Why conduct reactions at low temperature?

The other day I was talking to a synthetic chemist friend about conducting reactions at low temperature and I realized that there is another reason for doing this that is not always appreciated by beginning organic chemistry students. Most students think that the primary purpose of low-temperature reactions is to stop runaway exothermic reactions from getting out of hand and to tame explosive reagents. While this is a perfectly good reason, there is another reason connected to stereochemistry which occasionally necessitates these reactions.

Remember the all important thermodynamic relation ∆G = ∆H - T∆S and recall that life and laboratory chemistry are both games played within a 3 kcal/mol window. In this case the relevant equation would be the Arrhenius equation and the relevant free energy would be the free energy of activation (∆G††). Thus even a 1 kcal/mol energy difference between two transition states can favor the product corresponding to the lower energy TS by a substantial account; for instance you only need a 1.8 kcal/mol energy difference to effect a greater than 95% yield of the more stable species. This principle applies to everything, including conformers, stereoisomers and constitutional isomers. But the important variable for our discussion is the temperature T and it's clear that a lower temperature will affect the free energy favorably.

And that is precisely why it becomes so important in stereoselective reactions. If you are dealing with two diastereometric transition states resulting from attack of a chiral reagent on two enantiomers for instance, you only need a difference of 1.13 kcal/mol to generate a diastereomeric ratio of 95:5. But this phenomenon becomes even more pronounced at -78 degrees celsius which is the temperature of a standard liquid N2 acetone/dry ice bath. For instance, if you conduct a reaction giving you a 95:5 diastereomeric ratio at -78 degrees, the same reaction done at 23 degrees will give you only a 85:15 diastereomeric ratio. And if you look at the energy you need at 23 degrees to overcome that low ratio and bump it to 95:5, it's only 0.58 kcal/mol.

It's incredible to realize how so much of life and chemistry are governed by startlingly small differences in energy between large numbers. But there you have it; a very good reason to lower the temperature of your next aldol condensation to get better stereoselectivity. Make sure to emphasize that to your curious undergrad the next time he/she asks a question about low temperature reactions.