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Aluminum chloride (AlCl3) is soluble in benzene (to a slight extent) and in water because the aluminum-chlorine bond is covalent, but strongly polarized, due to the relatively high electronegativity of the aluminum atom (1.5 to 1.61 on Pauling scale). This causes aluminum valence electrons be shared between aluminum and chlorine atoms. Solid aluminum chloride is not bound together as tightly as is an ionic solid; therefore aluminum chloride molecules can leave the solid at a relatively low cost in energy.

The electron density at the aluminum atom is low, so the atom is attracted to any area of high electron density in a non-aqueous solvent. Thus there is a weak attraction of the aluminum atoms to the pi electron cloud in the benzene molecule, allowing a small amount of solubility. It is highly soluble in solvents with Lewis base character, such as nitrobenzene or ether. It is poorly soluble in methylene chloride or chloroform.

When anhydrous aluminum chloride is added to water, the aluminum chloride hydrolyzes, with the evolution of a large amount of heat and the formation of hydrochloric acid and aluminum hydroxide. Continued addition of aluminum chloride to this acidic mixture results in a clear solution of aluminum cations and chloride anions. The aluminum cation, having a large charge and a small radius, has a substantial heat of hydration.

The following is from an earlier version of this answer. I am not familiar with this area:

The molecule has a small radius, which allows it to fit between polar solvent molecules whose charges direct and "park" an AlCl3 molecule in place adjacent to a polar solvent molecule. Moreover, the solubility of the AlCl3 in polar solvents is enhanced by the aluminum ion's non valence electron pairs in the 2p6 orbitals being unshielded by the shift of the valence shell electrons toward the chlorine atoms.

However, my answer is rather superficial, and more thorough study on the subject is most recommended. internet inquiry keywords could be [shielding aluminum covalent ionic polar aprotic soluble].

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