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MARGINALIA

Long Live the Intermediate!

What’s in between in a reaction matters just as much as what sets it off

Roald Hoffmann

Making a Go of It

Suppose A and B are molecules that, according to the strict dictates of thermodynamics, should react spontaneously to give a product we will call P. (P could be more than one molecule.) Technically, what I mean by “should react” is that the Gibbs energy—that marvelous combination of enthalpy and entropy—decreases as A and B are transformed into P. In other words, the reaction liberates energy and, like water flowing downhill, should proceed spontaneously.

2012-03MargHoffmannFA.jpgClick to Enlarge ImageOften, however, the reaction does not go, even if we put in a moderate amount of energy via heat. The reason it doesn’t go is that the eventual payoff—the Gibbs energy that is waiting, so to speak, to be released in the reaction—is just not available to gently colliding molecules in thermal equilibrium. The reaction has an activation energy (a Gibbs energy, too), a hill that must be climbed before the energy that is set free in the reaction becomes available. The hill is represented in the top half of the figure at right. At ambient temperature and pressure, only an infinitesimal number of molecules acquire sufficient energy in collisions with each other to get over that hill. Tough on you, if you want the reaction to go, but too often true.

Here’s where the catalyst comes in. The sequence of reactions that transpires, called the mechanism of the reaction, is given below. Cat stands for the catalyst and Cat•A for another molecule, the reaction intermediate.

2012-03HoffmannEquation1

The energy profile that accompanies this sequence of two reactions, shown in the bottom half of the figure, is fundamentally different from that of the uncatalyzed reaction. Now the barriers to each reaction are much smaller—which means that one has found a good catalyst. The energy available at ambient temperature, or from slight heating, is now sufficient to coax the reacting molecules over both small hills. The reaction goes readily.

The catalyst gets intimately involved in the reaction and is regenerated. It vanishes, to reappear. Resurrected, it is ready, in principle, to escort another pair of molecules (one of A and one of B) through the reaction. It looks as though it could do so forever, as if one molecule of a catalyst could take, say, a tablespoon or a beakerful of matter through the paces. In reality, no catalyst does so well. There are molecular seductions or dead ends lurking in the solution. They “spoil” the catalyst, sour it, poison the process. One way or another, they pull the catalyst away from its appointed rounds. In the trade, a turnover number—the number of reactant molecules guided through the reaction by one catalyst molecule—is a measure of its efficiency. Turnover numbers of 105 are pretty good in the real world, perhaps good enough to build a factory on. The greater the turnover number, the more expensive you can afford the catalyst to be.




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