Write the equation for the reaction, if any, that occurs when each of the following experiments is performed under standard conditions.

a) crystals of iodine are added to an aqueous solution of potassium bromide.
b) liquid bromine is added to an aqueous solution of sodium chloride.
c) a chromium wire is dipped into a solution of nickle (II) chloride.

From the information given, how would I determine whether or not the reactions occur?

For all of them you can use a table of reduction potentials. Do you have that? If not, the Activity series will answer the Cr, Ni question. For the halogens, the reactivity goes from F2>Cl2>Br2>I2, meaning F2 will displace any ion (Cl^-, Br^-, I^-) below it. But not the other way around.

I have a table of reduction potentials, but I'm not really sure how to use it to solve this problem. A lot of the substances listed in the problems (for example, KBr) don't exist on the table. Would this mean that the reaction doesn't exist?

If a specific substance is not listed in your table of reduction potentials, it does not necessarily mean that the reaction doesn't exist. It may just mean that the reduction potential for that specific substance has not been measured or included in the table. However, you can still use the table to determine whether or not the reactions will occur.

To determine if a reaction will occur, you need to compare the reduction potentials of the two half-reactions involved in the process. The half-reaction with the higher reduction potential is more likely to occur and will act as a reducing agent, while the half-reaction with the lower reduction potential will act as an oxidizing agent.

Let's go through each reaction and explain the process of determining if they will occur:

a) Crystals of iodine (I2) are added to an aqueous solution of potassium bromide (KBr).

The relevant half-reactions for this reaction can be written as:

2I^- (aq) → I2 (s) + 2e^- (Reduction half-reaction)
2Br^- (aq) → Br2 (s) + 2e^- (Oxidation half-reaction)

To compare the reduction potentials, you need to locate the reduction potential values for I^- and Br^- in your table. Since you mentioned Br2 and I2 in your question, it implies that the reduction potentials of those species are available in your table.

Compare the reduction potentials of I^- and Br^-:

If E°(I^-) > E°(Br^-), then the reaction will occur.
If E°(I^-) < E°(Br^-), then the reaction will not occur.

b) Liquid bromine (Br2) is added to an aqueous solution of sodium chloride (NaCl).

The relevant half-reactions for this reaction can be written as:

2Br^- (aq) → Br2 (l) + 2e^- (Reduction half-reaction)
2Cl^- (aq) → Cl2 (g) + 2e^- (Oxidation half-reaction)

To compare the reduction potentials, you need to locate the reduction potential values for Br^- and Cl^- in your table.

If E°(Br^-) > E°(Cl^-), then the reaction will occur.
If E°(Br^-) < E°(Cl^-), then the reaction will not occur.

c) A chromium wire is dipped into a solution of nickel (II) chloride (NiCl2).

Since there are no halogens involved in this reaction, we can use the activity series instead of the reduction potentials. The activity series is a list of metals in order of their reactivity. If a metal is higher on the activity series than another metal, it can displace the other metal from its salt solution.

In this case, chromium (Cr) is higher on the activity series than nickel (Ni). Therefore, a reaction will occur, and the chromium wire will displace nickel from the nickel (II) chloride solution.

In summary, to determine whether a reaction will occur, you can use the table of reduction potentials or the activity series, depending on the specific elements and compounds involved in the reaction.