Application To Chemical Equilibrium
At equilibrium, the sum of the chemical potentials of the reactants is equal to the sum of the chemical potentials of the products. The Gibbs free energy change for the reactions, is equal to the difference between these sums and therefore, at equilibrium, is equal to zero. Thus, for an equilibrium such as
Substitute in the expressions for the chemical potential of each reactant:
Upon rearrangement this expression becomes
The sum is the standard free energy change for the reaction, . Therefore
K is the equilibrium constant. Note that activities and equilibrium constants are dimensionless numbers.
This derivation serves two purposes. It shows the relationship between standard free energy change and equilibrium constant. It also shows that an equilibrium constant is defined as a quotient of activities. In practical terms this is inconvenient. When each activity is replaced by the product of a concentration and an activity coefficient, the equilibrium constant is defined as
where denotes the concentration of S, etc. In practice equilibrium constants are determined in a medium such that the quotient of activity coefficient is constant and can be ignored, leading to the usual expression
which applies under the conditions that the activity quotient has a particular (constant) value.
Read more about this topic: Activity Coefficient
Famous quotes containing the words application, chemical and/or equilibrium:
“There are very few things impossible in themselves; and we do not want means to conquer difficulties so much as application and resolution in the use of means.”
—François, Duc De La Rochefoucauld (1613–1680)
“We are close to dead. There are faces and bodies like gorged maggots on the dance floor, on the highway, in the city, in the stadium; they are a host of chemical machines who swallow the product of chemical factories, aspirin, preservatives, stimulant, relaxant, and breathe out their chemical wastes into a polluted air. The sense of a long last night over civilization is back again.”
—Norman Mailer (b. 1923)
“They who feel cannot keep their minds in the equilibrium of a pair of scales: fear and hope have no equiponderant weights.”
—Horace Walpole (1717–1797)