# Chemical equilibrium

In chemistry, chemical equilibrium is a reaction condition or state in which the velocity of a process in one direction, e.g. forward reaction, is equal to the velocity in the opposite direction, e.g. reverse reaction, so that there is no net change and therefore no observable change in the composition of the system. [1]

History
In October 1873, August Horstmann, a student of Rudolf Clausius, Robert Bunsen, and Hans Landolt, famously announced the condition for chemical equilibrium to be that of maximum entropy. [2]

In 1884, Jacobus van’t Hoff, drawing especially on the work of Horstmann and partially on Hermann Helmholtz’s “On Thermodynamics of Chemical Processes” (1882), published his Studies in Chemical Dynamics, in which he demonstrated that heat of reaction is not a direct measure of affinity (see: thermal theory of affinity), introduced the double arrow sign$\rightleftharpoons \,$for denoting equilibrium, and wrote out an equation describing the variation of the equilibrium constant as a function of temperature. His starting point, according to American chemistry historian Mary Jo Nye, was reaction velocities, rather than a balance of opposing forces. He used the symbol A for the work (Arbeit) that is done by the force of affinity (Affinitat) that brings about the chemical reaction, and recognized the need to quantify the role of concentration of reactants in determining the rates of reaction. [3]

Hmolscience
In 1910, American physical chemist Wilder Bancroft, in his “A Universal Law” address, outlined a large number of non-typical chemical reaction examples, from animals to humans, wherein he say Le Chatelier’s principle applying. [4]

In 1917, American economist Julius Davidson, in his “One of the Physical Foundations of Economics”, cites Willard Gibbs’ 1901 Elementary Principles of Statistical Mechanics as a basis, he argues that the law of diminishing returns, in economics, is based on chemistry and physics, and compares human chemical reactions to basic equilibrium adjusting chemical reactions. Specifically, Davidson compares the reaction of ethanol CH3CH2OH and acetic acid CH3COOH to produce ethyl acetate CH3COOCH2CH3 and water H2O:

$CH_3CH_2OH +CH_3COOH \rightleftharpoons CH_3COOCH_2CH_3 + H_2O$

with different combinations of male-female reactions, such as follows:

 ≡ (model) American physical chemist Lawrence Henderson's 1935 isolated five component liquid and gas phase physico-chemical system example model, wherein he shows how the chemical equilibrium of the system, according to Le Chatelier's principle (and Gibbs methods), shifts when carbon dioxide CO2 is added, and goes on to assert that these reactive shifting equilibrium models apply universally to the social sciences, namely to connective semi-permeable boundaried (migrative) social systems. [2] Similar chemical-to-social equilibrium adjusting examples are found in the works of: Julius Davidson (1916), Frederick Rossini (1971), Christopher Hirata (2000), and Thomas Wallace (2009) .

In 1935, American physical chemistry trained physiologist Lawrence Henderson, in his Pareto’s General Sociology: a Physiologists Interpretation, goes through, in a step by step manner, an example Le Chatelier's principle like chemical equilibrium adjusting reaction, after which he discusses how, in outline, this logic was grasped at in the equilibrium sociology work of Vilfredo Pareto (Treatise on General Sociology, 1912), and how the modern path is involves the application of Willard Gibbs' chemical thermodynamics methods to the examination of social equilibrium adjustments. The isolated physico-chemical system he employs in his example is a gas phase of carbon dioxide CO2 in contact with a four component liquid phase system, namely an aqueous solution of carbonic acid H2CO3, sodium bicarbonate NaHCO3, monosodium phosphate NaH2PO4, and disodium phosphate Ha2HPO4, as depicted adjacent. Henderson assumes the concentration of water and system temperature to be constant, as a first approximation. The equilibrium chemical reaction for the liquid phase is: [6]

$H_2CO_3 + Na_2HPO_4 \rightleftharpoons NaHCO_3 + NaH_2PO_4$

The chemical equilibrium for this reaction, per ratio of concentration ratio of products over reactant is, according to Henderson, is:

$\frac{[NaHCO_3][NaH_2PO_4]}{[H_2CO_3][Na_2HPO_4]} = 3$

The equilibrium of the gas phase carbon dioxide shifting into free carbonic acid in the liquid phase is:

$[CO_2]_g = [H_2CO_3]_{aq}$

Henderson then defines the condition of equilibrium as reaction condition or state in which the velocity of a process in one direction, namely forward reaction, is equal to the velocity in the opposite direction, namely reverse reaction, so that there is no net change and therefore no observable change in the composition of the system. He then goes through an algebraic type of concentration calculation wherein he adds a 100 units of carbon dioxide CO2 gas to the the system, shows how so much carbon dioxide converts into liquid carbonic acid H2CO3, after which all the individual species concentrations adjust, at the end of which the second state equilibrium concentration ratio becomes 3.011, i.e. the original state equilibrium reaction velocities. On systems, Henderson explains:

“Isolation may be regarded as the case where exchanges between the system and the environment have the value zero. If these exchanges have some other known value, the requirements for logical analysis are likewise fulfilled, and the analysis ay not present any serious inconvenience. Thus a metal bar one end of which is being heated at a constant rate, or a country with constant immigration rate, may for certain purposes be treated as a system, without regard to the properties of the source of heat, or of the countries from which the immigrants come.”

