# Dilute solution model

In thermodynamics, the dilute solution model or “ideal dilute solution model” assumes the solvent obeys Raoult’s law and that the solute obeys Henry’s law. In real system applications, to correct for deviations from the ideal model, often concepts such as ‘activity’ are introduced.  The dilute solution model is often employed in electrochemical engineering applications.

History
The thermodynamic theory of a ‘dilute solution’, was introduced by German physicist Max Planck as part of his Lectures on Thermodynamics, sometime between the first edition 1897 and 1913 edition; a book which itself was an expanded version of his earlier 1893 Outline of General Thermochemistry, a summary of the results of his electrochemical and thermochemical investigations; investigations which trace to earlier 1889-90 papers of Planck published on the electromotive force. 

Ecological thermodynamics
The dilute solution model, in ecological thermodynamics, was first proposed for use in ecology by German ecological physicists Rainer Feistel and Werner Ebeling, in their 1981 “On the Thermodynamics of Irreversible Processes in Ecosystems”, as a way to represent a collection of species in an ecosystem based on the laws of thermodynamics and standard equations of mathematical ecology (e.g. the Lotka-Volterra equations).  In their paper, Feistel and Ebeling develop model of “ideal ecological solutions” using relations for the thermodynamic functions which correspond to Max Planck's theory of ideal anorganic solutions, wherein they derive several thermodynamic relations including an ecological-style first and the second law and a kinetic potential.  Features of the approach include:

• The assumption of organism 'death' if it reaches an equilibrium state.
• A concept of ecological pressure, corresponding to the osmotic pressure of a solution.
• The use of the fundamental Gibbs equation in its derivation.
• The ability to directly determine the Gibbs potential and free energy of an ecosystem as a sum of the number and variety of individuals of a series of species.
Danish chemical-ecology engineering ecologist Sven Jorgensen summarized the ecological version of the dilute solution as follows:

“We apply the Planck theory of a dilute solution when living organisms are considered as molecules of different chemical substances submerged into an environment, which is considered as a solvent.”

Jorgensen points out that in the vicinity of thermodynamic equilibrium, the 'living particles' must exist in their constituent forms, leading to results which resemble nothing more than an 'inorganic soup.' 

References
1. Engel, Thomas and Reid, Philip J. (2006). Physical Chemistry (pg. 193). Pearson Benjamin Cummings.
2. Jorgensen, Sven E. and Svirezhev, Yuri M. (2004). Towards a Thermodynamic Theory for Ecological Systems (dilute solution model, pg. 155). New York: Elsevier.
3. Lotka-Volterra equations – Wikipedia.
4. Feistel, Rainer and Ebeling, Werner. (1981). “On the Thermodynamics of Irreversible Processes in Ecosystems” (abs), Studia Biophys. 86: 237-44.
5. (a) Planck, Max. (1913). Vorlesungen über Thermodynamik (Lectures on Thermodynamics). (§ 249: Verdünnte Lösungen, pgs. 212-252). Berlin: Walter De Gruyter & Co.
(b) Barkan, Diana K. (1999). Walther Nernst and the Transition to Modern Physical Chemistry (Lectures on thermodynamics, pgs. 83-85). Cambridge University Press.