Super solubility from the Osmotic Standpoint. 259 



and on the right it is 



e-^:| [i - W - i f] + [' - f' - S f ]«*■* 



The total work done by external forces on the left is 



mSp , , . 



- , J (c 2 w — c 2 %), 



c 2 — G 2 



and on the right it is 



u 



B/> ~dc 2 dp J 1# 

 Equating the sum of these to zero we get 



dc 2 _ CyW — G 2 X — SiC 2 ■+■ s^ 



or 



dc 2 _ c 2 w — c 2 x — sjc 2 ' + sic 2 



These, remembering that w = c^ + c 2 s 2 and that a? = c 1 's l + c 2 's/> 

 reduce to 



dfy _ C 2 cJ(s l — a/) + g 2 c 2 {s 2 — s 2 ) 



rfp ~ (c 2 '— C 2 )S 1 trP ] /tlC2 



or 



dW _ ^lfa' ^ *i) + c 2 c 2 '(s 2 — s 2 ) 



dp ~ (c.-c.O^P/./tJ^ ■■•■•• W 



(10) A corresponding relation to that given in equation (2) 

 can be derived by putting dp = in Planck's equation, 

 No. 170 * ; we then get 



dc 2 _ C 2 (Ci1j*l + C 2 'Ij 2 ) , 



dt = *(c2'-c 2 )s 1 lfP 1 /^rc s , * * * • w 



where L : is the heat absorbed when unit mass of solvent 

 passes from the first to the second phase, and L 2 is the heat 

 absorbed when unit mass of solute passes from the first to 

 the second phase. 



(11) We are now in a position to deal with the osmotic 

 pressure-concentration curves. 



The most instructive case is that of two partially miscible 

 liquids ; and it may be mentioned that the main features of 

 the graphs give the phenomena both for ionized and non- 

 ionized liquids. 



* Planck's Thermodynamics, Ogg's translation, p. 194. 



S2 



