# Equilibrium constant

In chemistry, the equilibrium constant K is a value defining the ratio of the concentrations of the products to the concentrations of the reactants in a reversible chemical reaction, at the point when the reactants and products reach steady-state values, a point otherwise known as equilibrium. [1] Given a reversible reaction of the form:

$x A + y B \rightleftharpoons z C + w D$

where x, y, z, and w are the stoichiometric coefficients, the equilibrium constant is defined by follow equation:

$K = \frac{[C]^z [D]^w} {[A]^x [B]^y} \,$

where [A], [B], [C], and [D] are the concentrations of the various reactants and products at the equilibrium.
 An equilibrium constant spontaneity table showing the relationship between free energy change and the equilibrium constant. [6]

Thermodynamics
The driving force of any reaction are the various chemical affinities of the reactants and products, in relation to each other. The affinity A for an isothermal-isobaric reaction, is defined by the variation of the Gibbs free energy per change in the extent or progress of the reaction:

$A=-\left(\frac{\partial G}{\partial \xi}\right)_{p,T}$

or, in terms of Gibbs free energy change:

$A= -\Delta G \,$

at equilibrium the affinities will be satisfied, as quantified by the condition ΔG=0. This condition can be expressed in terms of the equilibrium constant as:

$\ \Delta G^\circ = -RT \ln K$

where by solving for K the one arrives at an expression:

$K = e^{\left (-\Delta G^\circ /RT \right )}$

relating the equilibrium constant to Gibbs free energy and temperature: [2]

History
In 1868, in order to ascertain molecular weights via a vapor density method, German chemist August Horstmann began to investigate the effect of temperature on the equilibrium constant for a dissociation process, beginning with the Clausius-Clapeyron equation, but extending it to apply to a substance that is dissociating. In 1872-73, Horstmann applied the entropy principle to the problems of chemical dissociation. [3] In October 1973, Horstmann announced the condition for chemical equilibrium to be that of maximum entropy. [4]

In the 1880s, work on the relation between, affinity, the equilibrium constant, and thermodynamics was further established by Dutch physical chemist Jacobus van't Hoff. The above derivation, in particular, seems to stem from van't Hoff's 1884 Studies in Chemical Dynamics. [5]

References
1. Daintith, John. (2004). Oxford Dictionary of Chemistry. Oxford University Press.
2. Perrot, Pierre. (1998). A to Z of Thermodynamics (Equilibrium constant, pgs. 100-03). Oxford: Oxford University Press.
3. Horstmann, August F. (1972). Ann. d. Chem. U. Pharm., 8. Suppl.-Bd., 112-13.
4. Horstmann, August F. (1973). “Theorie der Dissociation”, Liebig’s Annalen der Chemie und Pharmacie, Bd. 170 (CLXX), 192-210.
5. (a) Vant’ Hoff, Jacobus H. (1884). Études de Dynamique Chimique (Studies in Chemical Dynamics) Amsterdam: F. Muller & Co.
(b) Van’t Hoff, J.H. (1896). Studies in Chemical Dynamics: Revised and Enlarged by Ernst Cohen (trans. Thomas Ewan). London: Williams & Norgate.
6. LeMay, Eugene, Robblee, Karen M, Baell, Herbert, and Brower, Douglas C. (1996). Chemistry: Connections to Our Changing World (pg. 762). Prentice Hall.