LEWIS. — FREE ENERGY AND EQUILIBRIUM. 37 



In order to determine the actual dissociation in the above cases con- 

 ductivity determinations were made. I found in the case of zinc and 

 cadmium sulphates that the degree of the dissociation could not be found 

 from conductivity determinations on account of peculiarities which will 

 be discussed in a later paper. It was found, however, that in the case 

 of cadmium sulphate the dissociation is at least five or six times as 

 great in water as in fifty per cent methyl alcohol. In the first three cases, 



therefore, the value of is undoubtedly great enough to account for 



the values of -77=, found. 

 a 1 



On the other hand, in the case of thallium sulphate it was found possi- 

 ble to determine the degree of dissociation from the conductivity data. 

 In dilute solutions the dissociation in water and in fifty per cent methyl 

 alcohol was found to be practically the same. This is in complete agree- 

 ment with the result in case (5), where the temperature coefficient was 

 zero. In case (5), then, the only one in which all the data are available, 

 equation (60) is thoroughly verified. I hope to publish soon more com- 

 plete results on this subject. 



I wish to express my deep obligation to Professor Theodore W. 

 Richards for his encouragement and friendly criticism of this work. 



Summary. 



I. (a) A general equation for change of free energy is developed. 



(b) From this is derived a general expression for physico-chemical 

 equilibrium in homogeneous or heterogeneous systems, which includes as 

 special cases the law of isothermal mass-action and the laws of constancy 

 of distribution coefficients among several phases. 



(c) For change of equilibrium with change of temperature a formula 

 is derived of which the equation of van't Hoff is a specialized form. 



II. (a) The application of the general equations to gases yields an 

 equation of condition which with the aid of two familiar empirical obser- 

 vations is shown to be identical with the equation of van der Waals. 



(b) This equation of condition is applied to liquids in detail and special 

 cases are discussed. 



(e) A more complete equation is proposed, recognizing the variability 

 of specific heat with changing volume. 



(d) From the general equation a formula is obtained for equilibrium 



