E(cell) =E*(F-) -(RT/F) ln (a(F-)) -E(SCE)
or, at 25oC:
E(cell) =k -0.0257 ln (a(F-))
If a cell is constructed with a fluoride ISE combined with a SCE, calibration with
solutions of fluoride ions of known concentration enable the value of k to be
found. When the same cell is filled with an unknown solution, the fluoride ion
concentration may be determined. This is an example of direct potentiometry.
Other crystalline ion-selective electrodes use AgCl for Cl-, Ag 2 S for Ag+and
S^2 - , Ag 2 S +CuS for Cu^2 +and many more.
Liquid membrane electrodes are shown in Figure 3(a). Typically an
organophilic porous plastic membrane separates the internal reference from the
sample solution. Another reservoir contains a liquid ion-exchanger, which satu-
rates the pores in the membrane. The calcium electrode uses calcium dodecyl
phosphate [(RO) 2 PO 2 ] 2 Ca where R is the dodecyl radical, dissolved in dioctyl
phenylphosphonate.
The electrode response is given by:
E(Ca^2 +) =k +(RT/2F) ln (a(Ca^2 +))
Ion selective field effect transistors (ISFETs)
One disadvantage of the glass electrode for measuring pH is its fragility. A
modern development uses a field effect transistor where the gate surface is
coated with a material, often aluminum oxide, whose surface is sensitive to pH.
As the potential at the surface changes with pH, the current induced through
the transistor varies. A temperature diode, incorporated in the electrode
C3 – Potentiometry 71
Ag electrode
Leads to meter
Reference
electrode
Internal
solution
Glass electrode
O-ring
Gas-permeable
membrane
Liquid organic
ion exchanger
Porous plastic
membrane with
liquid ion exchanger
Aqueous solution
saturated with
AgCl and MCl 2
(a) (b)
Fig. 3. (a) Liquid ion exchange membrane electrode for M^2 +ions. (b) Gas sensing electrode
using glass ISE.