The reaction of a Grignard reagent ($R-Mg-X$) with carbon dioxide ($CO_2$) is a standard method for the preparation of carboxylic acids.

1. Nucleophilic Attack: The alkyl group ($R^-$) of the Grignard reagent acts as a nucleophile and attacks the electrophilic carbon of $CO_2$ ($O=C=O$).
2. Intermediate: This forms an addition product, a salt of the carboxylic acid ($R-COO^-Mg^+X$).
3. Hydrolysis: Upon acidification (hydrolysis with $H_3O^+$), the salt is converted into the corresponding carboxylic acid ($RCOOH$).

$R-Mg-X + O=C=O \rightarrow R-C(OMgX)=O \xrightarrow{H_3O^+} R-COOH$