Writing multiple steps for Ka and Ksp

[dennis-brodmann]

I found the following question about Ksp and Ka expressions from http://chemistry786.wordpress.com/2010/05/29/lies-my-chemistry-teacher-told-me-ka-vs-ksp/

"Ka means the ratio of a chemical reaction of an acid at equilibrium. The ratio is the product of the concentrations of products (right side) divided by the product of the concentrations of the reactants (left side). So basically, if you have an acid reacting with water like:

HF + H2O <–> H3O+ + F-

The Ka is ([H3O+][F-])/([HF]). Liquid water is never written in because numbers get huge and slightly messed up.

So if you have H2SO4, sulfuric acid, and you wanted to write the Ka of it, there would be two because it would have to lose the first hydrogen and then the second–both cannot come off at the same time. (We are pretending H2SO4 is not a strong acid at the moment)

Ex:

1) H2SO4 + H2O <–> HSO4- + H3O+

Then the HSO4- reacts with water

2) HSO4- + H2O <–> SO4(2-) + H3O+

There are two separate Ka’s. The Ka for the first reaction is:

1) Ka= ([H2SO4-][H3O+])/([H2SO4])

The second reaction Ka:

2) Ka= ([SO4(2-)][H3O+])/([HSO4-])

So if you want the Ka of the reaction of H2SO4 + 2H2O <–> 2H3O+ +SO4(2-), (which is adding the first two reactions essentially) you would do:

Ka(1) x Ka(2)

Now that is all fine and cute, but when we start talking about Ksp, it is a different game.

Ksp if the ratio of a chemical reaction of a solid dissociating at equilibrium. The ratio is the same like Ka–products over reactants. But because the reactant is a solid + H2O, the solid is not written in the expression (solids mess calculations up). So really, it is just the products. But the HUGE difference between Ka and Ksp is here:

Ca3(PO4)2<–> 3Ca(2+) + 2PO4(3-)

Ksp= ({[Ca(2+)]^3}{[PO4(3-)]^2})

**Ca3(PO4)2 is a solid, so it is not written in the expression**

***The ^3 and the ^2 are there just because they are the coefficients in front of the ions. That would hold true for any K expression–Ka, Kb, Kf, Ksp, Kc etc.***

In case you didn’t see it, look at how the equation is written–it went straight from Ca3(PO4)2 to separate 3Ca(2+) and 2PO4(3-).

**You CANNOT tell me that for Ka you will dissociate it step by step and multiply the individual Ka’s and for Ksp you will not dissociate step by step.**

Further more, by having separate Ka’s, at least you acknowledge the solution has a bit of H2SO4, HSO4-, SO4(2-), and H3O+. By writing that type of Ksp expression, you have completely neglected that Ca2(PO4)2 (2-) and Ca(PO4)2 (4-) and other ions that exist in the solution. There is more than just Ca3(PO4)2, Ca(2+) and (PO4)(3-) in that beaker!"

Anyway, my thoughts on the poster's question brought about even more questions which led me to an answer that I hope someone can verify.
A salt submerged in pure water would dissolve along the corners and edges first, since the lattice energy is weakest there. That being said, there is no preference in which ion dissociates from the crystal lattice first (i.e. calcium is not preferred over sulfate).
Is that why Ksp is not written in steps, such as in the acid dissociation constant, where it is clear that H+ is preferrably removed by the solvent?

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[SN2ed]

Thread moved. These questions belong in the Study Q&A forum only.