ARTICLES 239 



In bulk of solutions, let 



X = concentration of positive or negative ions. 

 In surface layer, let 



y = concentration of negatively charged diffusible ions. 



8 = concentration of positively charged ions bound by 

 electrochemical attractions. 

 /. y ^z == concentration of positively charged ions. 



From the relation just derived, 



X^ = y{y + z). 



The formula given by Donnan * for the potential difference 

 due to inequality in concentration of ions in surface layer and 

 bulk of solution is 



But m this case \ =— — — 



PC ^X 



RT 2x 



We may therefore write V = -^ ^^^ ^TiPvTJF+T) 



where z is either constant or has a limiting maximum value. 



limit ^ J 2x 



Hence ^=., ^^ =^ ^^^ V(4^) ^ ""' 



proving that the potential difference will diminish as the 

 concentration of electrolytes is increased, a result of con- 

 siderable theoretical importance. 



Surface Energies — A. Positive Surface Energy. — Surface 

 tension is due to intermolecular forces within the colloid par- 

 ticle. These are, however, dependent to a certain extent upon 

 the solvent with which the particle is in contact. In support 

 of this, it may be stated that the solution obtained by dis- 

 solving soap in water is colloidal, while under similar conditions 

 it forms a true solution in alcohol. Bredig has observed that 

 the surface tension of mercury in contact with dilute solutions 

 of its own salts is lessened by a potential difference across the 

 interface. It is a generally accepted statement that the ex- 

 istence of a potential difference lowers the surface tension of 

 the disperse phase, and experience seems to show that this is 

 true. Surface tension may also be lowered in the presence of 

 certain substances in the dispersion medium, but we will 

 return to this when dealing with coagulation. Donnan ^ has 

 developed an important theory of colloid state founded upon 



1 Zeit. Elektrochem., vol. xvii, p. 572, 191 1. 



2 Phil. Mag., vol. i, p. 647, 1901. 



