How to decide an ionic compound is soluble or insoluble?
Intro
Firstly, it’s a very complicated question. Many factors influence the solubility of compounds.
The basic guideline is:
If the intermolecular interaction between the compound and the solvent is greater than the intramolecular forces (ionic bonds, covalent bonds, etc.) then it is soluble.
If, on the contrary, intramolecular forces are stronger, it is not soluble or sparely soluble.
The solubility of ionic compounds
The basic guideline is:
Ionic compounds are soluble. The more ionic, the more soluble, since the interaction between ions and solvent (usually water) is strong enough to break up the lattice.
On the contrary, the less ionic, the lattice is harder to break since the solute-solvent interaction is not strong enough.
IG and other lower level chemistry defines ionic compounds in a very simple way:
It is a compound with metal and non-metal elements.
But even if it is metal plus non-metal, the compound can still be NOT 100% ionic.
Let’s examine 3 compounds:
1. Why is NaCl soluble in water? (solubility: 20 oC, 36.0 g/100 g water)
Recall the guideline: the interaction between the water molecules and Na+ and Cl- is bigger than the ionic bonding.
2. Why is CaI2 (solubility: 20 oC, 67.6 g/100 g water) less soluble than CaCl2 (solubility: 20 oC, 74.5 g/100 g water)?
They both have the same cation: Ca2+
The anion is different:
I- has a larger size of electron cloud than Cl-.
Thus I- is easier to be polarised - i.e. the electron cloud is more distorted.

When the electron cloud is more distorted, the negative charge and the positive charge are both lowered on the ions (since some of the electrons are moving towards the center and the positive and the negative charges can be regarded as partly canceled out).
When the charge on them is lowered, the ion-water interaction will be weaker. Thus it is harder to break the lattice.
What is more, when some electrons moves to the central part, these electrons are “shared” like covalent bond. Thus we say CaI2 has a higher decree of covalency.
A giant covalent compound is not soluble in water.
Electronegativity and ionic/covalent compound
Electronegativity means the ability to attract the electron pairs.

Metals in general are not attracting but losing electrons, thus they have very low electronegativity. The more non-metallic, the more electronegative, for example, F is the most electronegative.
Normally, if the difference in electronegativity is larger than 1.7, then it is more ionic than covalent; equals 1.7, 50% covalent 50% ionic; smaller than 1.7, more covalent than ionic.
Thus, you can also use this as a guideline to judge whether a binary compound (like NaCl) is ionic or not.
But this method is not applicable for compounds such as Na2CO3 or CaCO3.
Why is Na2CO3 soluble while CaCO3 not?
Na+ has a smaller size and a lower charge than Ca2+.
But the size difference is not that big: Na+ 9.5 nm, Ca2+ 9.9 nm
But the charge of Ca2+ is doubled.
Thus Ca2+ has a greater polarising power to cause a larger distortion of CO32-.
So that CaCO3 is less soluble than Na2CO3.