Your question is not clear but anyway, it's possible to convert palmitic acid to fatty acid methyl esters (FAMEs) with sodium methoxide as the catalyst, you can check in these articles:
In principle, a di- or- tricarboxylic acid is required to react with a diol or a triol in order to obtain a polyester. Palimitic acid, CH3(CH2)14—COOH, is a monocarboxylic acid which does not meet this requirement so the chemist has to approach the research project from another unusual way.
You need a triol (such as glycerol) or a polyol (such as polyvinyl alcohol –PVA-) but palimitic acid has to be activated by converting it into the acid chloride derivative. A carboxylic acid is converted into the reactive acid chloride derivative by refluxing it with thionyl chloride: RCOOH + SOCl2 → R-CO-Cl + SO2(g) + HCl(g)
The 2 gaseous side products will evolve from the top of the condenser leaving RCOCl in the reaction flask.
Afterwards, the fresh acid chloride of palmitic acid is reacted with the triol or with PVA. The first reaction will produce a triester of palmitic acid "which is one kind of oil or fat" & it may be denoted as polyester. The second will be polymer analogous conversion in which PVA is converted into a complex polyester but I do not expect total esterification.
This is a suggestion for a research that has not been done before & my advice is to get an approval about it from your supervisor or professor.
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