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The given reagent is used in which reaction: $ R-Mg-X $ to give product $ R-COOH $ .

Answer
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Hint :We know that it is a nucleophilic reagent that acts like a very strong base in chemical reactions. Its unique properties are due to the carbon-metal bond present in it and because carbon is bonded to metal, it can form carbanion in chemical reactions but it is important to keep it away from the moisture.

Complete Step By Step Answer:
A Grignard reagent is a chemical compound having the generic formula of $ R-Mg-X $ , while, X refers to a halogen and R refers to an organic group, primarily an alkyl or aryl group. These reagents behave as strong bases and thus react with the protic compounds. Grignard reagents are generally used synthetically to produce new carbon–carbon bonds. Grignard reagent reacts with crushed dry ice (i.e. solid carbon dioxide) in order to form salts of carboxylic acids. Now, these salts of carboxylic acids will undergo acidification with mineral acids to finally yield corresponding carboxylic acids.
The important observation is the nucleophilic addition of Grignard reagent over the substrate as alkyl carbanion is a very strong base and powerful nucleophile, that’s with compounds containing carbonyl carbons it readily forms nucleophilic addition product and common thing over here is the acidic work up to form the final product, because the addition compound formed after the nucleophilic addition of Grignard reagent over substrate will easily get hydrolyzed in acidic medium. The Grignard reaction refers to the addition of the Grignard reagents to an aldehyde or ketone that would then yield secondary or tertiary alcohol. However, the addition of Grignard reagent to formaldehyde leads to the formation of primary alcohol.
 $ R-Mg-X\xrightarrow{\text{ }C{{O}_{2}}\text{ }}RC{{O}_{2}}MgX\xrightarrow{\text{ }{{H}^{+}}\text{ }}RCOOH $ .

Note :
Remember that while preparing Grignard reagent it is important to have anhydrous condition because Grignard reagents react with water and form alkane. In fact with compounds containing active hydrogen like carboxylic acid, alcohol etc.