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I recently did a reaction in the lab where 10-camphor sulfonic acid was used as the catalyst instead of something more conventional like hydrochloric acid or sulfuric acid. Dry acetontrile was used as a solvent. The scheme is shown below:

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I'm not too sure why it is used. My initial thoughts are it's due to the solubility of 10-CSA in water/organic solvents. Alongside this using a conventional acid such as hydrochloric acid, the water content of the acid may affect the equilibrium. Although 10-CSA still has water in it, it would not be comparable to hydrochloric or sulfuric acid. 10-CSA also is quite bulky, which could provide some selectivity on which positions are deprotonated, although I don't see this as being likely due to its conjugate base having such a high pKa. Aside from this what else could be plausible explanation for the usage of 10-CSA?

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For a given protecting group, there is no single best way of introducing it, just as there is no single best way of oxidising an alcohol – the conditions you use depends upon the substrate you have and the tolerance of it towards things such as acid, base, and heat.

In your question you ask specifically about conditions to introduce a benzylidine acetal, namely why aqueous acids aren't used – the tl;dr answer is that they are!

Below is an excerpt from the section in Greene's Protecting Groups in Organic Synthesis that deals with formation of such a group:

  1. PhCHO, ZnCl2, 28°C, 4 h.
  2. PhCHO, DMSO, concd. H2SO4, 25°C, 4 h.
  3. PhCHO, TsOH, reflux, H2O, 72% yield.
  4. Sulfuric acid on silica gel, PhCH(OMe)2, 75–93% yield.
  5. PhCH(OCH3)2, I2, CH3CN, 60–89% yield.

Taken from: Greene's Protecting Groups in Organic Synthesis

What all of these conditions have in common is that some kind of acid catalyst is required. Mineral acids (sulfuric), Lewis acids (zinc chloride or iodine) and organic acids (tosic acid) have all been shown to work in the literature, and indeed most people involved in complex molecule synthesis will have tried most of them.

Which condition is most appropriate is a matter of context (and often a lot of screening). Solid organic acids (tosic acid, camphor sulfonic acid, pyridine para-toluene sufonate) are often used in late-stage synthesis as they're able to be dried, this allows the reactions to be conducted under (almost) anhydrous conditions. Use of sulfuric acid dictates that water (quite a lot of it) is present, which can knock off other delicate protecting groups/functionality in a molecule.

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