Dynamic Equilibrium - Examples

Examples

In a new bottle of cola the concentration of carbon dioxide in the liquid phase has a particular value. If half of the liquid is poured out and the bottle is sealed, carbon dioxide will leave the liquid phase at an ever decreasing rate and the partial pressure of carbon dioxide in the gas phase will increase until equilibrium is reached. At that point a molecule of CO₂ may leave the liquid phase, but then another molecule of CO₂ will pass from the gas to the liquid. At equilibrium the rate of loss of CO₂ is equal to the rate of gain. In this case, the equilibrium concentration of CO₂ in the liquid is given by Henry's law, which states that the solubility of a gas in a liquid is directly proportional to the partial pressure of that gas above the liquid. This relationship is written as

where k is a temperature-dependent constant, p is the partial pressure and c is the concentration of the dissolved gas in the liquid. Thus, the partial pressure of CO₂ in the gas has increased until Henry's law is obeyed. The concentration of carbon dioxide in the liquid has decreased and the drink has lost some of its fizz.

Henry's law may be derived by setting the chemical potentials of carbon dioxide in the two phases to be equal to each other. Equality of chemical potential defines chemical equilibrium. Other constants for dynamic equilibrium involving phase changes include partition coefficient and solubility product. Raoult's law defines the equilibrium vapor pressure of an ideal solution.

Dynamic equilibria can also exist in a homogeneous system. A simple example occurs with acid-base equilibria such as the "dissociation" of acetic acid, in aqueous solution.

CH₃CO₂H CH₃CO₂- + H+

At equilibrium the concentration quotient, K, the acid dissociation constant, is constant (subject to some conditions)

In this case, the forward reaction involves the liberation of some protons from acetic acid molecules and the backward reaction involves the formation of acetic acid molecules when an acetate ion accepts a proton. Equilibrium is attained when the sum of chemical potentials of the species on the left-hand side of the equilibrium expression is equal to the sum of chemical potentials of the species on the right-hand side. At the same time the rates of forward and backward reactions are equal to each other. Equilibria involving the formation of chemical complexes are also dynamic equilibria and concentrations are governed by the stability constants of complexes.

Dynamic equilibria can also occur in the gas phase as, for example, when nitrogen dioxide dimerizes.

2NO₂ N₂O₄;

In the gas phase, square brackets are not used as these indicate a concentration, instead a capitalised P is used to indicate partial pressure.