PH of weak acid/weak base salts

[dumuzi]

I'm trying to show my students that $CaCO_3$ is basic.
$Ca^2^+$ comes from $Ca(OH)_2$, which is a weak base due to it's low solubility. $CO_3^2^-$ comes from the weak acid $HCO_3^-$. To compare the two we compare:

1) $Ca^2^+ + H_2O --> Ca(OH)_2 + H_3O^+$

and

2) $CO_3^2^- + H_2O --> HCO_3^- + OH^-$

We want to compare the K values. It is clear that equation 2 will have a significantly larger K value and the solution will be basic, but where can a person find a K value for something like equation 1?
Are there charts for the Ka of metal ions?
What order of magnitude is it? I imagine Ka for 1 is <<< Kw

 

[GCT]

I don't think equation 1 will occur appreciably, calcium hydroxide is fairly soluble in water so you can reasonably neglect it; thus calcium is a spectator ion (solubility of calcium hydroxide is .18g/100mL).

 

[Nerro]

The first reaction isn't even correct and frankly I don't know why you think that a strong base like calciumhydroxide would create an acidic particle like $$H3O^+$$.

This reaction would occur:
$$Ca(H_2O)_6^{2+}(aq)+H_2O(l) \rightleftharpoons CaOH(H_2O)_5^+(aq)+H_3O^+(aq)$$ Which explains why a solution of $$CaCl_2$$ is acidic.

The second reaction is also incorrect since it's an equilibrium:
$$CO_3^{2-}(aq) + H_2O(l) \rightleftharpoons HCO_3^-(aq) + OH^-(aq)$$

 

[Borek]

$$Ca(OH)_2$$
pKb1 = 2.43
pKb2 = 1.40
(http://ifs.massey.ac.nz/resources/chemistry/dissociation/inorgbases.htm )

$$H_2CO_3$$
pKa1 = 6.37
pKa2 = 10.25

$$CaCO_3$$
pKso = 8.3

So the concentration of saturated $$CaCO_3$$ solution is $$7.1\cdot10^{-5}$$

pH calculated using BATE is 9.73.

(see http://www.chembuddy.com/?left=pH-calculation&right=pH-salt-solution for general approach to pH calculation of salt solution).

In fact final pH will be different, as you should take into account increased solubility of $$CaCO_3$$ (due to $$Ca^{2+}$$ and $$CO_3^{2-}$$ hydrolysis - although the first can be neglected, as $$Ca^{2+}$$ is dominant at 99.9% of total calcium concentration).