Enantiomers equilibria

The reaction is reversible and its stereochemical requirements are so pronounced that neither the cis isomer of fumaric acid (maleic acid) nor the R enantiomer of malic acid can serve as a substrate for the fumarase catalyzed hydration-dehydration equilibrium... 

Compound A can be resolved to given an enantiomerically pure substance, [a]p = —124°. Oxidation gives the pure ketone B, which is optically active, [aJo — —439°. Heating the alcohol A gives partial conversion (an equilibrium is established) to an isomer with [a]p = +22°. Oxidation of this isomer gives the enantiomer of the ketone B. Heating either enantiomer of the. ketone leads to the racemic mixture. Explain the stereochemical relationships between these compounds. 

To demonstrate the potential of the process in obtaining both enantiomers at a high purity, experiments were performed using racemic norephedrine as the compound to be separated. Two columns of seven small membrane modules were used. The enantiomer ratios in the outflows during start-up are shown in Fig. 5-15. It can be concluded that the system reaches equilibrium within approximately 24 h, and that both enantiomers are recovered at 99.3-99.8 % purity. 

The chromatographic resolution of bi-naphthol enantiomers was considered for simulation purposes [18]. The chiral stationary phase is 3,5-dinitrobenzoyl phenyl-glycine bonded to silica gel and a mixture of 72 28 (v/v) heptane/isopropanol was used as eluent. The adsorption equilibrium isotherms, measured at 25 °C, are of bi-Langmuir type and were proposed by the Separex group ... 

The separation of bi-naphthol enantiomers can be performed using a Pirkle-type stationary phase, the 3,5-dinitrobenzoyl phenylglycine covalently bonded to silica gel. Eight columns (105 mm length) were packed with particle diameter of 25 0 fiva. The solvent is a 72 28 (v/v) heptane isopropanol mixture. The feed concentration is 2.9 g for each enantiomer. The adsorption equilibrium isotherms were determined by the Separex group and already reported in Equation (28) [33]. 

The competitive adsorption isotherms were determined experimentally for the separation of chiral epoxide enantiomers at 25 °C by the adsorption-desorption method [37]. A mass balance allows the knowledge of the concentration of each component retained in the particle, q, in equilibrium with the feed concentration, < In fact includes both the adsorbed phase concentration and the concentration in the fluid inside pores. This overall retained concentration is used to be consistent with the models presented for the SMB simulations based on homogeneous particles. The bed porosity was taken as = 0.4 since the total porosity was measured as Ej = 0.67 and the particle porosity of microcrystalline cellulose triacetate is p = 0.45 [38]. This procedure provides one point of the adsorption isotherm for each component (Cp q. The determination of the complete isotherm will require a set of experiments using different feed concentrations. To support the measured isotherms, a dynamic method of frontal chromatography is implemented based on the analysis of the response curves to a step change in feed concentration (adsorption) followed by the desorption of the column with pure eluent. It is well known that often the selectivity factor decreases with the increase of the concentration of chiral species and therefore the linear -i- Langmuir competitive isotherm was used ... 

However, considering practical limitations, that is, the availability of optically pure enantiomers, E values are more commonly determined on racemates by evaluating the enantiomeric excess values as a function of the extent of conversion in batch reactions. For irreversible reactions, the E value can be calculated from Equation 1 (when the enantiomeric excess ofthe product is known) or from Equation 2 (when the enantiomeric excess ofthe substrate is knovm) [la]. For reversible reactions, which may be the case in enzymatic resolution carried out in organic solvents (especially at extents of conversion higher than 40%), Equations 3 or 4, in which the reaction equilibrium constant has been introduced, should be used [lb]. 

Natural systems may be quite complex. For example, the enantiomerization of phenoxyalkanoic acids containing a chiral side chain has been studied in soil using H20 (Buser and Muller 1997). It was shown that there was an equilibrium between the R- and 5-enantiomers of both 2-(4-chloro-2-methylphenoxy)propionic acid (MCPP) and 2-(2,4-dichlorophenopxy)propionic acid (DCPP) with an equilibrium constant favoring the herbicidally active / -enantiomers. The exchange reactions... 

There was still some room for uncertainty on this retention-retention mechanism. The argument was, if the unobserved tt-allyl Mo complex (such as 77 or B in Scheme 2.18) was more highly reactive towards sodium malonate than experimentally observed tt-allyl Mo complexes (such as 71, 74, and 80), the reaction should proceed through inversion (since there is an equilibrium between the two tt-allyl Mo complexes via the o-allyl complex.) If so, when the isolated Mo-complex 71 was subjected to the reaction, 71 must be equilibrated to the enantiomer of 71 via the o-allyl complex prior to reaction with a nucleophile. Therefore, reaction from the Mo complex 71 should proceed with less stereoselectivity than that from a mismatched branched carbonate. This hypothesis was examined, as shown in Scheme 2.26. 

