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The P-Block Elements

Question
CBSEENCH11007260

Suggest a reason why the B - F bond lengths in BF3 (130 pm) and BF subscript 4 superscript minus (143 pm) differ?
Or
Why B - F bond length in BF3 is smaller than the expected value?

Solution

In BF3, boron is sp2 hybridised and therefore BF3 is a planar molecule. It has a vacant 2p-orbital. F-atom has three lone pairs of electrons. In BF3 molecule, one 2p-orbital of fluorine atom overlaps sidewise with empty 2p-orbtial of boron to form pπ space minus space pπ back bonding (back donation) in which the lone pair is transferred from F to B as shown.

As a result of this back bonding (or black donation), the B-F bond acquires some double bond character. 
On the other hand in open square brackets BF subscript 4 close square brackets to the power of minus ion,  boron is sp3 hybridised and therefore open square brackets BF subscript 4 close square brackets to the power of minus is a tetrahedral molecule. B in open square brackets BF subscript 4 close square brackets to the power of minus ion does not have vacant p-orbital available to accept the electrons donated by the F atom. Hence open square brackets BF subscript 4 close square brackets to the power of minus ion, B -F is a purely single bond. Since double bonds are shorter than single bonds, therefore B-F bond length in BF3 is shorter (130 pm) than B-F bond length (143 pm) in  [BF4].