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My book says:

"At each electrode-electrolyte interface there is a tendency of metal ions from the solution to deposit on the metal electrode trying to make it positively charged. At the same time, metal atoms of the electrode have a tendency to go into the solution as ions and leave behind the electrons at the electrode trying to make it negatively charged. At equilibrium, there is a separation of charges and depending on the tendencies of the two opposing reactions, the electrode may be positively or negatively charged with respect to the solution. A potential difference develops between the electrode and the electrolyte which is called electrode potential."

My doubt is whether electrode potential develops after we connect the reduction and oxidation half cells or it develops as soon as we dip the metal in the solution of it's electrolyte before connecting it to other half cell? And if the electrode potential develops before connecting it to the other half cell why can't we measure the absolute potential difference(without using standard hydrogen electrode as reference)?

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When you dip the electrode into the solution, it is indeed possible that electrolyte may interact with the surface of the electrode and there may be a limited amount of "charge flow" in the form of the creation of surface bound species. Without a bias created with the addition of an other electrode, however this reaction will be self terminating and it would resemble something similar to a space charge layer that can be observed with semiconducting materials, i.e. charge would flow until their fermi levels equalized. The extent of this flow is minuscule and it essentially would create a surface dipole which can be thought of as a kind of potential, but the electrode potential is defined with respect to its counter electrode so they aren't quite the same thing.

Does that answer your question? Potentials are always with respect to something else so by the definition of your question, you would need the other electrode in there, but we can still have the potential of a certain subspecies of the electrode with respect to a different part of the electrode.

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