Question

Say you are given a buffer at 25 C in pH 6.881. The glass combination electrode gave a reading of -18.3 mV. When it was placed in a pH 4.002 buffer at 25 C, this same electrode gave a reading of +146.3 mV. What is the electromotive efficiency of the glass electrode? (3 sig figs)

Answer 1

Below is a typical combination pH electrode that incorporates a glass electrode and reference electrodes into a single cell.

Reference Electrode Glass membrane Reference Electrode

Ag(s)|AgCl(s)|Cl^-(aq)||H+ (aq, outside) : H+ (aq, inside),Cl^-(aq)|AgCl(s)|Ag(s)

The overall measured cell potential is

E = E_{outer reference} + E_{inner reference} + E_junction + E_glass

Since the reference electrode potentials and junction potential are constant, at 25 °C

E = Constant - [(2.303 R T / n F) log (a_{inner ion} / a_{outer ion})]

E = Constant - β (0.05916) pH

where β is the electromotive efficiency

Using the above equation, we have

-18.3 mV = Constant - β (0.05916) (6.881) =====> 0.0183 = (0.40707) β - Constant ------ (I)

146.3 mV =  Constant - β (0.05916) (4.002) =====> 0.1463 = Constant - (0.23675) β ----- (II)

(I) + (II) =====> 0.1646 = 0.17032 β

β = 0.1646 / 0.17032 = 0.966

Electromotive efficiency of the glass electrode = 0.966