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When you have two primary or two secondary alcohols on the same molecule, will both undergo oxidation or just one?

For example: 1,2-ethanediol with PCC (pyridinium chlorochromate). PCC will only form aldehydes with primary alcohols, but will BOTH alcohols in 1,2-ethanediol become oxidized or just one?

Another example is when 1,2-ethanediol is reacted with chromic acid H2CrO4. Primary alcohols with chromic acid will form carboxylic acids, but will BOTH oxidize or will only one?

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