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In electrolysis why do positive ions go to the cathode? Since the cathode is positive, won't the positive ions face repulsion at the cathode and would require more energy?

I understand that reduction happens at the cathode and positive ions reduce but somehow it does not make sense as positive - positive charges repel.

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TL;DR The cathode in an electrolytic process is considered to be negative, so there is actually no contradiction. The cathode is a positive electrode in a galvanic cell.

There are different notations for the sign ($\pm$) of the cathode used in the literature, which are determined, in particular, by the nature of the process. A very broad definition of a cathode is that it is the electrode of some device connected to the negative pole of the current source.

For electrolysis it is commonly believed that the "-" cathode is the electrode on which the reduction process takes place, and the "+" anode is the one where the oxidation process takes place. When the cell works (for example, during copper refining), an external current source provides an excess of electrons (negative charge) at one of the electrodes -- the cathode, where metal is reduced. On the other electrode, there is a lack of electrons and oxidation of metal takes place -- this is the anode.

At the same time, during the operation of a galvanic cell (for example, $\ce{Cu - Zn}$), an excess of electrons (and a negative charge) on one of the electrodes is provided not by an external current source, but by the actual oxidation reaction of the metal (zinc dissolution). Following the definition given, this electrode is an anode. Electrons passing through the external circuit participate in the reduction of copper, so the cathode will be a positive electrode in this case.

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    $\begingroup$ This confused the heck out of me for about the first 3 years as an undergraduate. I thought I had learned in basic chemistry that the "cathode" was a positive electrode, then we started doing electrolysis in biology labs where positively-charged things migrated towards the cathode, and it never made any sense to me. Finally, I had a professor explain the different notations, and it all made sense. I was not the only student who was enlightened. It would be smart if this were explained much earlier. $\endgroup$ – Cody Gray Jul 4 '17 at 6:40
  • $\begingroup$ @WilliamR.Ebenezer in the word "geochemistry" "geo-" doesn't stand for the planet Earth, rather for the ground or crust. "Geochemistry" applied to extraterrestrial space bodies (such as moons and planets) is perfectly fine, removing that tag made no sense to me. Plus, there probably were other minor formatting issues (I don't remember the details that you haven't addressed in your edit making it also incomplete. Both factors made me reject the edit and I think I did so rightfully. $\endgroup$ – andselisk Apr 15 at 12:36
  • $\begingroup$ @andselisk Alright, alright. Pardon the incompleteness of knowledge and sorry for making such a fuss out of it. $\endgroup$ – William R. Ebenezer Apr 15 at 15:36
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    $\begingroup$ @WilliamR.Ebenezer No prob at all, that's fine. I admit I also make erroneous decisions and my edits are also not perfect; for the future you probably might want to ask similar questions on Meta as it's more suited for the disputes like this, plus you get a spectra of opinions instead of only mine. $\endgroup$ – andselisk Apr 15 at 15:45
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You got it reversed.

The cathode is the electrode where cations discharge, hence the name.

BTW, effective electron flow in galvanic cells is always directed from the cathode to the anode. The 'change' of the polarity of electrodes is due to a change in perspective, not actual change of flow.

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