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In many japanese chemistry books for highschool students, it is written that AgF is soluble in water because compared to other silver halides ionic nature of Ag-F bond is greater. I don't think this is valid explanation, because what determines solubility must be free energy of the process not the nature of the bond. Am I thinking the right way?

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You are certainly correct. Whether something has more ionic or more covalent bonding does not in general correlate directly with solubility in water. Among alkaline earth fluorides (which all have network bonding and not discrete molecules) beryllium fluoride has the most solubility in water — and the most covalent character.

When push comes to shove, we really have no reliable way to predict the solubility of salts in water a priori.

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