Which of the following complex ions does satisfy the effective atomic number (EAN) rule?

Options

A. `[Pt(NH_(3))_(4)]^(2+)`
B. `[PtCl_(4)]^(2-)`
C. `[PtCl_(6)]^(2-)`
D. `[Fe(CN)_(6)]^(3-)`

Answer

To determine which of the given complex ions satisfies the Effective Atomic Number (EAN) rule, we will follow these steps:

### Step 1: Understand the EAN Rule
The EAN rule states that the effective atomic number of a metal in a complex should be equal to the atomic number of the nearest noble gas. The formula to calculate the EAN is:

\[ \text{EAN} = Z - O + (L \times 2) \]

Where:
- \( Z \) = Atomic number of the central metal atom
- \( O \) = Oxidation number of the central metal atom
- \( L \) = Number of lone pair donating sites from the ligands

### Step 2: Calculate EAN for Each Complex Ion

#### Complex 1: \([Pt(NH_3)_4]^{2+}\)
1. **Atomic number of Platinum (Pt)**: 78
2. **Oxidation state of Pt**: Let it be \( x \). Since NH3 is neutral, the equation is:
\[ x + 0 = +2 \implies x = +2 \]
3. **Number of lone pair donating sites**: NH3 is a monodentate ligand, and there are 4 NH3 ligands, so:
\[ L = 4 \]
4. **Calculate EAN**:
\[ \text{EAN} = 78 - 2 + (4 \times 2) = 78 - 2 + 8 = 84 \]

#### Complex 2: \([PtCl_4]^{2-}\)
1. **Atomic number of Platinum (Pt)**: 78
2. **Oxidation state of Pt**: Let it be \( x \). Since Cl is -1, the equation is:
\[ x - 4 = -2 \implies x = +2 \]
3. **Number of lone pair donating sites**: Cl is also a monodentate ligand, and there are 4 Cl ligands, so:
\[ L = 4 \]
4. **Calculate EAN**:
\[ \text{EAN} = 78 - 2 + (4 \times 2) = 78 - 2 + 8 = 84 \]

#### Complex 3: \([PtCl_6]^{2-}\)
1. **Atomic number of Platinum (Pt)**: 78
2. **Oxidation state of Pt**: Let it be \( x \). Since Cl is -1, the equation is:
\[ x - 6 = -2 \implies x = +4 \]
3. **Number of lone pair donating sites**: Cl is a monodentate ligand, and there are 6 Cl ligands, so:
\[ L = 6 \]
4. **Calculate EAN**:
\[ \text{EAN} = 78 - 4 + (6 \times 2) = 78 - 4 + 12 = 86 \]

#### Complex 4: \([Fe(CN)_6]^{3-}\)
1. **Atomic number of Iron (Fe)**: 26
2. **Oxidation state of Fe**: Let it be \( x \). Since CN is -1, the equation is:
\[ x - 6 = -3 \implies x = +3 \]
3. **Number of lone pair donating sites**: CN is a bidentate ligand, but here it acts as a monodentate ligand for EAN calculation, and there are 6 CN ligands, so:
\[ L = 6 \]
4. **Calculate EAN**:
\[ \text{EAN} = 26 - 3 + (6 \times 2) = 26 - 3 + 12 = 35 \]

### Step 3: Compare EAN with Noble Gas Atomic Numbers
- Noble gas atomic numbers: He (2), Ne (10), Ar (18), Kr (36), Xe (54), Rn (86)

1. **Complex 1**: EAN = 84 (not noble gas)
2. **Complex 2**: EAN = 84 (not noble gas)
3. **Complex 3**: EAN = 86 (equals noble gas - Rn)
4. **Complex 4**: EAN = 35 (not noble gas)

### Conclusion
The complex ion that satisfies the EAN rule is \([PtCl_6]^{2-}\) as its EAN equals the atomic number of the nearest noble gas (Rn).

### Final Answer
**The complex ion that satisfies the EAN rule is \([PtCl_6]^{2-}\)**.