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

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.

ReplyDelete"But this phenomenon becomes even more pronounced at -78 degrees celsius which is the common standard for reactions cooled to liquid nitrogen temperature."Doh! -78 C is the temperature of a dry ice/acetone bath, not a liquid N2 bath (which is at -196 C).

If you're exploiting the difference in the transition state energies between the two products, then your reaction is under kinetic control not thermodynamic control, and the relevant equation should be the Arrhenius rate equation not the equation for ΔG.

ReplyDeleteDoh indeed! Need. More. Coffee.

ReplyDeleteBryan: True, we are talking about the free energy of activation in the Arrhenius formula

∆G†† = ∆H†† - T∆S††

My Ph.D. supervisor had a graph of delta G vs. T inside his office door, just to remind us about this effect.

ReplyDeleteIndeed, my advisor had a table of ∆G vs K (eq.) in his office.

ReplyDeleteYour posts are always appreciated and thank you for them. In the latest, however, there seems to be some confusion about thermodynamic and kinetic drivers. The Arrhenius equation

ReplyDeletek = A exp(-Ea/RT)

expresses a *rate* constant in terms of an experimentally determined activation energy (Ea) and temperature (T). A small difference in Ea can result in significant rate differences, which are in turn amplified at lower temperatures. On the other hand

G = H - TS

is a thermodynamic expression (add necessary deltas) yielding an *equilibrium* constant,

K = exp(-[delta]G/RT).

(The latter has no direct rate component, and is the end result of a reaction run for a long enough period. Time-to-equilibrium expressions can be rather complex and are a function of stoichiometry.)