LEWIS. — A NEW SYSTEM OF THERMODYNAMIC CHEMISTRY. 279 



It is not possible from thermodynamics alone to predict how the 

 activity of each of the constituents of a binary mixture will change with 

 a change in composition. But if the change in one of the activities is 

 known, the change in the other may be found from the above simple 

 relation. 13 



Mixtures of More than Two Components. 



In the derivation of equations IX and XII no use was made of the 

 provision that the mixture contained but two constituents, and these 

 equations therefore show the effect of pressure and of temperature upon 

 the activity of one of the constituents of a mixture of any number of 

 constituents. In the same way that equations XI, XIV, and XV were 

 found we may obtain the following equations : 



( 

 ( 

 ( 



AV In ix + N 2 d In L + 2V 8 01n $ a + • • • \ v VATT 



= -rpp> AVI 



T, N HI 



= 0. XVIII 



P,T 



dNi 



Dilute Solutions. 



Equations XV and XVIII assume a very simple form when one of 

 the constituents of a mixture is present in such small amount as to 

 constitute a perfect solution. If a mixture consist of a very small 

 amount of a substance Xi and a large amount of a substance X 2 , we may 

 call the latter the solvent and the former the solute. If the solute is 

 extremely dilute, then, according to equation II, its activity & is pro- 

 portional to its concentration and therefore to JVi. Hence, 



dlnix = dlnNi, 

 and equation XV becomes, 



N 2 dlni 2 = -dX 1 , XIX* 



or </l n £ = _^i. XIX* A 



13 An approximate equation which is a special form of equation XV is 

 Duhem's equation for the vapor pressures of a binary mixture, namely, 

 N x d In p x + N. 2 d In p. 2 = 0. This equation is true only when the vapors obey 

 the gas law. See Lewis, Journ. Amer. Chem. Soc, 28, 509 (190G). 



