the concept of the chemical equilibrium. That section is followed by a short review of the use of statistical thermodynamics for the numerical calculation of thermodynamic equilibrium constants in terms of the chemical potential (often designated as (i). Lastly, this statistical mechanical development is applied to the calculation of isotope effects on equilibrium constants, and then extended to treat kinetic isotope effects using the transition state model. These applications will concentrate on equilibrium constants in the ideal gas phase with the molecules considered in the rigid rotor, harmonic oscillator approximation. 

Fig. 10.5 Distribution of exponents, Equation 10.21, for exact harmonic calculated equilibrium and TST kinetic isotope effects (Hirschi, J. and Singleton, D. A., J. Am. Chem. Soc. 127, 3294 (2005))...

If the isotope sensitive step is reversible the equations get more complicated and cannot be solved explicitly for the intrinsic isotope effects (unless Cf = 0, or the equilibrium isotope effect is unity). The last two equations in Equation 11.48 demonstrate that a normal deuterium kinetic isotope effect diminishes the apparent commitment if both isotopes are present. Thus 13(V/K) is smaller than 13(V/K)d when both isotope effects are related to the same step. 

Aqueous Solvent Equilibrium and Kinetic Isotope Effects... 

When isotopes are fractionated kinetically during chemical reactions, the isotope ratio shift of the reaction products relative to the reactants often depends on reaction mechanisms and rates. This contrasts with isotopic fractionations between phases in isotopic equilibrium, where the isotopic differences are thermodynamic quantities and thus do not depend on reaction mechanisms or rates. In this section, we briefly review the well-developed theory for kinetic isotope effects that appears in the S isotope literature. This background serves as a guide for interpreting and predicting Se and Cr isotope systematics. 

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