| Dear Vimal, The rate constant and the activation energy or free
energy of activation are related by the Arrhenius equation and the Eyring
equation, respectively. These are easily found in any physical chemistry
textbook / Wikipedia. From
there, it is much less trivial. To know how fast a reaction really is, one
must know the rate law and concentrations of the species in the rate law.
Computational chemists rarely have the ability to apply true experimental
conditions to our simulations. Furthermore, a computed activation barrier
may easily have an error of ±0.05 eV or more. This will lead to an
error in the absolute rate constant approaching a full order of magnitude.
For this reason, the ratio of rate constants (the relative rates) are more
typically discussed, since it is hoped the errors cancel in the division.
However, it is
certainly possible to put numbers into context. Consider the simplest case
of a unimolecular rate law and k determined from the Eyring equation at 298 K.
A barrier of ~0.4 eV gives a rate constant on the order of 1E5 1/sec.
That’s fast. Very fast. A barrier of ~1 eV gives a rate
constant on the order of 1E-5 1/sec. That’s not nearly as slow as
it might seem. A barrier of ~1.5 eV gives a rate constant on the order of
1E-14 1/sec. That’s very slow. Now consider the half-lives of those three
examples, which provides the same information > from a different perspective:
~1E-6 sec, ~1E4 sec, ~1E13 sec. The first is still obviously very,
very fast. This is similar to the barrier to the chair flip in
cyclohexane, which requires cryogenic temperatures to inhibit. It is now a
bit more clear that the 1 eV barrier has a half life that is still perfectly
reasonable if one is willing to wait a few days for the reaction to complete.
The 1.5 eV barrier, though… A half life of about 1 million
years is no one’s idea of “fast” except on a geologic or
cosmic timescale (all things are relative!). In summary, it is trivial to compute a unimolecular
rate constant from an activation barrier. After that, use the specifics of
your system to decide what is “fast” and what
isn’t. Cheers, Eric ---------------------------------------------------- Eric V. Patterson, PhD Director
of Undergraduate Laboratories Senior Lecturer Stony Brook University Department of Chemistry 3400 SUNY Stony Brook, NY 11794-3400 465 Chemistry eric.patterson*o*stonybrook.edu voice: (631) 632-7449 FAX: (631) 632-7960
|