What Are Equilibrium Constants?

Some chemical actions proceed irreversibly in one direction. One example of this is the burning of hydrogen (H) gas in oxygen (O) to produce water, as shown in the formula 2 H₂ + O₂ => 2 H₂O. The opposite reaction, 2 H₂O => 2 H₂ + O₂ does not occur under these conditions, no matter how much time passes. There are reversible reactions, as the chemist Claude-Louis Berthollet discovered in 1803. Reversible reactions proceed in one direction until the reverse reactions become the favored ones, resulting in equilibrium and making possible the calculation of equilibrium constants.

Such equilibrium constants have been derived from mathematical relationships revealed in time through the efforts of many scientists. These relationships utilize the ratios of concentrations of dissolved species in the reaction system. One simple example is the ionization of acetic acid. Another is the reversible breakdown of the gas dinitrogen tetroxide. In these, as in all examples, equilibrium constants are dependent upon system conditions such as temperature.

Acetic acid dissociates into a positive hydrogen ion plus a negative acetate ion. What makes the reaction a reversible one is that these ions can and will recombine into acid molecules. Other acetic acid molecules then dissociate to replace those that have recombined. The result is equilibrium, leading to a mathematical expression. Ion and acid concentrations relate to the equilibrium constant by the expression K = [H+][Ac-]/[HAc]. Logically, the equilibrium constant for the reverse reaction is the inverse of this K, because the acid concentration becomes the numerator and ion concentrations become the denominator.

For dinitrogen tetroxide, which contains nitrogen (N) and oxygen, the chemical reaction is written N₂O₄ ⇆ 2 NO₂. Any change in proportion of these two species in a closed system depends on the change in system pressure; for each molecule of tetroxide that decomposes, two molecules of nitrogen dioxide form, increasing the pressure. This requires energy and, beyond a point, disfavors the split. The equation reads K = [NO₂][NO₂]/[N₂O₄]. As for acetic acid, the equilibrium constant for the reverse reaction, as for all equilibrium constants for all reverse reactions, is the inverse of this K.

Irreversible reactions obey the same mathematical relationships as those reactions that are reversible. In such cases, however, the denominator becomes either 0 or infinity, if one examines the forward reaction or the reverse reaction. This suggests an equilibrium constant having an opposite value, of infinity or of 0. Such information is useless. Also interesting is the possibility of driving a reaction to completion, making it irreversible by removing one of the products from the system, such as through a semipermeable membrane that retains the reactants.