Suppose you are given the following experimentally observed facts regarding the reactions of silver ion.

(a) Ag^+ reacts with Cl^- to give white AgCl (s)
(b) Ag^+ reacts with ammonia to give a quite stable complex ion, Ag(NH3)2^+
(c) a black suspension of solid silver oxide, Ag2O(s), shaken with NaCl solution, changes to white AgCl(s).
(d) AgCl(s) will dissolve when ammonia solution is added, but AgI(s) does not dissolve under these conditions.

Write equations for any net reacts in the cases above; then, based on these observations, arrange each of the substances AgCl, AgI, Ag2O, and Ag(NH3)2^+ in such an order that their solutions with water would give a successively decreasing concentration of Ag+.

so I got
a) Ag^+ (aq) + Cl^- (aq) <-> AgCl (s)
and
b) Ag^+ (aq) + 2NH3 (aq) <-> Ag(NH3)2^+ (aq)

I'm not sure if those are correct, and have no idea how to do the other two, and I don't know how to arrange them.

Please help!

The two you have written are correct.

The Ag2O + NaCl gives the same AgCl as the other equations you have. d forms the same Ag(NH3)2^2+ as in the part above it so that isn't a new equation either.
Solubility of Ag^+ from high to low.
Ag(NH3)2^2+
Ag2O
AgCl
AgI

Your equations for parts (a) and (b) are correct. Now let's work on parts (c) and (d):

c) We are given that when a black suspension of solid silver oxide (Ag2O) is shaken with NaCl solution, it changes to white AgCl(s). This suggests that Ag2O is reacting with the Cl^- ions from NaCl to form AgCl(s).

Ag2O(s) + 2Cl^-(aq) -> 2AgCl(s) + O^2-(aq)

d) It is observed that AgCl(s) dissolves when ammonia solution is added, while AgI(s) does not dissolve under these conditions. This indicates that AgCl is more soluble in ammonia than AgI.

AgCl(s) + 2NH3(aq) -> Ag(NH3)2^+(aq) + Cl^-(aq)

AgI(s) does not react with ammonia.

Now let's arrange the substances in the order of decreasing concentration of Ag+ when dissolved in water:

1. Ag(NH3)2^+
2. AgCl
3. AgI
4. Ag2O

The complex ion Ag(NH3)2^+ will have the highest concentration of Ag+ when dissolved in water because it is quite stable. AgCl will have a slightly lower concentration since it can also dissolve in water. AgI does not dissolve under these conditions, so it will have a lower concentration. Ag2O does not directly release Ag+ ions when dissolved in water, therefore it will have the lowest concentration of Ag+ ions among the four substances.

Your equations for parts (a) and (b) are correct.

For part (c), you can write the equation as:
Ag2O (s) + 2Cl^- (aq) -> 2AgCl (s)

For part (d), you can write two equations:

AgCl (s) + NH3 (aq) -> Ag(NH3)2^+ (aq) + Cl^- (aq)

AgI (s) + NH3 (aq) -> No reaction

To arrange the substances in order of decreasing concentration of Ag+, you need to consider the solubility of each compound in water.

AgCl is soluble in water, so it will release Ag+ ions into the solution.
AgI is insoluble in water, so it will not release Ag+ ions.
Ag2O is not directly soluble in water, but it reacts with NaCl solution (as stated in observation (c)) to form AgCl, which is soluble in water.
Ag(NH3)2^+ is a complex ion formed with ammonia, so it will release Ag+ ions into the solution.

Based on this information, the substances can be arranged in order of decreasing concentration of Ag+ as follows:
Ag(NH3)2^+ > AgCl > Ag2O > AgI

So, when these substances are dissolved in water, the solution of Ag(NH3)2^+ will have the highest concentration of Ag+ ions, followed by AgCl, Ag2O, and AgI with decreasing concentrations.