#### 12 · How can we characterize a chemical equilibrium?

If the position of an equilibrium (that is, the composition of a chemical reaction system at equilibrium) can depend on the amounts of substances brought together (the "active masses" as defined by Guldberg and Waage's Law of Mass Action), an important question arises: is there a single, measurable property that is unique to any chemical reaction system that can be used to predict its equilibrium composition for all possible initial amounts of the substances involved in the reaction? The answer, which of course is "yes", first became evident through a careful examination of a reaction studied by Berthellot:

CH3COOH + C2H5OH CH3COOC2H5 + H2O

acetic acid ethyl alcohol ethyl acetate water

The product, ethyl acetate, is called an ester, so the reaction as a whole is known as an esterification reaction. By combining various amounts of acetic acid and ethanol, different amounts of products were obtained once the reaction came to equilibrium (it takes about an hour of boiling in the presence of HCl, which acts as a catalyst.)

expt. |  |  | initial concentrations | concns at eq, M/L |  |  | Kc
| CH3COOH | C2H5OH | CH3COOH | C2H5OH | CH3COOC2H5 | H2O |
1 | 1.00 | 0.18 | 0.829 | 0.009 | 0.171 | 0.171 | 3.9
2 | 1.00 | 1.0 | 0.333 | 0.333 | 0.667 | 0.667 | 4.0
3 | 1.00 | 2.0 | 0.142 | 1.142 | 0.888 | 0.858 | 4.5
4 | 1.00 | 8.0 | 0.034 | 2.034 | 0.966 | 0.966 | 3.9

The equilibrium concentrations that we might observe in each experiment are shown in the shaded region of the table. Although you can detect some pattern to these numbers if you examine them carefully, they don't tell us very much about the reaction itself. If, however, we substute them into the expression

we find that the results (shown in the rightmost column of the table) are about the same for each set of initial concentrations, the differences being due to experimental error. Their average value, Kc = 4.1, is a property of this particular reaction under the conditions of pressure and temperature at which it is being observed.

We call Kc the equilibrium constant in terms of concentrations. We use the term "constant" here with some reservation; quilibrium constants are highly dependent on the temperature, sometimes increasing with temperature and sometimes decreasing, depending on the particular reaction.

More generally, for a reaction having the form a A + b B Æ c C + d D, the equilibrium expression (the formula that defines K) is given by

in which the bracketed terms represent the concentrations of the various components. This can be generalized further by considering the coefficients of the reactants (a and b) as negative numbers, reflecting the fact that these components are consumed in the reaction. Denoting these stoichiometric coefficients by ni, the expression becomes

in which Ci represents the concentration of the ith component, or some function proportional to the concentration, such as the pressure for a gaseous substance. Take a few moments to see how this equation relates to the one above it. The main reason for showing this here is to introduce you to the P notation for denoting a product of an indefinite number of terms; you will also find that writing it this is a good way to impress your teachers, parents and friends.