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Trying to understand the chemistry of an iron carbon battery

I am trying to understand the chemistry that occurs in an iron carbon battery during charging.

The negative electrode is iron, the positive electrode is carbon. The electrolyte is iron(II) chloride.

I understand that ferrous chloride dissociates in water to Fe2+ and Cl- ions.

During charge the Fe2+ ions are attracted to to the negative iron electrode and the Cl- ions are attracted to the positive carbon electrode.

The Fe2+ ions combine with electrons from the power supply to form metallic iron that plates on to the iron electrode.

My problem is understanding what happens at the positive carbon electrode. I'm told that iron(II) chloride loses electrons to the positive electrode and becomes iron(III) chloride.

Fine, but how does this happen if all the Fe2+ ions are at the negative electrode?? How does this happen if the iron(II) chloride has dissociated in to ions??...there is no iron(II) chloride anymore. Especially if the ions are all surrounded by charged water molecules.

If the power supply drives all the Fe2+ ions to the negative electrode and Cl- ions to the positive electrode how can any Fe2+ ions even be at the positive electrode to somehow recombine with Cl- ions back in to iron(II) chloride that then loses electrons to the positive electrode and becomes iron(III) chloride??? Any help would be appreciated.

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