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This question pertains to the subject of electrochemistry --specifically a half-cell and not a full galvanic cell.

From what I understand, a half-cell has a potential of its own. This is voltage is measured relative to the Standard Hydrogen Electrode (SHE) because it is seemingly impossible to measure the voltage between the electrode and the electrolyte solution it is submerged in.

Question: Is the potential difference created due to the formation of the double layer on the electrode?

What I suspect: The electrons in the electrode are isolated by the double-layer away from the surplus of positively charged ions in the solution. Therefore, an ion would have to be "pushed through" the hill of potential that occurs when crossing the interface layer.

Is my understanding correct?

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Question: Is the potential difference created due to the formation of the double layer on the electrode?

No. The potential difference in a half cell is the voltage required for oxidation or reduction at the electrode (ie. Cu$^{2+}$ + 2e$^-$-> Cu) The double layer is a consequence of the redox reaction that creates a very thin charged layer at the electrode surface. This layer behaves like capacitor that causes a slight voltage drop for electrons that need to pass through the double layer to complete the redox reaction.

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