Analytical Chemistry - Systematic Treatment of Equilibrum

[ahhppull]

Homework Statement

Calculate the molar solubility of Ag2C2O4 (silver oxalate) in a solution that has a fixed H3O+ concentration of 1.0 x 10^-6 M.

Homework Equations

The Attempt at a Solution

I found the pertinent reactions, the charge balance and the mass balance so far, but I don't know what to do next.

Pertinent Reactions
Ag2C2O4(s) → 2Ag+(aq) + C2O4(2-)(aq) Ksp = 5.40 x 10^-12
H2C2O4(aq) + H2O(l) → HC2O4-(aq) + H3O+(aq)
HC2O4-(aq) + H2O(l) →C2O4(2-)(aq) + H30+(aq)

Charge Balance
[Ag+] + [H3O+] = 2[C2O4(2-)] + [HC2O4-]

Mass Balance
[Ag+] = 2[C2O4(2-)]
[Ag+] = 2{[C2O4(2-)] + [HC2O4-] + [H2C2O4]}

 

[Borek]

What reactions take place, what are equilibrium constants (other than Ksp you already listed) for them?

 

[ahhppull]

I found that Ka1 = 5.60 x 10^-2 and ka2 =5.10 x 10^-5. Another site listed 5.4x10^-2 and 5.4x10^-5.

EDIT: Actually, I finally found it in my textbook. Ka1 = 5.62E-2 and ka2 = 5.42E-5

 

[Borek]

Write formulas for both dissociation constants. Count your equations and your unknowns - are you ready to solve?

 

[ahhppull]

Hey Borek, I wrote out all the formulas. My question now is what exactly am I solving for? Am I suppose to solve for all the concentrations? [Ag+], [C2O4(2-)], [HC2O4-] and [H2C2O4]?

Also how am I suppose to solve for Ag+? Is it 5.4E-12 = [2x]^2 [x]?

 

[Borek]

Technically you should have a set of n-equations in n-unknowns - yes, solve for all unknowns and you are done.

Easier said than done, these are not linear equations, so you have to look for approximations or go numerical.

Also how am I suppose to solve for Ag+? Is it 5.4E-12 = [2x]^2 [x]?

It doesn't make sense to add another unknown x, you already have plenty of unknowns and this one is not going to make the problem much easier.