Boron halides are acidic in nature due to the presence of only six electrons in the valence shell of boron. However, BBr3 is more acidic than BF3 because the extent of backbonding is the most in BF3, as a result of which electron deficiency on boron is the least in BF3.
Basically the size of the vacant 2p orbital of boron and the 2p-orbital of fluorine containing the lone pair of electrons are almost identical, therefore the lone pair of electrons on fluorine is donated towards the B atom. As a result of this pπ-pπ back donation (from three fluorine atoms) and resonance, the electron deficiency of boron decreases and thus BF3 is a weak lewis acid. On the other hand, bromine is bigger in size than fluorine. Hence the extent of overlap between 2p orbital of boron and 4p orbital of bromine decreases and consequently the electron deficiency of boron increases. Because of this, BBr3 is a strong lewis acid.
For detailed information,
Actually the trend of lewis acid character are as…
BI3>BBr3>BCl3>BF3
Reason: This order of acidic strength can be easily explained on the basis of the tendency of the halogen atom to back -donate it’s lone -pairs of electrons to the boron -atom through P(pi)-P(pi) bonding.
As a result of P(pi)-P(pi) back donation &resonance , the electron-deficiency of B decrease & thus BF3 is the weakest lewis acid (among Borontrihalides).
As the size of halogens increases frm F to I , the extent of overlap b/w 2p- orbital of B & a bigger p-orbital of halogen decreases[3p-in Cl, 4p-in Br & 5p-in I] & consequently the electron - deficiency of B increases & thus lewis acid character increases Accordingly frm BF3 to BI3.