Supersolubility from the Osmotic Standpoint. 255 



(4) Before proceeding to the discussion of the osmotic 

 pressure-concentration curves, I will establish two propositions 

 which, indeed, are almost self-evident. 



It is impossible that osmotic equilibrium can exist when the rate- 

 of change of osmotic pressure with concentration is negative. 



Consider a beaker containing a mass of solution ; if it 

 were possible for the osmotic pressure to decrease with an 

 increase of concentration, then, no solution being perfectly 

 homogeneous^ assume that momentarily at the point A we 

 have an increase of concentration. Diffusion, being a direct 

 function of osmotic pressure, will cause the concentration of 

 one of the components at A to go on increasing until the 

 whole of it is concentrated there ; which is absurd ! 



(5) Tico solutions ivliich are in osmotic equilibrium with 

 a third solution are in equilibrium icith one another *. 



Consider the system shown in fig. 2, where A and B are 

 the two solutions in equilibrium with solution C — all three 

 being under the same pressure p, and ab and cd being- 

 membranes permeable to the common solvent. 



Fig. 2. 



3 



/>-* 



i <— p 



\<' ! [ 



Assume that the osmotic pressure of A is greater than that 

 of B, then (the necessary manipulation of shutters closing the- 

 membranes being understood) solvent will flow into. A 

 from B, but the concentration in B will thereby be increased 

 and will cause a flow of solvent into it from C, which in its 

 turn takes solvent from A, thus setting up perpetual motion. 

 A and B have therefore the same osmotic pressure, and C 

 can be replaced by the pure solvent under a suitable pressure 

 without disturbing the equilibrium. 



(6) The following thermodynamic relations must also be 

 established ; they were worked out at my suggestion by 

 Dr. C. V. Burton. The proof here given, though more 

 lengthy than that based on the thermodynamic potential, will 

 no doubt be more readily followed by physical chemists. 

 Let Pi and P 2 be the ordinary and conjugate osmotic pres- 

 sures respectively. 

 Ci „ c-2 be the number of grammes of solvent and 

 solute respectively in one gramme of solution. 

 s 1 „ s 2 be the spaces occupied in the solution by one 

 gramme of solvent and of solute respectively. 



* This can be derived from the " Law of the Mutuality of Phases" 



see Nernst, ' Theor. Chemistry/ 3rd English edition, p. 662. 



