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:

Electronic devices such as cell phones utilize batteries for power. A discharging battery converts the chemical energy associated with redox reactions to electrical energy that can be utilized to power the device. Kinetic energy is the energy associated with motion and is irrelevant to this question.

A charging battery behaves as an electrolytic cell. The process involves a nonspontaneous reaction; therefore, energy input is needed for charging a battery. This energy is provided by the electrical outlets that we use to charge our electronic devices, such as cell phones. Since it is nonspontaneous, the reaction occurring during charging has a positive Gibbs free energy.

Oxidation always occurs at the anode and reduction always occurs at the cathode, regardless of the type of cell. As mentioned previously, the charging battery requires energy input and behaves as an electrolytic cell. Exothermic reactions are characterized by a negative change in enthalpy. A reaction happening in an electrolytic cell is nonspontaneous. This means that the Gibbs free energy is always negative; however, other thermodynamic variables such as enthalpy and entropy can be either positive or negative. 

A charging battery consumes energy from a power source like an electrical outlet, whereas a discharging battery releases energy and powers a device; therefore, a charging battery behaves as an electrolytic cell whereas a discharging battery behaves as a galvanic cell. 

A discharging battery behaves like a galvanic cell; therefore, it is characterized by a spontaneous reaction. This means that the reaction happening in a discharging battery has a positive standard reaction potential. Given the information in the question, we will get a positive standard reaction potential if the lithium atom is oxidized (half reaction potential = ) and the manganese ion is reduced (half reaction potential = ). The total standard reaction potential is the sum of the half reaction potentials, . The oxidation of manganese and the reduction of lithium will yield a negative potential, not characteristic of a discharging battery. Note that one reaction has to be oxidation and one reaction has to be reduction.

First we need to convert minutes to seconds (10min=600s), and knowing that , we can calculate the amount of silver deposited as follows:

If we follow the units carefully, we see that all of the units cancel out to give us a value in grams of silver, which is what we are looking for.