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In the laboratory we are given numerous salts for analysis for cation and anion.

How can one decide which combination of cation and anion cannot form soluble salts in water so that after detecting an anion or cation we can automatically eliminate certain anions or cations which if forms salt with the respective cations and anions will not be soluble in water.

The anions are:

Sulphide, Carbonate, Chloride, Bromide, Iodide, Nitrate, Oxalate, Acetate, Sulphate, Phosphate

The cations are:

$\ce{Pb^{2+} , Cu^{2+} , Al^{3+} , Co^{2+} , Ni^{2+} , Mn^{2+} , Zn^{2+} , Ba^{2+} , Sr^{2+} , Ca^{2+} , Mg^{2+}}$.

The salts consist of only one cation and one anion each.

The explanation will surely come from chemical bonding with holding the parameters of lattice energy,solvation energy,size of cation and anion.

The analysis of this problem will I think help me to do the lab while understanding what exactly happens in mere trivial matter like solubilty and also will save time!

PS:

There are certain things I know like all inorganic nitrate salts are soluble in water, but why?

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    $\begingroup$ Are you asking how you can do a complex quantum chemical simulation using only pen and paper? I think you and I have very different definition of the phrase "mere trivial matter". This is something you struggle with even if you have a supercomputer at your disposal. Sometimes in Chemistry, you just have to know certain things, for example which salts happen to be not soluble in water. If everything would be easily solvable using pen&paper, there would be no need for anybody to study the field $\endgroup$ – Raditz_35 Aug 24 '18 at 14:24