Chemistry - Reactions between enantiomers in a racemic mixture

Solution 1:

If a chiral molecule (an enantiomer) can react with itself, dimerize for example, to form a new compound, then formation of this new compound would contaminate the racemic mixture.

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Perhaps more importantly is interaction of the racemic mixture with itself in the solid state. Just as the interaction between a right hand and left hand is different than the interaction between two right hands, the interaction between the R form and S form of the enantiomer will be different than the interaction between two R (or two S) forms.

In liquids and gases, molecular encounters are fleeting and cannot be preserved or "locked in" for significant periods of time as they can be in a solid. In other words, any favorable, lower energy molecular encounters are quickly broken apart by the energetically larger effects of thermal motion. However, when the racemic mixture is in a solid phase, if the interaction between R and R (or S and S) is lower in energy then the interaction between R and S, then the R and S enantiomers will tend to form separate crystals and a mixture of pure R and pure S crystals will result. Such mixtures are often termed "conglomerates". On the other hand if the interaction between R and S is more favorable (lower in energy), then a racemic compound or racemate is formed where each crystal contains R-S pairs.

A conglomerate, being a simple mixture, will show a melting point depression compared to the pure enantiomer. A racemic compound may have a melting point higher or lower than the pure enantiomer.

Further reading on racemic conglomerates and racemic compounds can be found here and here.

Solution 2:

This is a difficult question to answer without having specific compounds to work with, but let's say that you have a pair of enantiomers with a single stereocenter, so there's an (R)-enantiomer and an (s)-enantiomer. There are four possible reactions:

$\ce{R + R -> RR}$

$\ce{R + S -> RS}$

$\ce{S + R -> SR}$

$\ce{S + S -> SS}$

The set of products are four stereoisomers of which there are two pairs of enantiomers: (RR)/(SS) and (RS)/(SR). [Note that I'm assuming that the chemical reaction renders the (RS)/(SR) compounds asymmetrical. If they were symmetrical, then these would be achiral, meso compounds.]

Where this could get more interesting is that the rates of those reactions are not necessarily the same, since we have two chiral reactants interacting. Consider the transition states leading to RR and RS. Those transition states diastereomeric, and thus require different activation energies. This shouldn't be surprising since RR and RS are diastereomers, which have different energies. The reaction with the lower activation energy is called the matched case, and the reaction with the higher activation energy is called the mismatched case. I'm not aware of any chemistry where the possible starting materials are all stereoisomers of each other, but this phenomenon can be important for setting new stereocenters in compounds that already have stereocenters.