what is the purpose of exhaustive methylation (hoffman elimination)?

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orangeblossom

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I know MeI works to exhaustively methylate the N, so that it is NR4+. and I know NH2 is a bad leaving group.

is the purpose of methylation to produce a better leaving group (NR4+)?
And if so, why is NR4+ a good leaving group?

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Yes, the purpose is to make a good LG. When N(CH3)3 leaves, notice that it goes from being positively charged to neutral. This is precisely what makes it a good LG,
 
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