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My textbook doesn't say anything about this but does say that on addition of organolithium compounds to carbon dioxide, they give ketones and not carboxylic acids like grignard reagents. This has been attributed to the greater nucleophilic character of Organolithium compounds compared to grignard reagents. I see that greater polarity of the C-Metal bond must relate to this according to many websites but I cannot understand why! Also, during formation of the RLi compounds using alkyl halides, what does the alkyl halide dissociate into? Please help!

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Essentially, you are forming a carboxylate when you add the organolithium or Grignard compound to carbon dioxide, but the carboxylate may have covalent character in the metal-oxygen bond. Then this answer offers two hypotheses:

(1) Despite the difference in electronegativity, the lithium compound may be more covalent than the magnesium-halogen compound because the latter forms a three-center bond. This would tend to maintain more electrophilic character at the carboxylate carbon with lithium.

(2) The Grignard reagent imparts bulkier groups on the oxygen atoms, making the double addition required to form a ketone less favorable.

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When Li reacts with an alkyl halide, a salt (lithium halide) is formed, whose stability is the primary thermodynamic driving force of the reaction: $\mathrm{2Li}+\mathrm{RCl} \rightarrow \mathrm{RLi}+\mathrm{LiCl}$.

Due to the larger difference between the electonegativities of C and Li, the C-Li bond in organolithium compounds has more ionic character and C is more negatively polarized. The higher polarization makes R in RLi a harder nucleophile compared to RMgX, which explains why lithium organyls and Grignard reagents react differently when adding to certain carbonyl compounds.

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