##”BCl”_3## is the stronger Lewis acid.
We would expect ##”BF”_3## to be stronger, because ##”F”## is more electronegative than ##”Cl”##.
Chemists explain this unexpected result by an electronic argument and a steric argument.
The electronic argument — backbonding
The boron atom in ##”BF”_3## is ##sp^2## hybridized, with a vacant ##2p## orbital.
The ##”F”## atoms can also be ##sp^2## hybridised, with lone pairs in their ##2p## orbitals.
These ##”F”## orbitals can overlap with the orbital on ##”B”##, thereby increasing the electron density on the boron atom and making it less acidic.
This effect is called backbonding, because electron density is leaving the more electronegative atom.
In ##”BCl”_3##, the ##3p## orbitals on ##”Cl”## are bigger than the ##2p## orbital on ##”B”##, so orbital overlap is less efficient, and backbonding is less important.
Hence, the greater backbonding in ##”BF”_3## makes it a weaker Lewis acid.
The steric argument — ligand close-packing (LCP)
The LCP model is based on the observation that the ##”X”## atoms (ligands) in ##”AX”_n## systems are always the same distance from each other.
For example, the distance between the ##”F”## atoms in ##”BF”_3## and ##”BF”_4^-## is 226 pm, despite the longer ##”B-F”## distance in the tetrahedral structure.
(from alpha.chem.umb.edu)
It is as if the ##”F”## atoms are closest-packed (like in a crystal), with the ##”F”## atoms having a ligand radius of 113 pm.
When the ##”BF”_3## forms a Lewis complex, the ##”F”## atoms remain close-packed, but the ##”B-F”## bonds must become longer in the new tetrahedral geometry.
(from http://pubs.acs.org/doi/abs/10.1021/ic990713m)
It takes more energy to lengthen the short, strong ##”B-F”## bonds than the longer, weaker ##”B-Cl”## bonds.
Hence ##”BF”_3## is a weaker Lewis acid than ##”BCl”_3##.
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