178 THEORY OF COLLOIDAL BEHAVIOR 



the theory. From the equilibrium equation, x 2 y(y + z), it 

 follows that 



s = Vy(y + 2) 



If we substitute this value in the term for osmotic pressure 2y 

 -\-z-2x, we get 



2y + z - 2Vy(y+ z) 



When z is zero (at the isoelectric point), the whole term becomes 

 zero. At the isoelectric point we observe therefore the osmotic 

 pressure of the protein solution free from the disturbing effects 

 of the Donnan equilibrium. When we add acid to isoelectric 

 gelatin, z increases and so does y, but, as we have shown in 

 Table XIV of Chap. VIII, z increases at first more rapidly 

 than y and later more slowly. Hence, the value of 2y + z 



+ ), i.e.j the osmotic pressure, increases at first the more 

 acid we add to isoelectric gelatin until a maximum is reached. 

 When.?/ grows more rapidly than z, z becomes more and more 

 negligible in comparison to y and the value of the term 2y + z 

 2-\/y(y -J- z) diminishes again with increasing y, finally approach- 

 ing zero again as a limit. 



The curves representing the values for calculated osmotic 

 pressures differ in one or two respects from the curves represent- 

 ing the values for the observed osmotic pressures (Fig. 45). As 

 a rule, the calculated values are lower than the observed values 

 (though this is only partly true for Fig. 45). This is to be ex- 

 pected since the calculated curves do not include that part of the 

 osmotic pressure which is due to the protein particles and the 

 calculated curves must therefore be too low, though this is 

 (perhaps accidentally) not true for the descending part of the 

 curve (for lower pH) in Fig. 45. The slight discrepancies be- 

 tween observed and calculated values may be due to an uncer- 

 tainty in our calculations or to a simplification in our assumption 

 which is not justified. We assume, e.g., complete electrolytic 

 dissociation of all compounds, which may not be entirely correct. 



The discrepancies may also be due to an error in calculating z. 



f 7 /* r I 77 ji'y* -^ 77) 



We calculated z from where x and y were 



y 



the hydrogen ion concentrations determined electrgmetricaily. 



