Many elementary chemical reactions occur on extremely short time scales (down to femtoseconds). Special experimental and mathematical methods are required to study fast processes. Here, we will focus on reactions in solution. Some of the methods described here are also adaptable to gas-phase reactions, but there are also some gas-phase methods that are quite different from anything we would use in solution. Also note that this chapter does not provide a comprehensive survey of methods, even for reactions in solution. The intention is to discuss a few particularly important methods, which hopefully will give you a flavor of the various approaches available.

Flow methods

The continuous flow method

The basic idea behind the continuous flow method is very simple: the reactants are supplied at a constant rate into a tube where the reaction takes place. At constant flow velocity, positions in the tube correspond to specific times since mixing, the relationship between time and the distance from the mixing chamber L being t = L/v. By varying the flow speed or moving a detector along the length of the tube, we can therefore study the course of a fast reaction at our leisure.

A bimolecular elementary reaction requires that the two reactants meet. In solution, molecules are constantly bumping into other molecules, with the net effect that they wander randomly through the solution, which we call diffusion. In this chapter, we will study diffusion and its effect on chemical reactions, specifically focusing on the rate at which molecules meet each other. This will give us an upper bound on the reaction rate, which is useful for a number of purposes.

Diffusion

A molecule in solution is constantly surrounded by other molecules. All the molecules are constantly bumping into their neighbors. They move around the solution by sliding between their neighbors, much as you might slide between people tomake your way around a crowded room. This process is a form of diffusion, the random motion of molecules in space.

The central quantity in describing diffusion is the flux, which is the rate at which molecules cross an imaginary surface in space per unit area of this surface. The flux therefore has units of number per unit time per unit area (e.g. mol s-1 m-2). We're going to focus on diffusion in one dimension, where it's a little easier to picture what is going on. Imagine that we have a tube of cross-sectional area A. The tube is narrow enough that we can treat the concentration across the tube as being constant.

I have to admit that I wasn't fond of electrochemistry when I was a student. It has since grown on me. Looking back, I think that I was told too much in my first exposure to the subject. Electrochemistry is a fussy science, with all kinds of complications that can make it difficult to obtain reproducible data from experiments. If your professors tell you about all these complications up front, then it becomes difficult to appreciate the utility of the subject. You just lose track of the big picture in a haze of contact potentials and transference numbers. That being said, it's possible to go too far the other way and to leave out important details you ought to know about when studying electrochemistry. I'm going to try to steer a middle course, one that emphasizes that electrochemistry is one of the key ways to get thermodynamic data, but also one that points out some of the things you need to think about when you do electrochemistry. Hopefully, you'll come through this experience with more enthusiasm for electrochemistry than I had when I was in your place.

Free energy and electromotive force

In several of the problems in Chapter 7, we used the fact that the maximum electrical work can be calculated from the Gibbs free energy, the latter representing the maximum (reversible) non-pV work. Electrochemical cells convert chemical into electrical energy, or vice versa.

Chemistry is traditionally divided into a small number of subfields, namely organic, inorganic, analytical and physical chemistry. It's fairly easy to say what the first three are about, but it's much harder to define physical chemistry. The problem is that physical chemistry is all of the following simultaneously:

• A discipline in its own right, with its own set of problems and techniques;

• The source of the basic theory that underlies all of the chemical sciences;

• A provider of experimental methods used across the chemical sciences.

Note that “chemical sciences” includes biochemistry and materials science, among other fields that depend on physical chemistry for at least some of their theory and methods. Physical chemistry's large mandate means that it's difficult to put a finger on what it is exactly. It's a bit like chemistry itself that way: every time you come up with a definition, you immediately think of half a dozen things done under that heading that don't fit.

Rather than trying to give a simple, neat definition of physical chemistry, I'm going to tell you about the big theories that make up physical chemistry. Hopefully, this will give you an idea of what physical chemistry is about, even if we can't wrap it up in a neat package as we can with the other subfields of chemistry.

This chapter will introduce you to the analysis of a key class of kinetics experiments, namely initial rate experiments. We will consider only the simplest class of rate laws, those where the rate is proportional to some powers of the concentrations. This is a limited class, but one that comes up surprisingly often in practice. Initial rate experiments are also useful when a reaction has a complex rate law. However, complex rate laws are best understood in the context of a study of reactionmechanisms, so we put off this discussion for now.

Initial rate studies

Rate laws of chemical reactions are often complicated. They can depend on the concentrations of reactants, products, or other chemicals present in the system in almost arbitrary ways. It would be impractical to try to deal at once with all possible complications, so we often try to study reactions under conditions in which we can expect simpler behavior.

Perhaps the most widely used experimental simplification is the method of initial rates, which was briefly mentioned in Section 11.3. In this method, we study the reaction only for a very short time after initiation. During this time, the concentrations change very little so that a number of complications arising from changes in the reaction mixture over time are avoided. For instance, if we start with a mixture containing only reactants, then very little product will accumulate during the reaction and we can neglect the reverse reaction whose rate, according to the law of mass action, depends on the product concentrations.