The reacting Homo is the tertiary-amine nitrogen lone pair. The relevant LUMO is the C-I antibonding orbital, , of MeI. Backside lone-pair donation into that orbital forms N-C while weakening C-I. The neutral OH group is not first converted to an alkoxide in the stated reaction.
Draw a curly arrow from the nitrogen lone pair to methyl carbon, and a second from the C-I bond to I:This is concerted SN2 quaternization. The product is choline iodide; nitrogen has four carbon substituents and positive charge, while the alcohol remains OH.
Acetonitrile is suitable: it dissolves the organic reagents, is polar enough to stabilize the developing ionic products and is an aprotic, relatively unreactive medium. It does not strongly hydrogen-bond-solvate the amine lone pair or compete efficiently as the methylating nucleophile. Sufficient solubility and chemical compatibility matter as well as polarity.
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