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My teacher told me that the following is the mechanism for oxidation of primary alcohols to carboxylic acids:

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I've searched in books and online and didn't find a similar mechanism. For example, in Wikipedia:

Mechanism of oxidation of primary alcohols to carboxylic acids via aldehydes and aldehyde hydrates

Which is correct?

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Clayden et al., Organic Chemistry (2ed), p. 545 gives the reaction pathway as:

Oxidation of alcohols

Here's some evidence that supports this pathway. One of the most well-known methods to selectively oxidise primary alcohols to aldehydes, without further oxidation to the carboxylic acid, is by using pyridinium chlorochromate in dichloromethane as solvent. This presumably works because water is excluded, which prevents the hydrate from being formed. Clayden writes:

Aqueous methods like the Jones oxidation [n.b.: the Jones oxidation is $\ce{CrO3}/\text{aq. }\ce{H2SO4}$] are no good for this, since the aldehyde that forms is further oxidized to acid via its hydrate. The oxidizing agent treats the hydrate as an alcohol, and oxidizes it to the acid. The key thing is to avoid water, so PCC in dichloromethane works quite well. The related reagent PDC (pyridinium dichromate) is particularly suitable for oxidation to aldehydes.

If the reaction pathway was as your teacher taught you, then there would be no point in excluding water, since in that pathway water is not needed for the over-oxidation to the carboxylic acid.

The actual mechanism for the oxidation step is as follows (Clayden, p. 195):

Mechanism

If water is present, then the aldehyde product simply forms the hydrate and the mechanism for oxidation to the carboxylic acid is exactly the same, except that one of the hydrogens is replaced with an $\ce{-OH}$. Note that you need an $\ce{-OH}$ group on the starting material to form a chromate ester - that means that aldehydes will not undergo oxidation, but their hydrates (which are geminal diols) will.

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