The IUPAC name of `[Co(H_2NCH_2CH_2NH_2)_2 (NO_2)NO_5` is bis(enthane-1,2-diamine) dinitrito-N-cobalt(III) nitrate.It follows the following rules that.
(a)Cation is named first followed by anion.
(b) Ligands are named in an alphabetical order before the name of the central atom/ion.
( c)Name of anionic ligands end in "o" (ex.chlorido) those of neutral (and if cation) ligands are the same except aqua for `H_2O`, ammine for `NH_3` etc.
(d)Prefixes mono,di,tri,etc.are used to indicate the number of individual ligand.When the name of the ligands include a numerical prefix, then terms bis, tris, tetrakis are used.
(e)Oxidation state of the metal is indicated by Roman numeral in parenthesis.
(f) For cationic and neutral complexes, the metal is named same as the element and for anionic complex, the name of metal ends with suffix-ate.For some metals, the Latin names are used in the complex anions , e.g., ferrate for Fe, argentate for silver etc.
The IUPAC name of `Fe_4[Fe(CN)_6]_3` is :

Options

A. Iron(III) hexacyanidoferrate(III)
B. Iron(III) hexacyanidoiran (II)
C. Iron(II) hexacyanidoferrate(II)
D. Iron(III)hexacyanidoferrate(II)

Explanation

To determine the IUPAC name of the complex `Fe_4[Fe(CN)_6]`, we will follow the provided rules step by step.

### Step 1: Identify the Cation and Anion
The complex consists of two parts: the cation and the anion.
- The cation is `Fe^3+` (iron) which is present outside the brackets.
- The anion is `[Fe(CN)_6]^{4-}` (hexacyanoferrate).

### Step 2: Determine the Oxidation States
- The overall charge of the complex is neutral, so the total charge of the cation must balance the charge of the anion.
- The anion `[Fe(CN)_6]` has a charge of -4 (since it is a complex ion).
- Let the oxidation state of iron in the anion be \( x \). The cyanide ion (CN) has a charge of -1, and there are 6 of them, contributing -6 to the charge.
- Therefore, we can set up the equation:
\[ x + 6(-1) = -4 \implies x - 6 = -4 \implies x = +2 \]
- Thus, the oxidation state of iron in the anion is +2.

### Step 3: Naming the Ligands
- The ligand in the anion is cyanide, which is named as "cyano" when it is a neutral ligand. Since it is an anionic ligand, it will be named as "cyanido".
- There are 6 cyanido ligands, so we will use the prefix "hexa".

### Step 4: Naming the Cation
- The cation is iron with an oxidation state of +3. Therefore, it is simply named "iron".

### Step 5: Name the Anion
- The anion contains iron in the +2 oxidation state and is named "ferrate" because it is an anionic complex. Since there are 6 cyanido ligands, it will be "hexacyanidoferrate".

### Step 6: Combine the Names
- According to the IUPAC naming convention, the cation is named first followed by the anion. Therefore, we combine the names:
\[ \text{Iron(III) hexacyanidoferrate(II)} \]

### Final IUPAC Name
The final IUPAC name of the complex `Fe_4[Fe(CN)_6]` is:
**Iron(III) hexacyanidoferrate(II)**

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