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The tendency of $BF_3$, $BCl_3$ and $BBr_3$ to behave as Lewis acid decreases in the sequence
A
$BF_3 > BCl_3 > BBr_3$
B
$BCl_3 > BF_3 > BBr_3$
C
$BBr_3 > BCl_3 > BF_3$
D
$BBr_3 > BF_3 > BCl_3$
Detailed Solution
Boron trihalides are Lewis acids because boron has an empty 2p orbital and only six valence electrons.
The halogen can donate a lone pair from its filled p orbital into this empty 2p orbital of boron ($p\pi$–$p\pi$ back bonding), which reduces the electron deficiency of boron.
Back bonding is most effective in $BF_3$, because the 2p orbital of F matches the 2p orbital of B in size and energy; overlap is poorer with the 3p of Cl and poorest with the 4p of Br.
Extent of back bonding: $BF_3 > BCl_3 > BBr_3$, so the electron deficiency and Lewis acidity follow the reverse order.
Lewis acid strength: $BBr_3 > BCl_3 > BF_3$
The halogen can donate a lone pair from its filled p orbital into this empty 2p orbital of boron ($p\pi$–$p\pi$ back bonding), which reduces the electron deficiency of boron.
Back bonding is most effective in $BF_3$, because the 2p orbital of F matches the 2p orbital of B in size and energy; overlap is poorer with the 3p of Cl and poorest with the 4p of Br.
Extent of back bonding: $BF_3 > BCl_3 > BBr_3$, so the electron deficiency and Lewis acidity follow the reverse order.
Lewis acid strength: $BBr_3 > BCl_3 > BF_3$