950 



Dr. S. A. Shorter : Contribution to the 



(39) 



laws stated at the end of section 3 are true if the term 

 " partial pressure"" is substituted for " chemical potential." 



5. Solnbiliiy Influence. 



Suppose that a solid substance C 2 is in equilibrium with a 

 solution of C 2 in a liquid mixture of C and C v The con- 

 centration s 2 of C 2 in the mixture is determined as a function 

 of the pressure, temperature, and concentration s L of Ci, by 

 the equation 



f2(si,S2,p,0)=fa(p,O), .... (38) 

 where </> 2 is the chemical potential of 2 in the pure solid state. 

 Differentiating equation (38) with respect to s x we obtain 

 the equation 



ds 2 _ S 21 fa,s 2 ,p,^) 

 dsj S22O1, s 2 ,p, 0)' 



If we regard C as the solvent and O x as an added substance 

 whose effect on the solubility is being studied, then s 2 may 

 be termed the solubility of C 2 in the binary mixture of G 

 and CV Of course, if Ci is a liquid perfectly miscible with O , 

 this mode of defining the solubility is quite an arbitrary one. 



From equation (39) we see that the further addition of 

 C x increases or decreases the solubility of C 2 , according as it 

 lowers or raises the chemical potential of 2 . This, of course, 

 is evident from general considerations. If, for example, the 

 further addition of C 1 raises the chemical potential of C 2 , 

 then the addition of Oi to the saturated solution will make 

 the potential of C 2 greater than that of the solid C 2 , and in 

 the presence of the latter will cause a certain amount of C 2 

 to be precipitated. 



In the following table are given the results of measure- 

 ments of the solubility of cane-sugar (C 2 ) in mixtures of 

 water (C ) and alcohol (C])*. 



Table I. 

 Temperature 14° 0. 



V 



s 2 . 







1-94 





•087 



1-82 





•194 



1-70 





•328 



1-62 





•501 



1-44 





* Quoted byRothmund, Losichkeit und Losichkeitsbecinflussungy p. 140. 



