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One can use PCC (pyridinium chlorochromate) to oxidise an alcohol selectively up one level - to an aldehyde/ketone, without further oxidation to a carboxylic acid. Why is pyridinium important to this selectivity?

I understand that usually PCC is dissolved in dichloromethane and not in anything like THF, and this prevents the formation of a hydrate, which can then act "like" an alcohol in it's oxidation to a carboxylic acid, but I can't figure out why it's important that pyridinium is used.

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Though pyridinium chlrochromate (PCC) is a salt, the pyridnium cation is easily dissolved by a wide variety of organic solvents. As such, the chlorochromate anion then becomes dissolved in the organic solvent, and can oxidize $1º$ and $2º$ alcohols present in solution to carbonyls. Oxidation of carbonyls to carboxylic does not occur when using PCC for the very reason you said yourself—no water is present to hydrate the carbonyl species to its geminal diol to allow for further reaction.

Other benefits of PCC include that it is not particularly hygroscopic, is commercially available, and can be stored for some time, though other methods (Swern oxidaiton, Moffatt oxidation, Dess-Martin Periodinane) are generally preferred as the reaction workup for PCC can be tedious and the chromium(IV) species produced is toxic.

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