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Benzilic acid rearrangement

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nertz worm:
I have a question about benzilic acid rearrangement. I know how benzil can react with potassium hydroxide to produce benzilic acid, but I don't know the mechanism that is used in the production of its side product, diphenylmethanol. I thought about using Hofmann rearrangment to get rid of the C=O in the benzilic acid, but Hofmann can only be used for amides, right?

AWK:
This is decarboxilation of subsituted (electron withdrawing substituents) acetic acid. (like to nitroacetic or malonic acid).

movies:
The diphenylmethanol unit is still attached, right?  Check out this site:

http://www.organic-chemistry.org/frames.htm?http://www.organic-chemistry.org/namedreactions/benzilic-acid-rearrengement.shtm

The phenyl group shifts over into the adjacent carbonyl.

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