Calculate the EAN of central atom in the following complexes
`(a) [Cr(CO)_(6)]" "(b) [Fe(CN)_(6)]^(4-)" " (c ) [Fe(CO)_(5)] " " (d) [Co(NH_(3))_(6)]^(3+)`
`(e ) [Ni(CO)_(4) " " (f) [Cu(CN)_(4)]^(3-)" "(g)[Pd(NH_(3))_(6)]^(4+)" " (h) [PtCl_(6)]^(2-)`

Answer

To calculate the Effective Atomic Number (EAN) for the central atom in each of the given complexes, we will use the formula:

\[ \text{EAN} = Z - x + 2 \times \text{Coordination Number} \]

Where:
- \( Z \) = Atomic number of the central metal atom
- \( x \) = Oxidation state of the central metal atom
- Coordination Number = Number of ligands directly bonded to the central metal atom

Now, let's calculate the EAN for each complex step by step:

### (a) [Cr(CO)₆]
1. **Identify the atomic number (Z) of Chromium (Cr)**:
- \( Z = 24 \)
2. **Determine the oxidation state (x)**:
- CO is a neutral ligand, so the oxidation state of Cr is 0.
3. **Calculate the coordination number**:
- There are 6 CO ligands, so the coordination number = 6.
4. **Calculate EAN**:
\[ \text{EAN} = 24 - 0 + 2 \times 6 = 24 + 12 = 36 \]

### (b) [Fe(CN)₆]⁴⁻
1. **Identify the atomic number (Z) of Iron (Fe)**:
- \( Z = 26 \)
2. **Determine the oxidation state (x)**:
- CN is a -1 charge ligand. The overall charge is -4, so:
\[ x + (-6) = -4 \implies x = +2 \]
3. **Calculate the coordination number**:
- There are 6 CN ligands, so the coordination number = 6.
4. **Calculate EAN**:
\[ \text{EAN} = 26 - 2 + 2 \times 6 = 26 - 2 + 12 = 36 \]

### (c) [Fe(CO)₅]
1. **Identify the atomic number (Z) of Iron (Fe)**:
- \( Z = 26 \)
2. **Determine the oxidation state (x)**:
- CO is a neutral ligand, so the oxidation state of Fe is 0.
3. **Calculate the coordination number**:
- There are 5 CO ligands, so the coordination number = 5.
4. **Calculate EAN**:
\[ \text{EAN} = 26 - 0 + 2 \times 5 = 26 + 10 = 36 \]

### (d) [Co(NH₃)₆]³⁺
1. **Identify the atomic number (Z) of Cobalt (Co)**:
- \( Z = 27 \)
2. **Determine the oxidation state (x)**:
- NH₃ is a neutral ligand, so the oxidation state of Co is +3.
3. **Calculate the coordination number**:
- There are 6 NH₃ ligands, so the coordination number = 6.
4. **Calculate EAN**:
\[ \text{EAN} = 27 - 3 + 2 \times 6 = 27 - 3 + 12 = 36 \]

### (e) [Ni(CO)₄]
1. **Identify the atomic number (Z) of Nickel (Ni)**:
- \( Z = 28 \)
2. **Determine the oxidation state (x)**:
- CO is a neutral ligand, so the oxidation state of Ni is 0.
3. **Calculate the coordination number**:
- There are 4 CO ligands, so the coordination number = 4.
4. **Calculate EAN**:
\[ \text{EAN} = 28 - 0 + 2 \times 4 = 28 + 8 = 36 \]

### (f) [Cu(CN)₄]³⁻
1. **Identify the atomic number (Z) of Copper (Cu)**:
- \( Z = 29 \)
2. **Determine the oxidation state (x)**:
- CN is a -1 charge ligand. The overall charge is -3, so:
\[ x + (-4) = -3 \implies x = +1 \]
3. **Calculate the coordination number**:
- There are 4 CN ligands, so the coordination number = 4.
4. **Calculate EAN**:
\[ \text{EAN} = 29 - 1 + 2 \times 4 = 29 - 1 + 8 = 36 \]

### (g) [Pd(NH₃)₆]⁴⁺
1. **Identify the atomic number (Z) of Palladium (Pd)**:
- \( Z = 46 \)
2. **Determine the oxidation state (x)**:
- NH₃ is a neutral ligand, so the oxidation state of Pd is +4.
3. **Calculate the coordination number**:
- There are 6 NH₃ ligands, so the coordination number = 6.
4. **Calculate EAN**:
\[ \text{EAN} = 46 - 4 + 2 \times 6 = 46 - 4 + 12 = 54 \]

### (h) [PtCl₆]²⁻
1. **Identify the atomic number (Z) of Platinum (Pt)**:
- \( Z = 78 \)
2. **Determine the oxidation state (x)**:
- Cl is a -1 charge ligand. The overall charge is -2, so:
\[ x + (-6) = -2 \implies x = +4 \]
3. **Calculate the coordination number**:
- There are 6 Cl ligands, so the coordination number = 6.
4. **Calculate EAN**:
\[ \text{EAN} = 78 - 4 + 2 \times 6 = 78 - 4 + 12 = 86 \]

### Summary of EAN Values:
- (a) [Cr(CO)₆]: EAN = 36
- (b) [Fe(CN)₆]⁴⁻: EAN = 36
- (c) [Fe(CO)₅]: EAN = 36
- (d) [Co(NH₃)₆]³⁺: EAN = 36
- (e) [Ni(CO)₄]: EAN = 36
- (f) [Cu(CN)₄]³⁻: EAN = 36
- (g) [Pd(NH₃)₆]⁴⁺: EAN = 54
- (h) [PtCl₆]²⁻: EAN = 86