An electrolytic cell utilizes energy to facilitate a nonspontaneous redox reaction. This is different from a galvanic cell, which releases energy from a spontaneous redox reaction. A shared characteristic of both cells is that the oxidation half-reaction always happens at the anode and the reduction half-reaction always happens at the cathode. Note that a redox reaction always has an oxidation half-reaction and a reduction half-reaction.

The entropy of the reaction is typically negative for a nonspontaneous reaction. This is not true for all cases; therefore, the entropy could be positive or negative for an electrolytic cell. Electroplating involves reduction reactions that convert metal ions into solid metal. This solid metal is coated onto a metal plate. Since this involves a reduction reaction, it occurs at the cathode. 

Gibbs free energy is the “free” energy available that can be used to perform useful work. A negative Gibbs free energy corresponds to a spontaneous reaction, whereas a positive Gibbs free energy corresponds to a nonspontaneous reaction. Recall that a galvanic cell involves a spontaneous reaction, whereas an electrolytic cell involves a nonspontaneous reaction; therefore, the Gibbs free energy of the reaction is negative for a galvanic cell and positive for an electrolytic cell. 

Recall that galvanic cells carry out spontaneous reactions; therefore, they do not require energy. They release free energy that can be used to do work such as powering an electrical device (like cell phones).

Electrolytic cells, on the other hand, require energy because they carry out nonspontaneous reactions. They require the input of electrical energy. 

Galvanic cells are electrochemical cells that are characterized by a spontaneous redox reaction. To solve this question, we need to find the standard potential for each of the given reactions. Note that each reaction is a redox reaction; therefore, there is an oxidation half-reaction and a reduction half-reaction for each one.

The first reaction has a ferrous ion being reduced (gaining electrons) and lithium being oxidized (losing electrons). From the given information, we can deduce the standard potential for each half-reaction. The standard potential for reduction of iron is . Since the given standard potentials are for "reduction," the oxidation of iron is the opposite of the given value: . The total standard potential for this reaction is the sum of the standard potential for the half-reaction; therefore, the standard reaction potential for the first reaction is:

Since its standard reaction potential is positive, this reaction is spontaneous and occurs in a galvanic cell.

The second reaction has aluminum being oxidized () and a ferrous ion being reduced (). The standard reaction potential is ; therefore, this reaction can also occur in a galvanic cell.

The third reaction has a lithium ion being reduced () and an aluminum being oxidized (). The standard reduction potential is ; therefore, this reaction is nonspontaneous and cannot occur in a galvanic cell.

 has a higher standard reduction potential, and will therefore be reduced, meaning that lead will be oxidized. The anode is where oxidation takes place, and the cathode is where reduction occurs. Therefore, we assign the cathode to copper and the anode to lead.

In an electrolytic cell, the non-spontaneous reaction occurs. This means that Na is reduced (making it the cathode) and Mn is oxidized (making it the anode). The standard cell potential can then be calculated as follows: