LEWIS. — FREE ENERGY AND EQUILIBRIUM. 31 



preserve the equilibrium the osmotic pressure, not only of one but of each 

 of the constituents, must be the same in the two phases. No similar phe- 

 nomena have ever been observed in the case of solids dissolved in liquids, 

 but it seems not impossible that such may be found. Then a solid might 

 have two different solubilities in a solvent at one temperature, correspond- 

 ing to two concentrations in which the osmotic pressure would be equal 

 to the solution pressure. 



Distribution of a Solute between two Solvents. — The equation of equi- 

 librium when a substance is distributed between two solvents may be 

 found directly from equation (11a), simplified by the considerations 

 advanced on page 27, namely, 



P V= E T\n '''['''~^2 + ^. (44) 



n (vi — b) 



In all cases of this sort P Fis entirely negligible, and 



r,{ih-b)^ ^ 



where ^2 and Vi are the molecular volumes of the solute in the two sol- 

 vents ; b is the volume correction for the solute molecules ; r^ is the 

 volume correction for the first solvent, and 1\ that for the second. U is 

 the heat given off when one gram-molecule of the solute passes from one 

 solvent to the other. It equals the difference between the heats of 

 solution of the solute in the two solvents. In all ordinary solutions b is 

 negligible, and the equation becomes 



i?rin^-'-j- U=0. (46) 



Since this is the general equation of distribution of a substance between 

 two solvents, it will hold true in the special case in which the solutions 

 are in equilibrium with the solute in the solid form. If we represent by 

 Si and 8-2 the solubilities in gram-molecules of the solute in one litre of 



each of two solvents, then s^ = — and s, — — , and equation (44) 

 may be written 



i^rin'^'-f ?7=0; (47) 



or if TJ' is the heat of solution in the first solvent, TJ" in the second, 



R T\u '^ + U' - U" = Q, 



