$BCl_3$ exists as a monomer,whereas $AlCl_3$ is dimerized through halogen bridging. Give reason. Explain the structure of the dimer of $AlCl_3$ also.

$BCl_3$ does not dimerize because of the small size of the boron atom. Boron cannot accommodate four large-sized chloride ions around it due to steric hindrance.
$AlCl_3$ exists as a dimer in which $Al$ uses its vacant $3p$-orbital to coordinate with a $Cl$ atom from another $AlCl_3$ unit to complete its octet.
$AlCl_3$ achieves stability by forming a dimer,$Al_2Cl_6$,where two $Al$ atoms are bridged by two $Cl$ atoms. The structure consists of two $AlCl_4$ tetrahedra sharing a common edge.