When electrolyzing copper (ll) chloride, what reaction takes place at the anode? what reaction takes place at the cathode?

Copper ions are reduced into copper atoms.

Cu²⁺₍aq₎ + 2e⁻ →  Cu₍s₎

Explanation:

During electrolysis,  the positive H⁺ and Cu⁺ ions move to the negative cathode and negative OH⁻ and Cl⁻ ions move to the positive anode.

At cathode, copper ions are preferentially discharged due to the low electromotive force required to discharge them compared to the hydrogen ion. The copper ions gain the two electrons lost by the chloride ions when the are discharged. (2 Cl⁻₍aq₎ → Cl₂₍g₎ + 2e⁻)

Thus the half equation is as follows:

Cu²⁺₍aq₎ + 2e⁻ →  Cu₍s₎