Using diazomethane `(CH_(2)N_(2))` and any other appropriate reagents how can R-COOH be converted into:
(i) `R-CH_(2)COOH` (b) `R-COCH_(2)Cl` (c ) `R-COCH_(2)NH_(2)` (d) `R-CH_(2)COOC_(2)H_(5)` (e ) `R-COCH_(2)OH`?

Explanation

Diazomethane is used in the Arndt-Eistert Synthesis. This is a method of converting an acid ( aliphatic ,aromatic, alicyclic or heterocyclic) into the next higher homologue.
`R-overset(O)overset(||)C-Ohoverset(SOCl_(2))toR-overset(O)overset(||)C-Clunderset((-HCl))overset(CH_(2)N_(2))tounderset("Diazoketone")(R-overset(O)overset(||)C-CHN_(2))underset(Delta)overset(Ag_(2)O)tounderset("Ketene")(R-CH=C=O+N_(2))`
This rearrangement of diazoketone is called Wolff rearrangement.