46 DAVID R. BRIGGS 



volved be presented. No attempt will be made to cover, in an ade- 

 quate manner, the many ramifications of osmotic theory but some 

 mention of the factors that determine the validity of osmotic meas- 

 urements under various conditions must be considered prior to a dis- 

 cussion of methods. This summary will be limited to a brief exposi- 

 tion of: (1) the osmotic pressure relationships in dilute solutions of 

 low molecular substances where this property and the other colliga- 

 tive properties of the solutions approximately obey the ideal solution 

 laws as set forth by van't Hoff and Raoult, (2) the osmotic pressure 

 relationships in more concentrated solutions and in solutions of high 

 molecular substances, and, finally, (3) the effects of Donnan mem- 

 brane equilibria upon the osmotic pressure relationships in solutions 

 of colloid electrolytes. In the following theoretical section, subscript 

 1 refers to the solvent and subscripts 2 or higher refer to solute com- 

 ponents of the systems under consideration (1). 



1. In Dilute "Ideal" Solutions 



A satisfactory mathematical treatment of the laws governing 

 osmotic pressure and the other colligative properties of dilute solu- 

 tions has been derived on the basis of thermodynamic considerations 

 alone. The definition of osmotic pressure given above is arrived at 

 on this basis. When equilibrium has been established in an osmotic 

 cell consisting of a pure solvent phase separated from a solution 

 phase (containing the same solvent) by a semipermeable membrane, 

 an excess pressure equal to the osmotic pressure, tt, will prevail upon 

 the solution. The work required under this condition to transfer one 

 mole of the solvent from an infinite volume of the solution into the 

 pure state is equal to ttFi, i.e. : H*''*^ '^ "&" ('*<:i''iu^**hc^f ( ^\e,^i 



ttVi = — AFi 



where Vi is the partial molar volume of the solvent and A^i is the 

 work required to accomplish the transfer under reversible conditions 

 and is called the partial molar free energy change of the process. AFi 

 is related to the fugacity of the solvent in the solution, /i, and to the 

 fugacity of the solvent in the pure state, /i °, as well as to the vapor 

 pressure of the solvent in the solution. Pi, to the vapor pressure of the 

 solvent in the pure state. Pi °, and to the activity of the solvent in the 

 solution, tti (referred to the pure solvent as the standard state), by 

 the equation: 



i 



