Example: Potential Determining Ions

Till now we have looked at indifferent ions which do not change potential on surface. But when the surface consists of mobile ions (like H⁺ or -ions) which can go from surface to solution, the surface acquires excess charge due to the movement of mobile ions into the solution.

For example, let's consider a surface consisting of AH type of molecules in an electrolyte. Now the AH molecule can dissociate into A^- and H⁺ ions.

Further, if this AH molecule is part of another large molecule embedded in the underlying surface (like–COOH group at the end of a protein molecule), the H⁺ ions could move into the solution, leaving the surface with an excess negative charge at the  ions sites.

If K is the equilibrium constant then,

where,
 [AH] is the concentration of those sites which have not dissociated,

 is the concentration of ions on the surface and,

 [H+] is the concentration of hydride ions in the solution near the surface.

If [n₀] is the total number of sites/dissociable molecules at the surface then,

(10.8)

Combining equations (10.7) and (10.8), to eliminate  we have

Since the surface consists of single valence ions, the charge density could be written as:

(10.9)