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Q.
$AlCl_{3}$ forms dimer in vapour phase but $BCl_{3}$ does not because
NTA AbhyasNTA Abhyas 2020The p-Block Elements - Part2
Solution:
The formation of stronger backbond ( $3p \rightarrow 2p$ overlap in $BCl_{3}$ and weaker $3p \rightarrow 3p$ overlap in $AlCl_{3}$ ) reduces the electron deficiency of the central atom and thus dimerisation tendency is reduced. So $AlCl_{3}$ can form a dimer but $BF_{3}$ and $BCl_{3}$ cannot.