Converstion between 2cloro butane into 2methyl butanoic acid
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2-chlorobutane -----> Cl-Mg-butane using Mg metal in ether.
The magnesium metal inserts itself between the chlorine atom and carbon 2 atom of butane.
Now, carboxylation of a grignard gives you a carboxylic acid:
Cl-Mg-butane --------> 2-methylbutanoic acid using 1. CO2, ether and then 2. H3O+.
CO2 takes the place of the MgCl at the 2 position of butane, and once you add a proton source (H3O+) it becomes a carboxylic acid.
The carbon of the newly added COOH becomes part of the backbone of the molecule and using the proper nomenclature rules, now you have 2-methylbutanoic acid.
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