New Vistas in Reaction Kinetics

As a holdover from grad school, I still get a little pain in my stomach whenever someone mentions “kinetics studies.” I never had the displeasure of running one myself, but I’ve heard many stories of others’  painful nights camped out at the NMR, running hours-long kinetics runs on slow reactions. And really, not a whole lot has changed with respect to reaction kinetics over the years. Sampling rates have gotten larger, and the repertoire of analytical methods used to follow concentration(s) has grown, but the underlying theory of reaction kinetics has largely remained the same.

Historically, the development of reaction kinetics has been a story of increasing cleverness. At some point, someone figured out that using a reactant in “drowning” concentrations causes its concentration to remain basically constant over the course of the reaction, removing its influence on the reaction rate—and thus was born the “isolation method.” Yet another clever chemist figured out that only initial rates are necessary to determine kinetic orders, provided multiple runs of a reaction are feasible—and thus emerged the “method of initial rates.”

Why stop there? Increasingly complicated mechanisms (especially catalytic mechanisms) have created a demand for ever more clever methods of kinetic study. Plus, technological advancements are pushing the Δt between data points ever smaller and the sizes of data sets ever larger. Concentration versus time data are basically continuous these days (as are rate versus time data), so why not use the entire span of a kinetics run to the best of our ability? A recent article by Blackmond shows just how far this approach can take chemists studying reaction mechanisms. With data for just a couple of cleverly structured reaction runs, one can propose pretty good guesses for reaction mechanisms.

Reaction progress kinetic analysis (RPKA) is a sort of “kinetic analysis for the twenty-first century.” (Warning: studying RPKA leads to countless instances of “damn, I wish I’d thought of that” thoughts.) As the linked WP article suggests, the theoretical underpinnings of RPKA are not new, but it’s a useful re-imagining of classical kinetics in the context of catalyzed reactions. One of its most interesting notions is the idea of same excess: two runs of a one-to-one (A + B) reaction involving the same excess of A over B represent the same reaction at two different points in time. The run with smaller concentrations is just the run with larger concentrations at a later point in time.

However, subtle differences between the runs can point to mechanistic phenomena that are otherwise hard to spot. For example, say we ran the reaction A + B –(cat)–> A–B twice, using the following initial conditions:

Run I: [A] = 0.100 M, [B] = 0.075 M
Run II: [A] = 0.080 M, [B] = 0.055 M

Time t = 0 for Run II is just a later time point of Run I, with two critical differences:

  1. When [A] = 0.080 M and [B] = 0.055 M in Run I, some product is also present.
  2. When [A] = 0.080 M and [B] = 0.055 M in Run I, the catalyst has engaged in some turnovers.

We can shift the concentration-versus-time curve for Run II to the right until its t = 0 point coincides with a later time point in Run I and look for differences. Thanks to the clever design of the runs, any differences must be due either to product inhibition/acceleration (see point 1) or catalyst decomposition/generation (see point 2). Acceleration by product is essentially autocatalysis, while catalyst generation can occur if an off-cycle intermediate disappears as the reaction occurs. Further experiments can help distinguish these possibilities. Neat, eh?

Check out Blackmond’s article in the Journal of the American Chemical Society for more!

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