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. 

Enantiomeric recognition was clearly displayed in films spread from solution and films in equilibrium with their crystals, and was sharply dependent on the acidity of the subphase. Protonation of the amide group appeared to be necessary for spreading to stable monolayers. For example, the crystals of the racemate deposited on a 10n H2S04 solution at 25°C spread quickly to yield a film with an ESP of 7.7 dyn cm"1, while the single enantiomers spread only to a surface pressure of 3.9 dyn cm-1 (Table 1). Similar effects are observed at 15 and 35°C. The effect of stereochemistry on equilibrium spreading is even more pronounced at lower subphase acidities. On 6n sulfuric acid, the racemate spread to an equilibrium surface pressure of 4.9 dyn cm-1, while the enantiomeric systems spread to less than 1 dyn cm-1. 

These results for spread film and equilibrium spreading suggest that films of racemic N-(a-methylbenzy 1) stearamide may be resolved by seeding the racemic film with crystals of either pure enantiomer. Indeed, when a monolayer of racemic jV- (a-methylbenzyl) stearamide is compressed to 45 A2/molecule (27 dyn cm-1), deposition of a crystal of either R( +)- or S( — )-enantiomer results in a decay of surface pressure from the initial 28 dyn cm-1 film pressure to 3.0 dyn cm-1, the ESP of the enantiomeric systems on a pure 10n sulfuric acid subphase (Table 1). When the experiment is repeated with racemic crystals, the system reaches an equilibrium surface pressure of 11 dyn cm-1, nearly the ESP of the racemic crystal on the clean acidic interface. In either case, equilibrium pressure is reached within a two hour time period. 

To construct a triangular diagram consisting of two enantiomers and the solvent at constant temperature requires the determination of the concentration of the saturated solutions as a function of the total composition of the system, and the number and nature of the solid phases in equilibrium with the saturated solution. The determination of the solubility of mixtures of enantiomers is... 

In Fig. 24 points A and A represent the equal solubilities at the temperature T0 of the pure enantiomers, while E represents the solubility of the eutectic mixture. AEA is the solubility-composition curve, above which undersaturated solutions exist and below which a saturated solution is in equilibrium with the two solid phases, D and L. Figure 21 shows that, with an increase in temperature, A and A move toward the pure enantiomers D and L, while E moves toward the pure eutectic. All of these trends indicate an increase in solubility upon increasing the temperature. 

On the other hand, if the enantiomeric purity of the original solid is less than that of the eutectic (as in the case of M2 in Fig. 25b), crystallization results in a decrease in enantiomeric purity. For example, when sufficient solvent has been added to correspond to point P2, the tie line shows that the solid N2 contains less of the predominant enantiomer D than M2 and is in equilibrium with E, which corresponds to a saturated solution of the eutectic solid, e. When the system reaches the composition represented by point Q2, the solid that crystallizes out is the racemic compound, R, which is in equilibrium with the saturated solution, U2, containing the racemic compound and enantiomer D. 

If solvent is added to either of the solid eutectics represented by e or e in Fig. 25a or b, the undissolved solid retains this composition while the saturated solution maintains the composition E or E, respectively. Again, Gibbs phase rule [145,146] can provide further insight into these systems. If the solid enantiomers are solvated, the compositions of the equilibrium solids are displaced symmetrically along the DS or LS axes to an extent determined by the stoichiometry of the solvates. Similarly, if the racemic compound is solvated, the stoichiometry of the equilibrium solid is displaced from R along the line RS to an extent determined by the stoichiometry of the solvate. 

Certain pairs of enantiomers, such as 25°C solutions of camphor in aqueous ethanol (Fig. 26a), 2,2,5,5-tetramethyl-l-pyrrolidinoxy-3-carboxylic acid in chloroform (Fig. 26b), or carvoxime in hexane (Fig. 26c), cocrystallize throughout the entire range of mole fractions. The crystals that are in equilibrium with the saturated liquid solution are solid solutions (mixed crystals), since they constitute a single phase. The racemic solid solution is termed a pseudoracemate [141]. 

Figure 26 shows the ternary phase diagrams (solubility isotherms) for three types of solid solution. The solubilities of the pure enantiomers are equal to SA, and the solid-liquid equilibria are represented by the curves ArA. The point r represents the equilibrium for the pseudoracemate, R, whose solubility is equal to 2Sd. In Fig. 26a the pseudoracemate has the same solubility as the enantiomers, that is, 2Sd = SA, and the solubility curve AA is a straight line parallel to the base of the triangle. In Figs. 26b and c, the solid solutions including the pseudoracemate are, respectively, more and less soluble than the enantiomers. 

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