﻿334 Prof. J. N. Mukherjee on 



Both these factors tend to diminish the rate of increase of 

 the charge with rise in the concentration of hydrogen ions. 

 For acids with simple univalent anions, the electrical ad- 

 sorption at low concentrations can be left out of account in 

 view of the excessive mobilty of the hydrogen ions. 



A quantitative relationship can now be obtained between 

 the charge on the surface and the concentration of the acid. 

 Let x 1 be the rate of neutralization according to 2 (6) above. 

 We have then 



^K.^.Cho.-*- 3 ^, .... (7) 



where k is a constant. 



The density of the charge on the surface is proportional to 

 x 1 — which is a measure of the number of hydrogen ions 

 remaining in excess in the surface. If the thickness of the 

 double layer remains constant then the potential of the 

 double layer is proportional to the density of the charge : 

 that is, to x 1 . 



When all the hydroxy 1 ions in the surface layer are being- 

 neutralized according to 2 (b) the surface will have a maximum 

 charge determined by i( x." 



Putting x\/% = 0, since u x" is a constant, we have 



e*6, (8) 



and 6 represents the ratio of the hydrogen ions present in 

 excess at any instant in the surface layer to the maximum 

 number possible when the neutralization takes place only 

 according to 2 (b). The potential of the double layer can be 

 written as 



e = h . x 1 = k 2 . 6 = h . Oho . e-*- ^ . U H o, . . (9) 



or # = £ .Cho.^-*/ t .U H o, (10) 



where k\, Ic 2 , fe, Ic and /3 denote constants. 

 Similarly, for alkali solutions we have 



e=ko.Gom.e-^^.UoKi. ...... (11) 



The maximum charge, being determined by a, will be the 

 same with alkali as with acid. Of course, the influence of 

 the oppositely charged ion in the acid or the base is being- 

 neglected. 



Case 2. — 2 he surface is not chemically inert : preferential 

 adsorption of one ion is possible. 



A review of the literature shows that surfaces in contact 

 with water are seldom neutral. They are generally more err 

 less negatively charged. This is intelligible in view of the 



