Among the following select the order of decreasing `EAN` valuse
`[cr(CO)_(6)]`
(II) `[Cr(CO)_(6)]^(Θ)`
(III) `[Cr(CO)_(6)]^(o+)`

Options

A. `IgtIIgtIII`
B. `IIIgtIIgtI`
C. `IIgtIgtIII
D. II=IgtIII

Answer

To determine the order of decreasing Effective Atomic Number (EAN) values for the complexes \([Cr(CO)_6]\), \([Cr(CO)_6]^{\Theta}\), and \([Cr(CO)_6]^{o+}\), we will follow these steps:

### Step 1: Calculate the EAN for \([Cr(CO)_6]\)

1. **Identify the oxidation state of Chromium (Cr)**:
- Since CO is a neutral ligand, it does not contribute to the oxidation state.
- The overall charge of the complex is 0.
- Let the oxidation state of Cr be \(x\):
\[ x + 0 = 0 \implies x = 0 \]

2. **Use the EAN formula**:
\[ \text{EAN} = Z - n + 2 \times L \]
where \(Z\) is the atomic number of the metal, \(n\) is the oxidation state, and \(L\) is the number of lone pair donating sites.

- Atomic number of Cr = 24
- Oxidation state \(n = 0\)
- Number of CO ligands = 6 (each CO has 1 lone pair donating site):
\[ L = 6 \]

3. **Calculate EAN**:
\[ \text{EAN} = 24 - 0 + 2 \times 6 = 24 + 12 = 36 \]

### Step 2: Calculate the EAN for \([Cr(CO)_6]^{\Theta}\)

1. **Identify the oxidation state of Chromium (Cr)**:
- The overall charge of the complex is -1.
- Let the oxidation state of Cr be \(x\):
\[ x + 0 = -1 \implies x = -1 \]

2. **Use the EAN formula**:
- Atomic number of Cr = 24
- Oxidation state \(n = -1\)
- Number of CO ligands = 6:
\[ L = 6 \]

3. **Calculate EAN**:
\[ \text{EAN} = 24 - (-1) + 2 \times 6 = 24 + 1 + 12 = 37 \]

### Step 3: Calculate the EAN for \([Cr(CO)_6]^{o+}\)

1. **Identify the oxidation state of Chromium (Cr)**:
- The overall charge of the complex is +1.
- Let the oxidation state of Cr be \(x\):
\[ x + 0 = +1 \implies x = +1 \]

2. **Use the EAN formula**:
- Atomic number of Cr = 24
- Oxidation state \(n = +1\)
- Number of CO ligands = 6:
\[ L = 6 \]

3. **Calculate EAN**:
\[ \text{EAN} = 24 - 1 + 2 \times 6 = 24 - 1 + 12 = 35 \]

### Step 4: Order the EAN values

Now we have calculated the EAN values for all three complexes:
- EAN for \([Cr(CO)_6]\) = 36
- EAN for \([Cr(CO)_6]^{\Theta}\) = 37
- EAN for \([Cr(CO)_6]^{o+}\) = 35

### Final Order of Decreasing EAN Values:
\[ [Cr(CO)_6]^{\Theta} > [Cr(CO)_6] > [Cr(CO)_6]^{o+} \]