Moreover, in rather telling postulation, which juxtaposes the earlier century Le Chatelier principle based sociology of Vilfredo Pareto with the later century free energy minimization bases sociologies of the late 20th century burgeoning human free energy theorists (e.g. Christopher Hirata, 2000), we fine the following very excellent statement:

“Another characteristic of many ideal systems that is, in general, indispensable in order that conditions shall be determinate is the establishment and use of some definition of equilibrium or some criterion of equilibrium, whether in the case of statical equilibrium or in the case of dynamical equilibrium. This criterion is often of such a character that some function like entropy or energy assumes a maximum or a minimum value or, as in the case of the derivatives or variations of such functions, vanishes. In the case of Pareto’s social system the definition of equilibrium takes a form that closely resembles the theorem of Le Chatelier in physical chemistry, which expresses a property of physico-chemical equilibrium, and which may be deduced from the work of Gibbs.”

Very excellent postulate indeed!

Verbal statements or assertions about chemical equilibrium models being the basis of social equilibrium models seem to exist in large numbers. In 2006, American science writer Tom Siegfried, for example, gave the following verbal statement: [7]

“In a chemical reaction, all the atoms involved are seeking a stable arrangement, possessing a minimum amount of energy. It’s because of the laws of thermodynamics. And just as in a chemical reaction all the atoms are simultaneously seeking a state with a minimum energy, in an economy all the people are seeking to maximize their utility. A chemical reaction reaches an equilibrium enforced by the laws of thermodynamics; an economy should reach a Nash equilibrium dictated by game theory.”

Siegfried footnotes this statement with the following:

“As one reviewer of the manuscript for this book [Steven Strogatz or Mario Livio?] pointed out, it is not necessarily true that all economic systems converge to equilibrium, and that in some cases a chaotic physical system might be a better analogy than a chemical equilibrium system. The idea of equilibrium is nevertheless an important fundamental concept, and much of modern economics involves efforts to understand when it works and when it doesn’t.”

Here we see the influence of the late 20th century far-from-equilibrium theories (Ilya Prigogine, 1972), chaos theory, nonequilibrium thermodynamics, self-organized criticality (Per Bak, 1987), etc., that have led some to believe that human societies exist at very far from equilibrium or even at the "edge of chaos" (Len Fisher, 2009), a very common belief for many modern people.

The above footnote also brings to mind the Harvard Pareto circle effect on the assimilation of Gibbs-Pareto equilibrium models into the mind of sociologist George Homans. Adrift after graduating from Harvard in the depression year of 1932, Homans accepted an invitation of Henderson to sit in on his first series of seminars on Pareto. Toward the end of the conference, in 1934, lawyer Charles Curtis, a friend of the Homans’ family, also an attendee of the seminar, suggested that they collaborate on an exposition of Pareto’s sociology. The result was the 1934 An Introduction to Pareto. At this point, it seems, Homans gave what seems to be summaries of what he had just absorbed, e.g. “most societies at most times” have a tendency to be in equilibrium. Sixteen years later, at the time of his 1950 The Human Group, Homans had grown more, and he had begun to rethink his earlier formulations of equilibrium. He now wrote: “some social groups under some circumstances” are in equilibrium. Moreover:

“Not every state of a social system is a state of equilibrium, nor does every social system ‘seek’ equilibrium.”

In 1961, at the time of publication of his Social Behavior: its Elementary Forms, his views diverted even more: (Ѻ)

“Equilibrium is not a state toward which all creation moves.”

Here, it seems, Homans is grasping with vestiges of coupling theory? Or possibly, on a remote chance, he had begun to read up on nonequilibrium state theory and or nonequilibrium thermodynamics?

References
1. Henderson, Lawrence J. (1935). Pareto’s General Sociology: a Physiologists Interpretation (pg. 75). Harvard University Press.
2. (a) Horstmann, August F. (1872). “Article”, Ann. d. Chem. U. Pharm., 8. Suppl.-Bd., 112-13.
(b) Horstmann, August F. (1973). “Theory of Dissociation” (“Theorie der Dissociation”), Liebig’s Annalen der Chemie und Pharmacie, Bd. 170 (CLXX), 192-210.
3. Nye, Mary Jo. (1993). From Chemical Philosophy to Theoretical Chemistry: Dynamics of Matter and Dynamics of Disciplines, 1800-1950 (pg. 119). University of California Press.
4. Bancroft, Wilder D. (1910). “A Universal Law” (abs), Address of the retiring President of the American Chemical Society, Minneapolis, Dec 28; in: Journal of the American Chemical Society (1911), 33:91-120; in: Science (1911), 33:159-79.
5. Davidson, Julius. (1919). “One of the Physical Foundations of Economics” (abs), Quarterly Journal of Economics, 33: 717-24.
6. Henderson, Lawrence J. (1935). Pareto’s General Sociology: a Physiologists Interpretation (§:Note 3, pgs. 74-81; §:Note 4, pgs. 81-90). Harvard University Press.
7. Siegfried, Tom. (2006). A Beautiful Math: John Nash, Game Theory, and the Modern Quest for a Code of Nature (pg. 60). National Academies Press.