Write true or false: `EAN` rule is followed by `K_(4)Fe(CN)_(6)` complex .

Answer

To determine whether the EAN (Effective Atomic Number) rule is followed by the complex \( K_4[Fe(CN)_6] \), we will follow these steps:

### Step 1: Define the EAN Rule
The EAN rule states that the effective atomic number (EAN) of a metal in a coordination complex can be calculated using the formula:
\[ \text{EAN} = Z - n + 2m \]
where:
- \( Z \) = atomic number of the central metal atom,
- \( n \) = oxidation state of the central metal atom,
- \( m \) = total number of electrons donated by the ligands.

### Step 2: Identify the Central Metal Atom and Its Atomic Number
In the complex \( K_4[Fe(CN)_6] \), the central metal atom is iron (Fe).
- The atomic number of iron (Fe) is \( 26 \).

### Step 3: Determine the Oxidation State of Iron
To find the oxidation state of iron in the complex, we can set up the following equation based on the charges:
- Each cyanide ion (CN) has a charge of \(-1\).
- Since there are 6 cyanide ions, their total contribution is \(-6\).
- The overall charge of the complex is neutral (0).

Let \( x \) be the oxidation state of iron:
\[ x + 6(-1) = 0 \implies x - 6 = 0 \implies x = +2 \]
Thus, the oxidation state of iron is \( +2 \).

### Step 4: Calculate the Total Number of Electrons Donated by the Ligands
Each cyanide ion (CN) donates 2 electrons. Since there are 6 cyanide ions, the total number of electrons donated is:
\[ m = 6 \times 2 = 12 \]

### Step 5: Substitute Values into the EAN Formula
Now we can substitute the values into the EAN formula:
\[ \text{EAN} = Z - n + 2m \]
Substituting the known values:
\[ \text{EAN} = 26 - 2 + 2(12) \]
Calculating this gives:
\[ \text{EAN} = 26 - 2 + 24 = 48 \]

### Step 6: Compare EAN with the Atomic Number of the Nearest Noble Gas
The effective atomic number (EAN) we calculated is \( 48 \). The atomic number of the nearest noble gas, which is krypton (Kr), is also \( 36 \). Since \( 48 \) is not equal to \( 36 \), we conclude that the EAN rule is not followed.

### Conclusion
The statement that the EAN rule is followed by \( K_4[Fe(CN)_6] \) is **False**.

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