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Correct IUPAC name of [Co(NH3)3(NO2)3] is:
(A) Triammine Trinitro-N-cobalt (III)
(B) Triammine Trinitro-N-cobalt (II)
(C) Triammine cobalt (III) nitrile
(D) Triamminetrinitro-N-cobaltate (III)

Answer
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Hint: The given compound is the non-ionizable cation of the coordinate complex. According to the IUPAC system, given ligands that donate an electron to central metal through a coordinate bond are named first. If more than one ligands are present then the naming of ligands takes place according to alphabetical order. After this, the name of the central metal ion is written with its oxidation state in brackets.

Complete Step by Step Solution:
Non-ionizable (cation) part of the coordinate complex is given as [Co(NH3)3(NO2)3]. For naming it as per the IUPAC system, we need to first write the names of ligands, NH3 and NO2 that are ammine (ammonia change to ammine) and nitro (nitrogen dioxide change to nitro). Where tri in the given compound is representing a number of that ligand, three ammonia (triammine), and three nitrogen dioxide (trinitro).

As there are two ligands thus naming of these two ligands takes place alphabetically. As word ‘a' of ammine comes first then the word ‘n’ of nitro alphabetically. Thus, it comes first in naming both ligands such as triammine trinitro. After this, the name of the central metal (Co) ion is written, cobalt with its oxidation state.

All the six ligands tend to donate electron through the coordinate bond to the central metal.Let oxidation state of cobalt say x, NH3 is a neutral ligand thus, do not have any charge and NO2 has charge of -1 such as:
x + 3(O) + 3(-1) = 0 (no charge on cation complex)
x – 3 = 0
x = +3
Thus, the correct option is A.

Note: In a given compound ligand, NO2 is a bidentate ligand that can donate through both oxygen and nitrogen but as nitrogen has less affinity toward its lone pair, it will donate more easily than oxygen. Therefore N is used after the name of nitro such as nitro-N.