What is the difference between carbon dioxide, and silicon dioxide? How do we formulate the solubility product for the salt #A_2B_3#

As you know, carbon dioxide and silicon dioxide are isoelectronic. They are not isostructural. The shortness of the (first-row) #C-O# bonds allows effective overlap between the p -orbitals of #C# and #O#, in addition to the strong #sigma# bond formed. The result is a #C=O# double bond. On the other hand, the corresponding p -orbitals on second row #Si# are too diffuse to allow effective #pi# bonding between #Si# and #O#, with the result that #O# bridges to another silicon to form an infinite array of #Si-O-Si-O# bridges that have no molecular boundary.

As to your #A_2B_3# salt, do you mean a salt of the form such as calcium phosphate, i.e. #Ca_3(PO_4)_2#? Such a salt would be particularly insoluble (as are most phosphates).

We would write the equation for its dissolution in water for as:

#Ca_3(PO_4)_2(s) rarr 3Ca^(2+)(aq) + 2PO_4^(3-)(aq)#

The solubility constant is as standard, the concentrations of the ions raised to the power of their stoichiometric coefficients:

#K_(sp) = [PO_4^(3-)]^2[Ca^(2+)]^3#

Alternatively, consider the solubility of ferric sulfate:

#Fe_2(SO_4)_3(s) rarr 2Fe^(3+) + 3SO_4^(2-)#

#K_(sp) = [Fe^(3+)]^2[SO_4^(2-)]^3#

This should not be too water soluble, but check this.

If this is not want you wanted I apologize.