Electrode system for measuring pH:

Therefore, the boundary potential is a measurement of the hydrogen ion activity or the pH of the external solution. To measuring pH along with glass electrode the arrangement shown in Figure are generally employed. This arrangement has glass electrode along with Ag/AgCl internal reference electrode and external reference electrode like as saturated calomel electrode (SCE). For such arrangement complete cell might be represented as:

Figure: A typical electrode system for measuring pH

The cell potential is expressed as

E_cell  = (E _ind ) -  E_SCE + E_j

where E_SCE is the potential because of external reference electrode, E_j is liquid-junction potential, and E _ind is electrode potential of the glass electrode, which is actually a combination of  three components: (i) the boundary potential, E_b, (ii) the potential of the internal Ag/AgCl reference electrode, and (iii) the asymmetry potential, E_asy.

From Eq., substitute the value of E_b.

Thus, E_cell  = (E_b   +  E_Ag/AgCl   +  E_asy)  -  E_SCE + E_j

Alternate the value of Eb in this equation

E_cell  = (K₁   + 0.0591 log a₁ +  E_Ag/AgCl   +  E_asy) - E_SCE + E_j

or E_cell  = E*   + 0.0592 log a₁   =  E*   -  0.0591 pH

where E* is a constant, it includes all the constants and near constant source of potentials, i.e. potential of both reference electrodes, liquid-junction potential between the external reference electrode and the solution, asymmetry potential and internal boundary potential.