Chemical equilibrium, isotope effects

The Heisenberg Uncertainty Principle, describing a dispersion in location and momentum of material particles that depends inversely on their mass, gives rise to vibrational zero-point energy differences between molecules that differ only isotopically. These zero-point energy differences are the main origin of equilibrium chemical isotope effects, i.e., non-unit isotopic ratios of equilibrium constants such as K /Kj) for a reaction of molecules bearing a protium (H) atom or a deuterium (D) atom. 

Enzymes, enantoselectivity, 148 Equilibrium chemical isotope effects, 28 for NCMH model, 40-41 ESI-MS analysis... 

Chemical isotope effects are divided into two classes—those affecting the position of the equilibrium in a chemical reaction and those affecting the rate of a chemical reaction. Equilibrium isotope effects have their origin in the fact that the extent to which any chemical reaction goes is governed by the number of possible ways it can proceed (the phase space available). The more equally probable reaction paths available, the more likely the reaction will go. To illustrate this point, consider the exchange reaction... 

Chemical isotope effects are divided into two types equilibrium and kinetic. The latter are of particular importance in palaeolimnology (and other branches of the sedimentary N cycle) and are typically associated with complex, irreversible, biologically mediated reactions. A characteristic, but not invariable aspect of kinetic isotope fractionation is a marked discrimination against the heavier isotope, snch that the product of the reaction is enriched in N relative to the substrate. 

Figure 3.12 Equilibrium deuterium isotope effects on C chemical shifts of p-diketones as a function of the mole fraction. (Reproduced from Bordner et al. [21]. Copyright (1989), with permission of Wiley-VCH.)...

The measurement of deuterium isotope effects on chemical shifts is a useful tool for studies of tautomeric equilibrium (for details see the reviews 42 44). The deuterium isotope effect AX(D) is defined as the difference between chemical shifts in deuterated and non-deuterated sample [26]. 

The deuterium isotope effects on chemical shift consists of intrinsic isotope effect (direct perturbation of the shielding of X atom) and equilibrium isotope effect (perturbation of the equilibrium caused by the isotopic substitution). The values of deuterium isotope effects are to some extent independent of chemical shifts and allow determination of the mole fraction of the forms in equilibrium. 

T. Deuterium isotope effects on 13 C chemical shifts In the studies of proton transfer equilibrium of Schiff bases, the most informative are deuterium isotope effects measured for carbons bonded with proton donor groups (C-2 or C-7 for gossypol derivatives). For imines in which... 

The position of the proton transfer equilibrium for the Schiff bases being derivatives of rac-2-aminobutane [24] or rac-a-methylbenzylamine [25] and their adducts with dirhodium complex has been estimated in CDCI3 solution on the basis of measurements of deuterium isotope effects on 15N chemical shift.12 It was shown that adduct formation significantly influenced the position of the equilibrium which was manifested by AN(D) values. 

Isotopes of hydrogen. Three isotopes of hydrogen are known H, 2H (deuterium or D), 3H (tritium or T). Isotope effects are greater for hydrogen than for any other elements (and this may by a justification for the different names), but practically the chemical properties of H, D and T are nearly identical except in matters such as rates and equilibrium constants of reactions (see Tables 5.1a and 5.1b). Molecular H2 and D2 have two forms, ortho and para forms in which the nuclear spins are aligned or opposed, respectively. This results in very slight differences in bulk physical properties the two forms can be separated by gas chromatography. 

Isotope Effects on Equilibrium Constants of Chemical Reactions Transition State Theory of Isotope Effects... 

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. 

The statement applies not only to chemical equilibrium but also to phase equilibrium. It is obviously true that it also applies to multiple substitutions. Classically isotopes cannot be separated (enriched or depleted) in one molecular species (or phase) from another species (or phase) by chemical equilibrium processes. Statements of this truth appeared clearly in the early chemical literature. The previously derived Equation 4.80 leads to exactly the same conclusion but that equation is limited to the case of an ideal gas in the rigid rotor harmonic oscillator approximation. The present conclusion about isotope effects in classical mechanics is stronger. It only requires the Born-Oppenheimer approximation. 

Wolfsberg, M. and Kleinman, L. I. Corrections to the Bom-Oppenheimer approximation in the calculation of isotope effects on equilibrium constants, in Rock, P. A., ed. Isotopes and Chemical Principles, ACS Symposium Ser. 11, 64 (1975). 

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