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Lewis acidity is a function of electron deficiency on the acceptor atom, which in this case is $\ce{B}$ and $\ce{Al}$ respectively.

Back donation is better as is the case of $\ce{B}$, due to better 2p overlap compared to 3p overlap, then the electron deficiency on the $\ce{B}$ atom should be lesser, as it's deficiency is getting filled better; but then how is $\ce{BCl3}$₃ stronger acid than $\ce{AlCl3}$, or am I mistaken?

Three things to note

  1. This question came in the IIT- joint entrance examination in 2017, this examination rarely has factual inconsistencies. And if they do, then they get the answer key changed. For this question, it was clearly given as The lewis acidity is indeed more for $\ce{BCl3}$. So any answers which conclude it has grey zone won't be accepted unless a source is cited which states so while giving an example of the solvent dependency.

  2. I want a clear clarification of why my reasoning is giving the incorrect answer

  3. Please ensure the answer has citations
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    $\begingroup$ Related:chemistry.stackexchange.com/questions/80263/… $\endgroup$ – Nilay Ghosh Jan 3 at 13:13
  • $\begingroup$ @NilayGhosh they are two totally different questions. The one you referred to is comparing halides of boron and Al, I want to compare one specific halide between Al and B $\endgroup$ – Haha Hahaha Jan 3 at 15:58
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As you are probably aware, generalizations like "$\ce{BCl3}$ is a stronger Lewis acid than $\ce{AlCl3}$" can be problematic, as the results can be dependent on the base used and the conditions (eg solvent choice).

That said, a common context for this ranking is with respect to carbonyl bases, such as in a Friedel-Crafts acylation. For these bases, $\ce{BCl3}$ is generally observed to be a stronger Lewis acid than $\ce{AlCl3}$.

To understand this observation, we need to consider what happens during the acid-base reaction. For $\ce{BCl3}$, it is likely that the dissolved molecule is a monomer and retains the trigonal planar geometry with some $\pi$ bonding occuring. In the reaction with base, the $\pi$ bonding must be broken and the geometry changed to tetrahedral. The driving force is the formation of the new $\ce{Cl3B-O=R}$ bond.

In contrast, $\ce{AlCl3}$ is most likely present in solution as the $\ce{Al2Cl6}$ dimer, with no $\pi$ bonding. Here, the oxygen of the base displaces the chloride in order to form the Al-O bond of $\ce{Cl3Al-O=R}$.

Although the B-O bond is stronger than the Al-O bond, it is difficult to predict the relative contributions of the changes in $\ce{BCl3}$ vs those in $\ce{Al2Cl6}$ because the reactions are so different, and we rely primarily on empirical results for ranking. However, some groups have attempted computational approaches. Some examples are:

Laszlo, P. and Preston, M. Determination of the Acidity of Lewis Acids. J Am Chem Soc (1990) 112:8750-8754.

Jonas, V., Frenking, G., and Reetz, M.T. Comparative Theoretical Study of Lewis Acid-Base Complexes of $\ce{BH3}$, $\ce{BF3}$, $\ce{BCl3}$, $\ce{AlCl3}$, and $\ce{SO2}$. J Am Chem Soc (1994) 116:8741-8753. DOI:10.1021/ja00098a037

UPDATE based on updated question: For a specific counter example, there is a report that in a competition experiment in which excess chloride ion was added to a solution containing $\ce{BCl3}$ and $\ce{AlCl3}$, $\ce{AlCl4-}$ was observed to form, but no $\ce{BCl4-}$ was detected, indicating a stronger Lewis acidity of $\ce{AlCl3}$ towards the soft Lewis base chloride ion. I have seen mentions of similar trends with other soft Lewis bases, but haven't chased down the references.

Glavincevski, B. and Brownstein, S.K. Complexing and exchange of boron, aluminum, and gallium chlorides with some Lewis bases (1981) Can J Chem 59:3012-3015. DOI: 10.1139/v81-436

That paper also discusses some solvent effects, particularly acetonitrile, which as a Lewis base can form complexes with the acids.

The clear explanation of why your reasoning is incorrect is that you are not accounting for the stronger bond with B. As discussed in the references I gave, Al-O bonds are calculated to be nearly completely ionic, whereas those with B are partially covalent, so for the heterolytic cleavage reaction separating the acid from the base, the enthalpy change is greater for the boron complexes.

That explanation is also consistent with the trend reversal for soft Lewis bases, which will not form a strong covalent bond with boron.

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  • $\begingroup$ Hey @andrew thats a good start, but could you edit your answer sccording to the guidelines you have added. Although your answer is pretty good $\endgroup$ – Haha Hahaha Jan 10 at 14:30
  • $\begingroup$ Well, but why shall I consider the $\ce{Al-O}$ or $\ce{B-O}$ bond strength, I want to compare lewis strength, isn't it purely a function of electron deficiency? So assuming by the medium is not basic and the $\ce{M=O}$ bond is not formed, why is $\ce{BCl3}$ still stronger? $\endgroup$ – Haha Hahaha Jan 11 at 5:43
  • $\begingroup$ "Electron deficiency" is a vague qualitative concept. You need to consider both the initial state (which is what electron deficiency refers to) and the product state. In the reaction with an oxygen base, B is calculated to have a more covalent bond, so its "deficiency" is better satisfied than Al's, which is calculated to have a mostly ionic bond. With other bases, this may not be true. That's why rankings of Lewis acidity can only be done with respect to a specific base or class of bases (and a specified solvent or lack thereof). $\endgroup$ – Andrew Jan 11 at 12:52
  • $\begingroup$ I recommend reviewing the various approaches to quantifying Lewis acidity and basicity - eg Pearson HSAB, Drago EC, etc. They are only accurate if they include parameters from both the base and the acid, and they generally refer only to gas phase or completely unreactive solvents. $\endgroup$ – Andrew Jan 11 at 12:54
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    $\begingroup$ No, you seem to be missing the main point, which is that the order of acidity is dependent on the choice of base. Solvent also matters, but most rankings are assumed to refer to gas phase/unreactive solvent unless otherwise stated. Look at the papers I cited - $\ce{BCl3}$ is stronger with carbonyl bases, but $\ce{AlCl3}$ is stronger with $\ce{Cl-}$ as base. $\endgroup$ – Andrew Jan 11 at 15:33

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