Selective Precipitation Chemistry Problem

[frozonecom]

Homework Statement

A solution of $AgNO_{3}$ is added to a solution containing 0.100 M $Cl^{-}$ and 0.100 $CrO_{4}^{2-}$.

What will be the concentration of the less soluble compund when the more soluble one begins to precipitate?

Homework Equations

Ksp AgCl = $1.82 x 10^{-10}$
Ksp Ag2CrO4 = $1.2 x 10^{-12}$

The Attempt at a Solution

So, by calculating for their molar solubilities, I would know which one would precipitate first (which one is more soluble or less soluble)

(2x)^2 (x) = Ksp Ag2CrO4
x=Molar solubility of Ag2CrO4 = 6.69 x 10^-5 M
(x)(x) = Ksp AgCl
x= Molar solubility of AgCl = 1.35 x 10^-5 M

Thus, Ag2CrO4 is more soluble and AgCl is the less soluble compound.

Now, how will I find the concentration of the less soluble compound when the more soluble one begins to precipitate?

Please guide me. Here's my attempt for a solution.

The more soluble compound, Ag2CrO4 will begin to precipitate at this Ag+ concentration

[Ag+]^2 [CrO42-] = Ksp Ag2CrO4
[Ag+] = sqrt( Ksp Ag2CrO4 / [CrO42-] ) = 3.46 x 10^-6 M

Now, how would I find the concentration of AgCl in the solution? Again, here is my attempt:

I think, I should substitute the Ag+ concentration at the formula

[Ag+][Cl-] = Ksp AgCl

, But, is the Cl- concentration that I will get equal to the concentration of AgCl in the solution? I'm very confused. :(. Anyway, here's an attempt:

[Cl-] = Ksp AgCl / [Ag+] = 5.26 x 10^-5 M

I mean, the answer CAN be plausible since the concentration seemingly decreased. Is it correct guys?

I think what I am having problem with is that why would the concentration of AgCl be equal to the equilibrium conc of Cl- ?

 

[frozonecom]

Anyone here who can help me? Our test didn't include anything like this (thank god), but anyway, I still feel the need to learn this kind of stuff. It looks simple but I still can't be certain about this.

Please help.

 

[Borek]

Sorry, somehow I missed your post earlier.

What you did is correct. I guess the wording of the problem is wrong - it is a classic question, asked every year everywhere, and it always asks about concentration of the ion (Cl^- here) and not "compound". Compound is ambiguous in this context which is why you are confused.

 

[frozonecom]

Sorry, somehow I missed your post earlier.

What you did is correct. I guess the wording of the problem is wrong - it is a classic question, asked every year everywhere, and it always asks about concentration of the ion (Cl^- here) and not "compound". Compound is ambiguous in this context which is why you are confused.

Oh. Truth be told, I was wacking my head finding a similar problem in textbooks & internet and like you said, it's concerned only on the final equilibrium concentration of an ion. Thanks.

I guess it's time to suggest to our institute to revise their laboratory manual, or at least their self-assesment questions. It has become more of a confusion rather than a help.

Again, thank you very much. :)