358 ELECTRICAL CHARGES OF COLLOIDAL PARTICLES 



and the following row the pH outside after the experiment was finished 

 (i.e. after 20 hours), and the sixth row gives the difference pH inside 

 minus pH outside. The reader will notice that this difference is 

 always negative with one exception which is obviously an error. The 

 last two rows give the calculated p.d. (i.e. the value 58 (pH inside 

 minus pH outside)), and the observed p.d. Observed p.d. means 

 the millivolts between the solution of Na gelatinate and watery 

 solution measured directly in the Compton electrometer, as described 

 in preceding papers. 



It is obvious that there is no quantitative agreement between the 

 observed and calculated p.d. near the isoelectric point, probably on 

 account of the CO2 error. As soon as the pH is above 7.0 the agree- 

 ment between observed and calculated p.d. becomes better so that 

 we are entitled to say that the difference of potential between a Na 

 gelatinate solution and an outside solution is due to the Donnan 

 equilibrium which forces the expulsion of NaOH from the inside into 

 the outside solution. As a consequence the pH inside becomes 

 lower than the pH outside. 



///. Valency Effect on the p.d. 



It had been shown in a preceding paper that the charge of a solution 

 of gelatin sulfate is lower than a charge of a solution of gelatin chloride 

 or gelatin phosphate or any other gelatin-acid salt with a monovalent 

 anion of the same pH and the same concentration of originally iso- 

 electric gelatin.^ It should, however, be pointed out that on the 

 basis of the theory the ratio of the charges in the two cases should be 

 exactly as 3:2. It is needless to say that if we can prove that this 

 postulate is fulfilled the probability that the charges of micellae are 

 due to the Donnan equihbrium becomes very strong. 



The equilibrium equation which is of the second degree when the 

 anion is monovalent, e.g. CI, in the case of gelatin chloride, becomes 

 of the third degree when the anion is bivalent, e.g. SO4, in the case 

 of gelatin sulfate. Let x be the concentration of hydrogen ions and 

 CI ions of the outside, y that of the H and CI ions of the free HCl 

 inside the gelatin chloride solution, and 2 the concentration of the CI 

 in combination with gelatin. Then the equilibrium equation is, 



