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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.

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