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First, draw an AlCl3 molecule, in dot-structure. You will see that in the molecule, Aluminum has only 6 electrons, 3 of which are shared with the chlorine atoms. It needs 2 more electrons to become more stable (8 electrons in the outer shell is usually stable). Now look at the chlorine atom in the AlCl3 molecule.It has 8 electrons, and thus, it is somewhat "stable". If a Chlorine atom from ANOTHER AlCl3 molecule formed a dative bond with the Aluminum atom(a dative bond is a covalent bond where both shared electrons come from just one species. In this case, both electrons come from the chlorine atom), this Al atom would now have 8 electrons as well. That is why AlCl3 exists as a dimer- as Al2Cl6 . It's structure is shown in this picture.

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