Grignard reagents ($RMgX$) react with solid carbon dioxide (dry ice) in the presence of dry ether to undergo nucleophilic addition. The nucleophilic alkyl or aryl group ($R^-$) from the Grignard reagent attacks the electrophilic carbon atom of $CO_2$. This results in the formation of an intermediate adduct, which is a magnesium salt of a carboxylic acid represented as $RCOO^-Mg^+X$. Subsequent hydrolysis of this intermediate salt with a dilute acid ($H_3O^+$) yields the corresponding carboxylic acid ($RCOOH$).