why the electrode potential arise at the electrode in contact with its ionic solution?
In its most basic form, the case of a metal electrode, some metal dissolves from the electrode surface. In doing so, insoluble metal atoms become soluble metal ions. That process involves separating electrons from those atoms. The ions go off into solution and the electrons remain behind on the electrode. The electrons give the electrode a negative charge.
Because electrochemical reactions are heterogeneous. The reactions will only occur at the electrode interface so of course the electrode potential is found at the interface.
That's too strong a statement, they can occur as well in the solution, when both reduced and oxidized substances are dissolved.
but how can a metal dissolve to its own solution.
2Na + H2O -> 2NaOH + H2
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