Calucating the solubility product of Silver Chloride

[aati2sh]

Homework Statement

A sample of AgCl was treated with 5ml of 2M Na₂CO₃ solution to produce Ag₂CO₃. The remaining solution contained 0.003 g of Cl^- per litre. Calculate the solubility product of AgCl.(Ksp of Ag₂CO₃ = 8.2 ×10^-12)

Homework Equations

ksp of AgCl = [Ag⁺]×[Cl^-]
ksp of Ag₂CO₃ = [2Ag⁺]²×[CO_3^--]

The Attempt at a Solution

I couldn't think of any idea. So, entered this forum. Please help.

 

[Borek]

Can you calculate concentration of Cl^-?

There was a huge excess of carbonate. Did it concentration change much?

 

[aati2sh]

Yes. I calculated the concentration by dividing gm/litre by 35.5 to give molarity. But, I don't know where to go beyond.

 

[Borek]

I asked you a question, have you tried to answer it?

 

[aati2sh]

I don't know how to start.

 

[Borek]

Try to describe what is happening in the solution when the carbonate is added.

 

[aati2sh]

I tried this:
Ksp of Ag₂CO₃ = [2xSolub.]²x[Solub.]
=> Solubility = 1.270334x10^-4 = [Ag⁺]
Now,
[Cl^-]=0.003/35.5 M = 8.45 x 10^-5
Ksp of AgCl = 1.270334x10^-4 x 8.45 x 10^-5 = 1.073 X 10^-8.

Why was concentration and volume of Na2CO3 was given if this is correct?