Reduction reactions are characterized by a gain of electrons whereas oxidation reactions are characterized by a loss of electrons. Recall that elements on the right side of the periodic table have the tendency to gain electrons to complete the octet. Groups such as chalcogens (group VI) and halogens (group VII) have six and seven valence electrons, respectively; therefore, they only need a few electrons to have eight valence electrons and complete the octet. Since halogens tend to gain electrons, they typically undergo reduction.

Alkaline earth metals (group II) and transition metals have few valence electrons; therefore, they tend to lose electrons and undergo oxidation. Noble gases are nonreactive elements and do not undergo reduction or oxidation.

For this problem, we need to figure out the oxidation states of manganese in each compound. Oxygen typically has an oxidation number of  and potassium has an oxidation number of . For Compound A, there are two oxygen molecules; therefore, oxygen contributes a total charge of . Since manganese dioxide is a neutral molecule, the manganese in it will have an oxidation number of . For Compound B, four oxygen atoms contribute a charge of  whereas one potassium atom contributes a charge of ; therefore, the manganese in potassium permanganate will have an oxidation number of . Conversion of manganese from Compound A to manganese in Compound B involves the removal of electrons—three electrons, specifically, because its charge has to change from  to ; therefore, this reaction is characterized as an oxidation reaction.

A reaction that has both reduction and oxidation half reaction is called a redox reaction. It involves one or more atoms gaining electrons (reduction) and one or more atoms losing electrons (oxidation). Recall that single displacement reactions involve the replacement of an element in a compound with another element. An example of single replacement reaction is shown below:

In this reaction, a sodium atom replaces a calcium atom in calcium sulfate. If we calculate the oxidation numbers for sodium and calcium, we can see that sodium loses an electron (the oxidation state goes from  to ) whereas the calcium ion gains two electrons (goes from  to ); therefore, this is a redox reaction. All single displacement reactions follow this general trend and are characterized as redox reactions.

Reaction of sodium chloride and calcium sulfate is as follows:

If we calculate the oxidation state of each atom we will notice that oxidation number doesn’t change; therefore, this isn’t a redox reaction.

Oxidation involves a loss of electrons whereas reduction involves a gain of electrons. This means that oxidation generates electrons as products whereas reduction consumes electrons as reactants. Note that oxidation and reduction reactions can be distinguished by looking at oxidation states. If the oxidation state of an atom becomes more positive, then it underwent an oxidation reaction, and if the oxidation state becomes more negative, then that atom underwent a reduction reaction.

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: