THE GENERAL CONDITIONS OF VALIDITY OF THE 

 PRINCIPLE OF LE CHATELIER.^ 



By Alfred J. Lotka. 



Received May 20, 1921. Presented by Raymond Pearl. 



The derivation of the principle of Le Chatelier from the laws of 

 thermodynamics is familiar. 



We may approach a converse problem. What, in the broadest 

 terms, are the conditiolis which a system must satisfy in order that the 

 principle shall apply to it? The interest of this problem arises from 

 the fact that we have reason to suspect these conditions may prove 

 broader than the domain within which the laws of thermodynamics 

 are conveniently applicable.^ We may therefore expect that a satis- 

 factory solution of the converse problem may enable us to make 

 rigorous application of the principle to systems to which, from lack of 

 sufficient data it may be impossible, or from other causes it may be 

 inconvenient to apply thermodynamic methods. 



Consider a system whose state is defined in terms of a variable x 

 and a paramenter G. The system is one of that class, the history of 

 which follows a law 



f = /(.T, 60 (1) 



(For example, it may consist of a mixture of (^i— 2x) mols H2O 

 vapor, (yl2+ 2a:) mols of hydrogen, and (^3+ a:) mols of oxygen at 

 2000 deg. C. in a rigid enclosure of volume G\ A\, Ai, A3 being con- 

 stants, namely initial masses). It is understood that other para- 

 meters besides G may enter into the function/, but it is unnecessary 

 to set them forth explicitly, since in the reflections which follow only 



1 Papers from the Department of Biometry and Vital Statistics, School of 

 Hygiene and Public Health, Johns Hopkins University, No. 37. 



2 See Ehrenfest, Zeitschr. fiir phys. Chem. 1911, vol. 77, pp. 227, 244; 

 Wolchonsky, Jl. Russ. Phys. Chem. Soc, 1912, vol. 44, pp. 305, 310; Chwol- 

 son, Lehrbuch der Physik, 1909, vol. 3, p. 547; Bancroft, Jl. Am. Chem. Soc, 

 1911, p. 92; Fournier d'Albe, Contemporary Chemistry, 1911, p. 38; Lowy, 

 Kosmos, 1911, p. 331; Le Dantec, La Stabilit6 de la Vie, 1910, p. 25; L. 

 Fredericq, Arch, de Zool. Exp. et Gen., ser. 2, vol. 3, 1885, p. XXV; Spencer, 

 First Principles, chapter 22, section 173, Burt's Edition, p. 433. For further 

 historical and bibliographic notes see Duhem, Traite d'Energetique, 1911, 

 vol. 1, pp. 523, 524. 



