Overview of Equilibrium and Kinetics

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John's Trout
When our son John was almost four, his grandfather took him and his sister Anne (six) fishing. They went to a trout farm, where success was guaranteed. Anne caught a big trout. When John landed an even bigger specimen, tears welled up in his eyes. As he explained to his grandfather, "I wanted to catch a little one!"
{By the time they got home to display their trophies, John (left) had recovered his composure.)
[Adult fisherfolk sometimes express the same point of view. Professor Faller, an avid fisherman, tells me that in fishing for tuna you want to hook a little one (say 50 pounds). A tuna of this size can be landed by an individual sport fisherman, but if you hook a 500 pounder, forget it.]

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We are now at the juncture between understanding the structure of organic molecules and understanding (and predicting) their reactions. We relate the equilibria and rates of organic reactions to the structure of molecules through the concepts of energy and entropy. In this way we use statistical ideas to achieve enormous simplification of our thinking.

In order to appreciate the necessity for simplification we glance first at what we might see if we could directly observe reaction trajectories in progress (as is almost becoming possible for very simple reactions in the gas phase). Then we introduce the concept of the potential energy surface as a tool for thinking about reactions. We will see that these detailed approaches are much too detailed for practical use in organic chemistry. We want to catch a little one.

Then we look at the statistical shortcuts that will allow us to discuss reactions efficiently using the Boltzmann Factor and Transition State Theory. Finally we will look at free-radical substitution reactions which illustrate the application of these ideas.

While thinking about statistics it is worth pausing a moment to express our gratitude, as chemists, for Avogadro's Number. When we do experiments, we are usually working with a significant fraction of a mole of molecules. Suppose our sample were only ~0.1 mmol (e.g. a cubic sucrose crystal about 3 mm on an edge); this is still 10²⁰ molecules. Each of these molecules behaves slightly differently in detail (at what exact moment it collides with other reagent and solvent molecules, and at what angle, and in what phase of vibration and rotation, and how hard). So if one makes an overall observation, such as whether molecules did or did not react, one expects statistical fluctuations. The size of such fluctuations tends to be roughly parallel to the square root of the size of the sample.

For example, if we could do an experiment with only 4 molecules and observed that 2 reacted, we would expect fluctuations of +/- 2. That is, if we repeated the experiment, we would expect sometimes to find no reacted molecules and other times to find 4. This is not impressive reproducibility.

But with a sample of 0.1 mmole we would have 10²⁰ molecules, and the expected fluctuations would be +/- 10¹⁰. At first glance this seems a very large fluctuation, but in fact it is teeny compared to the sample size, 10¹⁰/10²⁰ is only 0.00000001%. So chemistry experiments under identical conditions should be precisely reproducible, within our ability to measure, and statistical mechanics predictions based on proper theory should be much more accurate than the limits of experimental error. In chemistry we don't normally worry about fluctuations due to small sample size. This is a fabulous advantage compared to public health studies of a rare disease or studying the efficacy of a drug candidate on a sample of a dozen patients, or even a thousand. When we measure results as chemists, we measure probabilities directly.

We'll be studying kinetics and free radical reactions next semester.

Here are relevant web pages:

Remember that the first two web pages (trajectories and potential energy surfaces) serve to illustrate how such detailed treatments have much more information than we want to deal with (like the big trout). So don't feel responsible for really detailed mastery of this material.

As always, the readings provide support for what we say in lectures, and you are not responsible for more detail than was presented in lecture. The web pages serve in part to provide more background for those who are curious. (You definitely don't need to follow the links within these pages to derivations that explain why Eyring tilted his axes or how to derive the Boltzmann distribution analytically.)