Fatty acids from natural sources are long-chain unbranched carboxylic acids that contain an even number of carbon atoms. Outline steps to convert the readily available dodecanoic acid (lauric acid) into the rare tridecanoic acid.
First, reduce the carboxylic acid to dodecanol. Second, use PBr₃ to give 1-bromododecane. Third, prepare the Grignard reagent using magnesium and ether. Fourth, add the Grignard reagent to carbon dioxide, followed by acidification in workup.