132 THEORY OF COLLOIDAL BEHAVIOR 



The fifth vertical column of the table shows that at first the 

 value - increases with increasing addition of acid until pH = 4.03, 



\j 



and that with the addition of more acid the value - diminishes 



again. A comparison of the last and second last vertical columns 

 shows that the observed and calculated P.D. agree. 



The Donnan equilibrium thus explains mathematically why 

 the P.D. rises at first when HC1 is added to isoelectric gelatin 

 until the pH is 4.03, and why the P.D. drops when the pH falls 

 below 3.8. No other colloidal theory is able to explain the 

 curves in Fig. 41. 



THE VALENCY EFFECT 



Figure 41 shows that the P.D. curves for gelatin chloride and 

 phosphate are considerably higher than the curve for gelatin 

 sulphate. The same valency effect was observed for the osmotic 

 pressure curves, the viscosity curves, and the curves for swelling. 

 It can be shown that the Donnan theory demands that for the 

 same pH and the same concentration of originally isoelectric 

 gelatin the P.D. of gelatin chloride and gelatin sulphate should 

 stand in the exact ratio of 3 : 2, and it is one of the most convincing 

 proofs of the correctness of the theory that the calculated values 

 for the P.D. of these two gelatin salts agree with this postulate. 

 By calculated values we mean the value 59 (pH inside minus 

 pH outside). 



The proof that the values for pH inside minus pH outside and, 

 hence, the P.D. of the solutions of the two gelatin salts must 

 show the ratio of 3 : 2 is as follows : 



The equilibrium equation for gelatin chloride is of the second 

 degree, namely, 



x _ y + z 

 y~ x 

 and we have just seen that by proper substitution the 



P. D. =^ log ( 1-f -) millivolts. 

 z \ y/ 



The equilibrium equation which is of the second degree when the 

 anion is monovalent becomes of the third degree when the anion 



