Inner and outer hydrated layers:

If glass electrode is placed in a test solution its glass membrane will have an inner and outer hydrated layers and potential difference is developed due to the difference in hydrogen ion activities between test solution and outer hydrated surface of glass electrode as well as inner solution and inner hydrated surface. This potential is called boundary potential and it varies with the activity or pH of the solution. Whole boundary potential is the potential difference among both the boundary potentials. We can write chemical equation for both the boundary potentials

H⁺ Gl^-  (s)   ↔ H⁺  (aq) +  Gl^-                                        (1)

 Outer surface of glass        Outer solution

 H⁺ Gl^-  (s)  ↔ H⁺  (aq) +  Gl^-                                        (2)

 Inner surface of glass Inner solution

For the Eq. 1, the boundary potential is

E₁ ∝ (a₁ -  a_h)

where a₁ and a_h are the activity of the hydrogen ions in the test solution and the outer hydrated layer, respectively. As same for Eq. (3.4), the boundary potential is

E₂  ∝   (a₂ -  a_h)

while the activity of inner solution is a₂.

Thus, overall boundary potential,

E_b  =  E₁  - E₂ ∝ (a₁ - a_h)  - (a₂ - a_h)

If we assume that the activities of the hydrogen ions in the inner and outer hydrated layer are the similar, the above equation could be written as:

E_b ∝ (a₁   - a₂)

Other than the activity of the hydrogen ions in the inner solution is a constant and this equation decreases to:

E_b ∝ a₁

E_b   could be expressed for could in Nernst form:

E_b  = E₁   - E₂   = 0.0591 log   a₁ /a₂

E_b = K₁ + 0.0591 log a₁   = K₁ - 0.0591 pH                                         ... (3.5)

where K₁ is constant, it includes the constant factor related to hydrogen ion activity of within solution, a₂, which is, 0.0591 log a₂.