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The order of decreasing Lewis acid character as per online sources is as follows:

BCl3 > AlCl3 > GaCl3 > InCl3

Reason cited is: As we move down the group, the size of atom increases, and as a result, the tendency to attract electrons decreases. This leads to a decrease in Lewis acid nature down the group.

However, it is also known that BF3 is the weakest Lewis acid among the boron trihalides on account of back bonding effect (BI3 > BBr3 > BCl3 > BF3) as the energy gap between boron and fluorine (2p-2p) is less resulting in a stronger bond and the energy gap between boron and iodine (2p-5p) is the most, resulting in the weakest bond.

Why can't we apply the above explanation to BCl3, AlCl3, GaCl3, InCl3 as well, saying that Al and Cl should have the least energy gap (n=3 for both) and thus have the strongest bond and weakest Lewis acid character.

Please feel free to point out any fundamental mistakes in my assumptions and reasoning as I am still figuring things out and may have a limited/incorrect understanding of back bonding.

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