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We know that almost all salts with sodium as cation are water-soluble. But there are a few examples where the salt is water-insoluble; such as sodium bismuthate, sodium fluorosilicate, and much more.

I think that's because water can't separate the ions in these examples. But if true, are there other factors that cause this strange solubility in some sodium salts?

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Having fluorine as the element ionically bonded to sodium is one factor that inhibits solubility. Like all other pretransition metal ions (which are hard acids), bonding to fluorine bases is typically stronger than bonding to similarly charged bases containing other elements, making the lattice energy/solvation balance less favorable.

We can see this in the binary compounds, which means halides (other ionic binary compounds of sodium react with water). Usually we do not list sodium fluoride as an "insoluble" sodium compound. But the respective Wikipedia articles show that it has seven times less solubility in water than sodium chloride (molar basis), and sodium bromide is similar to the chloride rather than the fluoride.

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