Calculation of a Metastable Boundary

There is a second way of calculating the same kinds of diagrams using the alternative variable pe rather than Eh. Because this is another way of doing exactly the same thing, it could be argued that the new variable pe is unnecessary and redundant. However, the pe and Eh scales differ numerically, and pe calculations are now used about as frequently as Eh, so it is worthwhile discussing the use of this second variable. 

The concept of pe as a means of describing oxidation potential was popularized by the Swedish chemist Lars Gunner Sillen in the 1960s (see review by Truesdell, 1968). The idea was to develop an analogy between pH, which refers to hydrated protons, and pe, which would refer to hydrated electrons. Like the proton, the electron 

To develop the mathematical description of pe, start by considering the half-cell reduction reaction  

If all reactants and products (except the hydrated electron) are in their standard states, 5 = 1, and (18.41) becomes 

The superscript ° on pe° indicates that the activities of all reaction constituents except the electron are in their standard states when (18.42) applies. The energy level of the electron would be different in different half-cells and need not be considered to have a standard state. 

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