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I would expect a lower yield for Br2 because you are not just bubbling Cl2 in aqueous MgBr2! Once you start, there is also some now free Br2 available to react with the chlorine! The neglected competing reaction is: $\ce{Br2 + Cl2 ⇌ 2 BrCl}$ See this paper to get an idea of the affinity for the formation of the interhalogen compound. But that is still ...
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{...