Question

Why is it not possible to measure the single electrode potential?

Answer 1

Electrode potential of an electrode is the potential or voltage difference of a cell which is combined with a standard hydrogen electrode and the electrode whose potential is to be measured. It is the resultant potential difference between a point on the electrode and a point in the bulk of the electrolyte, which occurs due to the transfer of charged particles as well as adsorption of polar molecules. The potential of the standard hydrogen electrode is always taken as zero.

Complete answer:
A standard electrolytic cell consists of two electrodes and an electrolyte solution. The electrodes may be dipped in different electrolyte solutions and connected by a salt bridge. In an electrolytic process, oxidation occurs at one electrode and reduction occurs at the other electrode. The overall electrode potential of the cell, is the difference between the emf’s of the cathode and the anode.
The electrolytic cell involves both the oxidation and reduction reactions. The occurrence of just oxidation or reduction is not possible, as both are required for a cell to operate. In a galvanic cell the oxidation and reduction occur simultaneously. For the measurement of the electrode potential, two electrodes must be combined such that the redox reaction can take place.
Hence half a cell containing a single electrode cannot exist independently, and its potential cannot be measured.

Note:
The cell potentials are commonly measured using the Nernst Equation. The equation can be given as:
${E_{cell}} = E_{cell}^0 - \dfrac{{2.303RT}}{{nF}}\ln \left( {\dfrac{{\operatorname{Re} duction}}{{Oxidation}}} \right)$
$E_{cell}^0$ is the standard electrode potential which can be calculated by the formula: $E_{cell}^0 = E_{cathode}^0 - E_{anode}^0$.