(a) Organolithium reagents such as methyllithium (CH₃Li) react with carboxylic acids to give ketones. Two equivalents of the lithium reagent are required, and the ketone does not react further. Suggest a mechanism for this reaction that accounts for these facts.

(b) Give the product of the reaction given in part (b) of Fig. P20.51.

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(a) (b) R-C-OH + 2H3C-Li OH CH3 Figure P20.51 CH, given off ether + 2CH3CH₂ Li ether H3O+ H3O+ R-C-CH3 + 2Li+