How Fast Is The Fastest Possible Chemical Reaction?
In this section of the notes we talk quite a lot about the rates and relative rates of reactions, i.e. what makes one reaction faster than another. A different question might be how fast can the absolute rate of a chemical reaction actually get? What is the absolute upper limit?
How fast a reaction can go depends upon the particular reaction type, and also upon exactly what question you are asking. For example, the rate of the SN2 reaction that we will study later in the course depends upon the concentration of the alkyl halide and the nucleophile. Actually we are being very sloppy with our terminology. Asking how fast a reaction isn't interesting, since for an SN2 the reaction gets faster simply by increasing the concentration of nucleophile or alkyl halide. We really should be talking about the rate constant, since this is the fundamental property of the reaction (that determines the activation energy). A fast reaction is characterized by a large rate constant.
So, how large can the rate constant of a reaction be? This question has been asked by chemists not only because fast reactions are desirable (for reasons I won't get into here), but as a test of fundamental chemical (kinetic) reaction theories. Even though we now know a lot about what controls the relative rates of chemical reactions, predicting from first principles how fast a reaction will go is still considered very difficult. All very interesting I hear you say, but what has this go to do with "real life"? Admittedly not a lot to do with your "real life", but it had a lot to do with mine!
Before coming to ASU I worked on the simplest of all chemical reactions, i.e. transferring a single electron from one molecule (a Donor, D) to another molecule (an Acceptor, A). Such an electron transfer would convert the A into an anion and the D into a cation (a radical anion and radical cation actually, but let's not go there!). Examples of the structures of the actual donors and acceptors are shown below.
The reaction is characterized by a rate constant, ket. We combined experimental measurements of the ket, a theoretical analysis of the reaction and some special spectroscopic measurements to get a complete picture of the process, and were actually able to predict the rate constants of some of the electron transfer reactions quite accurately! We published a whole series of papers on this work, the simplest is probably one that appeared in the journal Accounts of Chemical Research entitled Dynamics of Bimolecular Photoinduiced Electron-Transfer Reactions. If you click on the title you can read the paper, but I wouldn't recommend it unless you are suffering from severe insomnia!
The work was quite physical (i.e. not very organic) and electron transfer is hardly a "real" chemical reaction. So, when I came to ASU and found that I had to teach organic chemistry, I was prompted to wonder if we could take what we learned from the electron transfer work to a real organic reaction, and perhaps work out how to predict the rate constant of a "real" reaction, for example simple bond breaking.
We started with an unusual reaction (for reasons again I don't want to get into here) that involved breaking the N-O bond in the following radical reactions. Here, the -R means that variously substituted radicals were studied. We measured the kbr, examined the reactions in a computer using fundamental chemical structure theories (this is the quantitative quantum theory methods that I mentioned in class), and developed a theoretical description of the reactions.
When we do reaction energy diagrams in class, they are "qualitative", i.e. the general shapes are correct, but the quantitative details are missing. However, WE get real Quantitative Reaction Energy Diagrams, as shown below for several of the bond-breaking reactions :) The slowest reaction is given by the red curve, the fastest by the blue curve. Do you see the significant detail in these diagrams (hint, it is BLUE).
So, are these bond breaking reactions fast? Yes! All of those represented on the diagram take place in less than a millionth of a second, with most taking place in less than a billionth of a second!! How do you measure reactions that fast? It would take too long to explain the details, but the technique uses very fast pulsed laser techniques. The apparatus in our lab looks sort of like this:
What about the Blue reaction curve above? What is its activation energy? It doesn't have one, does it?? This reaction occurs is less than a billionth of a billionth of a second! It is so fast that we can't even measure the rate on the ASU femtosecond laser system. This reaction is one of the fastest ever measured, and I think that we got the best evidence to date of a truly barrierless chemical reaction. I am pretty pleased with this :)
Even better, we were able to construct a theoretical model of the reactions that describes them as a more accurate 3-D surface, shown below, rather than the 2-D reaction energy diagrams shown above. The reactions proceed as indicated by the arrows, with the barrierless one on the right going downhill ALL the way! We recently published a paper on this project entitled Kinetics of Reductive N-O Bond Fragmentation: The Role of a Conical Intersection. Again, if you click on the title you can read the paper. Again, I wouldn't recommend it!