http://www.chemicalforums.com/index.php?topic=73202.0 Here's the old topic, from what I've read everything is pretty clear except 4.

I just want to know if my assumptions are correct(maybe you have used an equation solver to get the accurate answer, I didn't find one to deal with the explicit form of the equation, maybe you can recommend me one? ):

K

_{sp}=[Ca

^{2+}]

^{3}[PO

_{4}^{3-}]

^{2} Now, a small amount of phosphate dissociates: PO

_{4}^{3-} + H

_{2}O

HPO

_{4}^{2-} + HO

^{-}. Assuming that [OH

^{-}]=[ HPO

_{4}^{2-}], I have x

^{2}/(S-x)= K=kw/ka

_{3}=10

^{-1.6812}.

Therefore S= (x

^{2}+ Kx)/K. So, [Ca

^{2+}]=S= (x

^{2}+ Kx)/K and [PO

_{4}^{3-}]=S-x=x

^{2}/K.

Everything right until here, but here comes the interesting part: Given we have a saturated solution of a poorly soluble compound, we expect the pH to be less than , say, 10 ( the idea is that [HO

^{-}]<<K=10

^{-1.6812}, and therefore S≈x). Hence, we obtain a solvable equation:

x

^{7}=K

_{sp}*K

^{2}, which leads to x=10

^{-4.0023}, and S=9.9946*10

^{-5}.

I also obtain pH=9.9977, which is in accordance with my assumption( of course, mathematically, this doesn't prove anything, but I've seen that most problems deal with their assumptions just like this)

What do you think?