4. Electrochemical cells

4.6. Potentiometry

Potentiometric methods provide an accurate means to measure the cell potential. In an elementary measurement, the Nernst equation is applied to find the relation between the concentration and the measured cell potential. Potentiometric measurements can be used to determine, for example, standard potentials, concentrations of electroactive species, mean activity coefficients of electrolytes, acid and base constants, stability constants of complexes, and equilibrium constants of redox reactions. An example of determining the standard potential of the Ag/AgCl electrode was presented in chapter 4.3.1.

The best-known example of a widely used potentiometric measurement is the determination of pH. A pH meter typically uses an Ag/AgCl as the reference electrode and what is known as the glass electrode as the working (or indicator) electrode. The glass electrode is an example of ion-selective electrodes, which are used in various chemical environments to determine concentrations. The heart of an ion-selective electrode is a semipermeable membrane; the potential difference across the membrane depends only on the concentration of the species of interest.

The tip of the glass electrode is made of glass, and the inside of the electrode holds HCl solution at the constant concentration. The electrodes (the reference and indicator electrodes are usually made into one structure) are immersed in the studied solution. The potential change across the glass membrane is dependent on the activity difference between protons in the inner liquid and the studied solution. The Ag/AgCl reference electrode detects this potential. According to the Nernst equation:

\displaystyle E=\text{constant}-\frac{RT}{F}\ln\left(\frac{a_{\text{inner}}}{a_{\text{solution}}}\right) (4.50)

where a is the activity of proton. Changing to the Briggs logarithm and setting the temperature to 25 °C gives

\displaystyle E=\text{constant}-0.0592 \cdot\text{pH}(\text{ Volts}) (4.51)

The pH meter has a very high input impedance, i.e. it does not allow practically any current to flow across the glass electrode, which ensures the quasi-equilibrium condition. The constant in equation (4.51) is ill defined and typical for each electrode. Usually, it is determined by calibrating the pH meter with known buffer solutions. If temperature changes, the slope of the line E – pH will change. In digital pH meters, calibration is carried out automatically with two buffer solutions and the calibration line according to (4.51) is calculated.

The operation of the glass electrode is based on ion-exchange properties of the silicate matrix of the membrane. Glass is made of a three-dimensional, irregular network of silicon and oxygen. Some of the oxygen atoms are negatively charged, and this charge is balanced in the structure with, for example, sodium or lithium ions. These small cations can move in the structure and hence carry the electric charge. When a glass electrode is immersed in water, the outer layer of the glass will exchange some of the alkali metal ions for protons in the water; it will work as an ion-exchanger. This ion-exchange equilibrium is affected by the pH of the solutions. The activity of a proton will therefore set to a particular value on the hydrated layer on the surface of the glass. This will form a pH-dependent potential difference across the membrane. The proton concentration inside the electrode is kept constant and the pH of the studied solutions can be determined through calibration. By changing the type of glass used, sodium, potassium or silver ion concentrations can also be determined.

More common types of ion-selective electrodes are liquid membrane electrodes or solid membrane electrodes.  Ion-selective electrodes are available at least for the following cations: ammonium (NH4+), barium (Ba2+), calcium (Ca2+), cadmium (Cd2+), copper (Cu2+), lead (Pb2+), mercury (Hg2+), potassium (K+), sodium (Na+), silver (Ag+) and for the following anions: bromide (Br−), chloride (Cl−), cyanide (CN−), fluoride (F−), iodide (I−), nitrate (NO3−), nitrite (NO2−), perchlorate (ClO4−), sulfide (S−) and thiocyanate (SCN−). Ion-selective electrodes can also be found for gases. In these electrodes, a gas-permeable membrane separates the inner solution from its exterior. Enzyme electrodes have a gel layer containing a particular enzyme as the selective membrane. When using ion-selective electrodes, one has to keep in mind that the electrode potential is a function of activity, not concentration. As activity is a function of the ionic strength of the solution, in order to obtain reliable results, the ionic strength of the solutions (calibration solutions and the studied solution) must be kept constant.