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 to, application, chemical and/or equilibrium:
“It would be disingenuous, however, not to point out that some things are considered as morally certain, that is, as having sufficient certainty for application to ordinary life, even though they may be uncertain in relation to the absolute power of God.”
—René Descartes (1596–1650)
“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)
“If Thought is capable of being classed with Electricity, or Will with chemical affinity, as a mode of motion, it seems necessary to fall at once under the second law of thermodynamics as one of the energies which most easily degrades itself, and, if not carefully guarded, returns bodily to the cheaper form called Heat. Of all possible theories, this is likely to prove the most fatal to Professors of History.”
—Henry Brooks Adams (1838–1918)
“That doctrine [of peace at any price] has done more mischief than any I can well recall that have been afloat in this country. It has occasioned more wars than any of the most ruthless conquerors. It has disturbed and nearly destroyed that political equilibrium so necessary to the liberties and the welfare of the world.”
—Benjamin Disraeli (1804–1881)