[Radu]

     I have a problem, I have to calculate the solubility ( the aparent solubility) of Ca₃(PO₄)₂ in pure water, given k_s=2.22*10^-25.
      ka₁=10^-2.12493; ka₂=10^-7.2076; ka₃=10^-12.318758;
   
       Here's what I did:
                   Besides ionic dissociation of calcium phosphate, the following equilibrium establishes:
                           PO₄^3-+H₂O HPO₄^2- + HO^-. , K=K_w/ka₃ = 10^-1.6812 .

               Creating a table with the extent of this reaction at equilibrium, I obtain x as a function of aparent solubility, that is to say I solve the equation x²/2S-x = K.
             Then I write K_s= (3S)³*(2S-x_(S))², but it is not analitically solvable.
         Any easier ways of treating this problem?
             

[Sabinol]

Shouldn't the solubility be:
2S = [HPO₄^2-] + [PO₄^3-]
and, knowing that K= K_w/Ka₃ = [HPO₄^2-][HO^-]/[PO₄^3-]
you will get :
2S = [PO₄^3-] (1 + K_w/Ka₃[HO^-])
which is equivalent to:
2S = [PO₄^3-] (1 + [H⁺]/Ka₃)
and, because K_s = [Ca²⁺]³*[PO₄^3-]²
substituting [PO₄^3-] with something you can easily derive from the formula above and [Ca²⁺] = 3S, you will get :
K_s = (3S)³*(2S)²/(1 + [H⁺]/Ka₃)²
which is a solvable equation if you know the solution's pH (in this case 7, obviously ) )

[Radu]

 It's not 7, not even near 7, that's the problem. There've been more discussions about this here:
            http://www.chemicalforums.com/index.php?topic=73202.0
   

[Sabinol]

Yes, I was just looking on the topic.. Seems like I underestimated the problem