[onenameless]

Hello, my problem states:
You are to find an unknown silver salt, AgX, by investigation of its solubility in ammonia solution. Exactly 1.0 litres of 2.0M NH3 was required to completely dissolve the sample, which was known to be comprised of 5.75 x 10^-3 moles of the pure salt. Determine the ksp of the salt and its likely identity given the following:
1) Ag⁺ + NH₃ <--> Ag(NH₃)⁺ K1 = 2 x 10³M^-1
2) Ag(NH₃)⁺ + NH₃ <--> Ag(NH₃)₂⁺ K2 = 6.9 x 10³M^-1
Assume that mols X = mols Ag in the pure salt and that ionic strength effects can be ignored

So what I did was i set up some equations:

Ag⁺ + NH₃ <--> Ag(NH₃)⁺
Ag(NH₃)⁺ + NH₃ <--> Ag(NH₃)₂⁺
NH₃ + H₂O <--> NH₄⁺ + OH^-
2H₂O <--> H₃O⁺ + OH^-


1) [Ag] + [Ag(NH3)] + [Ag(NH3)2] = [X]
2) Conc of NH3 = 2.0M = [NH3] + [NH4] + [Ag(NH3)2] + [Ag(NH3)]
3) [H3O] + [NH4] = [OH] = 10^-7
4) [Ag] + [Ag(NH3)] + [Ag(NH3)2] + [H3O] = [OH] = 10^-7
ksp = [Ag][X]

Ok so i set up my equations like so, can anyone confirm whether they're correct or not?

[Borek]

Equations are wrong, you need to elaborate about what you are trying to do, as I am not able to guess what is what of what.

Can you tell what is [X^-] (almost) without further calculations?

[bobdylan18]

Just for confirmation, did you guys get identity of unknown X to be Br^-?

[onenameless]

Well, i tried to establish the mass balance equation which is number 1. I figured that we don't know what the initial concentration of X is, but as the last sentence of the problem says, the number of moles of X is equal to the number of moles of Ag. Therefore, in solution Ag reacts in multiple steps and so the concentration of each of these products ([Ag] + [Ag(NH3)] + [Ag(NH3)2]) added should be equal to the sum of Ag.

Equation 2 is based on the fact that we know the concentration of NH3 added which was 2.0M initially, but after it was added to the solution, we see that NH3 also reacts in multiple reactions so the concentration of NH3 (which is 2.0M) is a summation of [NH3] + [NH4] + [Ag(NH3)2] + [Ag(NH3)].

Equation 3 is the standard water dissociation reaction, however, since ammonia also reacts with water giving us ammonium and hydroxide, we need to incorporate both of these values into the equation so that the concentration of hydroxide (which is 10^-7) is equal to the concentration of hydronium and ammonium.

Equation 4 is just charge balance.

So I did some substitutions and rearrangements, and I believe we need to make an assumption that the concentration of Ag(NH3)2 and Ag(NH3) can be neglected since (based on the k value) they will not be so significant in concentration.

[Borek]

Well, i tried to establish the mass balance equation which is number 1. I figured that we don't know what the initial concentration of X is, but as the last sentence of the problem says, the number of moles of X is equal to the number of moles of Ag. Therefore, in solution Ag reacts in multiple steps and so the concentration of each of these products ([Ag] + [Ag(NH3)] + [Ag(NH3)2]) added should be equal to the sum of Ag.

OK. Let's call it AgX mass balance.

Equation 2 is based on the fact that we know the concentration of NH3 added which was 2.0M initially, but after it was added to the solution, we see that NH3 also reacts in multiple reactions so the concentration of NH3 (which is 2.0M) is a summation of [NH3] + [NH4] + [Ag(NH3)2] + [Ag(NH3)].

Mass balance of ammonia then. But the equation is wrong. [Ag(NH₃)₂⁺] contains two ammonia molecules.

Equation 3 is the standard water dissociation reaction, however, since ammonia also reacts with water giving us ammonium and hydroxide, we need to incorporate both of these values into the equation so that the concentration of hydroxide (which is 10^-7) is equal to the concentration of hydronium and ammonium.

This is completely off - Kw requires a product, not a sum. You need two equations - one for water equiblrium (Kw), the other for ammonia equilibrium (Kb or Ka). Finally, you can't assume [OH^-] is 7, that would mean neutral solution, but you have added ammonia, so solution is basic.

Equation 4 is just charge balance.

And it is again wrong - charge balance has to account for X^- presence.