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so i'm pretty sure the silver halides are a type of salt, because they are ionic compounds. Also, I think the polarizability is how readily an anion will have a distorted electron shell (a higher polarizability means a greater covalent character). So AlF is the most soluble in water because F has the least polarizability compared to Cl, Br, and I. AlI is the least soluble in water because I is the most polarizable. It is really large and has lots of electrons, so the electron cloud will be more pulled towards the Ag cation, giving it a more covalent character.
Moreover, this is just another example of covalent character within ionic bonds. Ions which cause large distortion, such as AlI, are described as being highly polarizable. This causes the ionic bond to have more covalent bond character.
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