[Big-Daddy]

No. The reverse action is happening when applying energy. And there are 10g of both reactants.

How do we know there is no CoO₂ nor LiC₆ initially present, it is not stated in the question? And if they are, the formal cell reaction CoO2 + LiC6  LiCoO2 + 6C should be the one proceeding, so why is the opposite direction proceeding?

[Rutherford]

Because that's how a secondary cell works.

[Big-Daddy]

I see, this is true. But then isn't there a problem with the question wording - because the electrolysis is making a reaction occur where there is oxidation (LiCoO2 -> Li+ + e- + CoO2) at the cathode and reduction (6C + Li+ + e- -> LiC6) at the anode?

[Rutherford]

The reduction must always happen at the cathode, but the cathode is not the same in the galvanic and the electrolytic cell, so that can be confusing here.

[Big-Daddy]

The reduction must always happen at the cathode, but the cathode is not the same in the galvanic and the electrolytic cell, so that can be confusing here.

Cathode is defined as the electrode at which the reduction (more positive EMF) reaction occurs forward. How is it defined for electrolysis then?

[Rutherford]

Reduction happens in electrolysis, too, but the galvanic and the electrolytic cell cathodes aren't the same, see what reaction will happen at the first and what at the second one.