128 



CARNEGIE INSTITUTION OF WASHINGTON. 



(3) The laws of chemical equilibrium. Erskine D. Wilhamson and George W. Morey. 



J. Am. Chem. Soc, 40, 49-59 (1918). 



In examining the complicated chemical systems which present themselves 

 in the study of geophysical problems it is found that the approximate for- 

 mulas used for dilute solutions break down and prove worse than useless even 

 for qualitative application. The monumental work which the genius of 

 Willard Gibbs evolved in 1876 remains the safest guide and that to which 

 reference must necessarily be made. The extremely mathematical setting 

 with which he surrounds his arguments has militated against the general use 

 of his results by chemists, and a consequence of this is that much ink has been 

 spilled in proving, by roundabout and far from rigid methods, theorems 

 which are either explicitly stated by Gibbs or are so readily deducible from 

 his equations as to be implicit in his work. This paper has therefore been 

 written as an attempt to popularize, in so far as such a term can be used in 

 this connection, the derivation of the fundamental equations and to deduce 

 from them such additional formulas as are found necessary for the derivation 

 of the theorems bearing on the chemical side of equilibrium. The applica- 

 tions of these theorems to actual cases will be discussed in later papers. (See 

 Abstract No. 4.) 



(4) Pressure-temperature curves in monovariant systems. George W. Morey and Erskine 



D. Wilhamson. J. Am. Chem. Soc, 40, 59-84 (1918). 



Willard Gibbs, in his paper "On the equilibrium of heterogeneous sub- 

 stances," derives the following expression (equation 129) giving the relation 

 between the variations in pressure and temperature in monovariant systems: 



dP 

 dT 



mi 

 tni 

 mi 



mi 

 mi' 

 m% 



■r\n\\ rtln-if-i' mn+i 



mi" 

 mz" 



mi" 



Wn-i-l" 



mi 

 m,i! 

 ma' 



TOl 



m-^ 

 mz 



Vn \-l mn+l Wn-t-l 



ma" 



TOn+,« 



From the form of this equation, it follows that whenever there is a linear 

 relation between the composition of n or fewer phases in a system of n com- 

 ponents, the equation representing the relation between the variations of 

 pressure and temperature in a monovariant equilibrium, i. e., an equilibrium 

 between n-\-l phases, reduces to an expression which contains only terms relat- 

 ing to the phases between which the above-mentioned linear relation holds. 

 From this fact may be deduced the following theorem : 



Whenever, in a system of n components, a linear relation exists between the 

 composition of n or fewer phases, the pressure-temperature curves of all mono- 

 variant equilibria containing these phases coincide. When all the reacting phases 

 are of constant composition, the curves will coincide throughout their course; 

 when the composition of some or all of the phases is variable, and they only 

 casually have such a composition that the above linear relation is possible, then 

 the curves are tangent. 



