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Can't we perform Fischer esterification using methanol to make a methyl ester from a carboxylic acid?

If so, why might we use diazomethane? Would the release of nitrogen gas confer an entropic advantage to the reaction? As I understand, the Fischer esterification process is an equilibrium process and at equilibrium there is often significant amounts of both product and reactant. So we might have to add excess alcohol to drive the reaction to the right.

I ask because my book just presents the use of diazomethane as a way of making methyl esters without any discussion of why might someone do this rather than just use a few gallons of methanol.

On the other hand I know from working in a research lab that methanol is poisonous and protocol calls for its use in a fume hood ... could that be another reason? On the other hand diazomethane is also toxic (and explosive to boot) ... so I would definitely be inclined to use that in a fume hood (perhaps more so than when using methanol).

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Both methods are used in practice (and a a lot more exist). Diazomethane is a last resort method when everything else fails. For example you might have a molecule that is acid sensitive or heat sensitive and then $\ce {MeOH/H^+}$ is out of the question. Although diazomethane is an excellent reagent to do the job, as it works selectively with almost every substrate, to give good yields under mild conditions, generally no extensive work-up or purification are required, it has some major disadvantages: It is not commercially available, it has to be prepared fresh before the reaction using a (somewhat) specialised equipment and a toxic starting material (Diazald). It is explosive and very toxic and obviously can not be stored. An alternative to using diazomethane is TMS diazomethane that is stable enough to be stored as a solution and it is commercially available however it is not innocent at all as this article shows.

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