Final answer:
At the cathode of an electrolytic cell with molten KCl and ZnCl2, the chloride ions are reduced to chlorine gas. This corresponds to option (c) 2Cl^-→ Cl2(g) + 2e-. Option C is correct.
Step-by-step explanation:
The student has asked which reaction occurs at the cathode of an electrolytic cell containing a mixture of molten KCl and ZnCl2.
In this electrolytic process, the reduction reaction occurs at the cathode. Reduction is the gain of electrons. Considering the options given, and knowing that the electrolyte is molten, water is not present, and thus options (b) and (d) which involve water are not applicable.
Option (a), Zn(s) → Zn2+(aq) + 2e- is an oxidation process and thus, cannot be the reaction at the cathode. The correct reaction is option (c), 2Cl-→ Cl2(g) + 2e-. Here, chloride ions (Cl-) receive electrons to form chlorine gas (Cl2), which is the process occurring at the cathode.