170 THEORY OF COLLOIDAL BEHAVIOR 



and by Procter and Wilson (1916) l for the calculation of the 

 swelling (see Chap. XI). Since, however, the application of 

 the theory is simpler in the case of osmotic pressure than in the 

 case of swelling, it may be well to discuss osmotic pressure 

 experiments first. 2 



Let y be the concentration of the H and Cl ions of the free HC1 

 inside a gelatin chloride solution (containing 1 gm. of originally 

 isoelectric gelatin in 100 c.c.), z the concentration of the Cl ions 

 held by the gelatin ions, and a the sum of the concentrations of 

 the gelatin ions and non-ionized molecules of gelatin. For the 

 sake of simplification we assume complete electrolytic dissociation 

 of the gelatin chloride and of the HC1. In this case the osmotic 

 pressure of the inside solution is determined by 



2y + z + a 



Since, however, the outside solution is at equilibrium not H 2 O 

 but HC1 solution in the example selected a HC1 solution of 

 about pH 3.0 the observed osmotic pressure is the difference 

 between the osmotic pressure of the inside solution and the 

 osmotic counterpressure of the outside -solution. 



Let x be the concentration of the H ions in the outside solution, 

 then the osmotic counterpressure of the outside solution is 

 determined by 2x. 



Hence the observed osmotic pressure of the gelatin chloride 

 solution is determined by 



2y + z + a - 2x 



The osmotic pressure is observed experimentally, y can be 

 calculated from the pH inside, and x from the pH outside. 

 z can be calculated from Donnan's equilibrium equation 



x 2 = y(y + z} (1) 



(x + y)(x -y) 



y 



where x, y, and z have the significance stated above. The z 

 thus calculated differs, however, from the z obtained from the 



1 PROCTER, H. R., J. Chem. Soc., vol. 105, p. 313, 1914. PROCTER, H. R. 

 and WILSON, J. A., J. Chem. Soc., vol. 109, p. 307, 1916. 

 2 LoEB, J., J. Gen. Physiol, vol. 3, p. 691, 1920-21. 



