Analogy With PH
Just as the transfer of hydrogen ions between chemical species determines the pH of an aqueous solution, the transfer of electrons between chemical species determines the reduction potential of an aqueous solution. Like pH, the reduction potential represents an intensity factor. It does not characterize the capacity of the system for oxidation or reduction, in much the same way that pH does not characterize the acidity.
In fact, it is possible to define pE, logarithm of electron concentration in a solution, which will be directly proportional to the redox potential. Sometimes pE is used as a unit of reduction potential instead of Eh, for example in of environmental chemistry.
The actual value of electron concentration is not measurable as it is of order of 10^-55 M, yet it is thermodynamically a well defined quantity. What matters is the logarithm of the quotient of concentration of electrons in one solute with respect to the other, and that is, via Nernst equation, proportional to the redox potential. If we normalize pE of hydrogen to zero, we will have the relation pE=16.9 Eh at room temperature. This point of view is useful for understanding redox potential, although the transfer of electrons, rather than the absolute concentration of free electrons in thermal equilibrium, is how one usually thinks of redox potential. Theoretically, however, the two approaches are equivalent.
Conversely, one could define a potential corresponding to pH as a potential difference between a solute and pH neutral water, separated by porous membrane (that is permeable to hydrogen ions). Such potential differences actually do occur from differences in acidity on biological membranes. This potential (where pH neutral water is set to 0V) is analogous with redox potential (where standardized hydrogen solution is set to 0V), but instead of hydrogen ions, electrons are transferred across in the redox case. Both pH and redox potentials are properties of solutions, not of elements or chemical compounds per se, and depend on concentrations, temperature etc.
Read more about this topic: Reduction Potential, PE
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“The whole of natural theology ... resolves itself into one simple, though somewhat ambiguous proposition, That the cause or causes of order in the universe probably bear some remote analogy to human intelligence.”
—David Hume (1711–1776)