Enantiomers thermodynamic equilibria

Categories that cause problems for this definition of chemical substance include (1) enantiomers (species containing equal amounts of two optical isomers, like I- and d-tartaric acid) (2) azeotropic mixtures (3) dissociative compounds in equilibrium (4) certain types of mixed crystals or other polymorphic compounds (e.g,d- and /-camphoroxime) (5) synthetic polymers (6) many biochemical compounds (7) systems that are not in "pure" thermodynamic equilibrium and (8) isotopes. In each case, pragmatic decisions have to be made, as the notion of pure substance cannot be essen-tialized. There are no competing definitions of "pure substance" that can avoid the need for "inspired adhoccery" to deal with difficult cases. 

Phase transition is a fundamental defining characteristic of this approach to pure substances. Hence substances that exist in one phase only, easily decompose, only occur in solution, etc. can only be included by analogy. Timmermans [1928, 23-53] lists the following potentially difficult cases for the molar approach of substance definition as summarised in this section azeotropic mixtures, dissociative compounds in equilibrium, enantiomers and racemates ( 18), certain types of mixed crystals or other polymorphic compounds, polymers ( 16), many biochemical compounds, and systems that are not in thermodynamic equilibrium. 

Further, the chiral discrimination model via the formation of ionic diastereomers, as proposed by Bhushan and Parshad [8] in Scheme 13.1, was viewed by Kowalska and coworkers [11] in terms of the energy difference for ion-pair formation (i.e., in the formation of the two diastereomeric salts). Ibuprofen is a carboxylic acid and, therefore, apt to dissociate (and form an organic anion) and the separation of the two enantiomers of ibuprofen can be achieved only because the thermodynamic equilibrium constants (K) for the ion-pair formation process for the two enantiomers (Ki and K2, respectively) have different numerical values. From the theory of adsorption liquid chromatography, it is well known [15] that the thermodynamic equilibrium constant of adsorption, K, can be defined as follows ... 

By taking into account the latest results on the behaviour of systems far away from equilibrium, Kondepudi and Nelson (1985) were able to show by calculation that L-amino acids are slightly favoured. There is a very tiny stabilisation effect due to the weak interaction amplification mechanisms cause this effect to reach 98% of the probability that L-enantiomers of amino acids are favoured for incorporation into polymers. The amplification mechanisms are explained by the thermodynamics of irreversible systems. 

Alcohols will serve as hydrogen donors for the reduction of ketones and imi-nium salts, but not imines. Isopropanol is frequently used, and during the process is oxidized into acetone. The reaction is reversible and the products are in equilibrium with the starting materials. To enhance formation of the product, isopropanol is used in large excess and conveniently becomes the solvent. Initially, the reaction is controlled kinetically and the selectivity is high. As the concentration of the product and acetone increase, the rate of the reverse reaction also increases, and the ratio of enantiomers comes under thermodynamic control, with the result that the optical purity of the product falls. The rhodium and iridium CATHy catalysts are more active than the ruthenium arenes not only in the forward transfer hydrogenation but also in the reverse dehydrogenation. As a consequence, the optical purity of the product can fall faster with the... 

Chiral N/O-acetals may racemize in the solid state when water of crystallization is present. Examples are the epimerizations of the oxazolidines 97 that contain water from their preparation by stereoselective condensation. Thus, the kinetically preferred products 97a,b (which are admixed to the thermodynamically more stable products 98a,b) epimerize within some weeks in the solid state to give enantiopure 98a,b [661 (Scheme 9). It appears that the N/O-acetal hydrolyses and recloses. Solid-state racemizations are quantitative if the 1 1 equilibrium between the enantiomers is obtained. Therefore they do not really fulfill the criterion of only one product. Numerous examples in the organo-metallic field are listed in [671 and [681. 

IfK2, kl9 k u and k2 had the same values as K 2, k u k l9 and k 2, then the optical purity of the product, RH, would be determined solely by the value of the diastereomeric equilibrium constant Kv If, however, the primed and unprimed constants were different, the final optical yield could be determined by both thermodynamic and kinetic factors, and in one extreme could result in the observation that the preferred enantiomer of the product originated in the minor dia-stereomer. Clearly, kinetic factors can be important since the steric interactions of the initial two diastereomers are different and these could affect the rate constants of the reaction. Moreover, the o--alkyl intermediate is chiral, as shown for one of the initial olefin diastereomers in Figure 4, and the rate of hydrogen addition and insertion... 

Photosensitized deracemization, or enantiomerization, is a method for shifting the equilibrium between enantiomers through the excited-state interaction with a chiral sensitizer. This is unique to photochemistry, as the ground-state thermodynamics do not allow the deviation of the equilibrium constant from unity. However, only a limited amount of effort has hitherto been devoted to this unique methodology. Thus practically only two types of substrate, i.e., sulfoxide and allene, have been subjected to photosensitized deracemization (Scheme 4), and the reported examples do not appear to be very successful. 

Because enantiomers of the same compound have many of the same thermodynamic properties, including solubility character sties in nonchiral solvents, they are particularly difficult to separate in equilibrium processes. 

However, if the van t Hoff plots are linear, it indicates that the retention and/or selective processes governing the separation are unchanged over the temperature range studied. Furthermore, it can be assumed that a separation is a) thermodynamically reversible, b) (AH) and (AS) values are temperature independent, c) the enantiomers are retained in single associative mechanism, and d) a solvation-desolvation equilibrium does not obscure the association process of the enantiomers with the... 

Biochemistry s hidden asymmetry was discovered by Louis Pasteur in 1857. Nearly 150 years later, its true origin remains an unsolved problem, but we can see how such a state might be realized in the framework of dissipative structures. First, we note that such an asymmetry can arise only under far-from-equilibrium conditions at equilibrium the concentrations of the two enantiomers will be equal. The maintenance of this asymmetry requires constant catalytic production of the preferred enantiomer in the face of interconversion between enantiomers, called racemization. (Racemization drives the system to the equilibrium state in which the concentrations of the two enantiomers will become equal.) Second, following the paradigm of order through fluctuations, we will presently see how, in systems with appropriate chiral autocatalysis, the thermodynamic branch, which contains equal amounts of L- and D-enantiomers, can become unstable. The instability is accompanied by the bifurcation of asymmetric states, or states of broken symmetry, in which one enantiomer dominates. Driven by random fluctuations, the system makes, a transition to one of the two possible states. 

Special situation (c). A is a chiral molecule subject to inversion. The enantiopreferential binding to B can then affect the equilibrium between the enantio-mers to make the total of A non-racemic (an excess of one enantiomer). Generally, the preferred enantiomer is thermodynamically stabilized. This is the so-called Pfeiffer effect . An example is given by the addition of labile [Fe(phen)3] + to DNA where the observed... 

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