Pick out the correct statement with respect to `[Fe(CN)_6]^(3-)`

Options

A. It is `sp^3 d^2` hybridised and tetrahedral.
B. It is `d^2 sp^3` hybridised and octahedral.
C. It is `dsp^2` hybridised and square planar.
D. It is `sp^3 d^2` hybridised and octahedral.

Explanation

To solve the question regarding the complex ion \([Fe(CN)_6]^{3-}\), we need to determine its oxidation state, hybridization, and geometry. Here’s the step-by-step solution:

### Step 1: Determine the Oxidation State of Iron (Fe)
To find the oxidation state of iron in the complex \([Fe(CN)_6]^{3-}\), we can set up the following equation:

Let the oxidation state of Fe be \(x\). The cyanide ion (CN) has a charge of -1, and since there are 6 cyanide ions, their total contribution to the charge is \(6 \times (-1) = -6\).

The overall charge of the complex is -3. Therefore, we can write the equation:
\[ x + 6(-1) = -3 \]
This simplifies to:
\[ x - 6 = -3 \]
Solving for \(x\):
\[ x = -3 + 6 = +3 \]
Thus, the oxidation state of Fe in \([Fe(CN)_6]^{3-}\) is +3.

### Step 2: Determine the Electron Configuration of \(Fe^{3+}\)
Iron (Fe) has the electron configuration of Argon (Ar) followed by \(3d^6 4s^2\). When it loses three electrons to form \(Fe^{3+}\), two electrons are removed from the 4s subshell and one from the 3d subshell:
\[ Fe^{3+} = Ar \, 3d^5 \]

### Step 3: Consider the Ligand Field and Electron Pairing
Cyanide (CN) is a strong field ligand, which means it can cause pairing of electrons in the d-orbitals. In the case of \(Fe^{3+}\) with a \(3d^5\) configuration, the presence of strong field ligands like CN will lead to the pairing of electrons.

The electron configuration after pairing will be:
- 3d: 5 electrons (all paired)
- 4s: 0 electrons
- 4p: 0 electrons

### Step 4: Determine Hybridization
To determine the hybridization, we need to look at the number of orbitals involved in bonding. Since we have 6 ligands (CN), the hybridization can be determined as follows:
- 2 d-orbitals (from 3d)
- 3 p-orbitals (from 4p)

Thus, the hybridization is:
\[ d^2sp^3 \]

### Step 5: Determine the Geometry
For a complex with \(d^2sp^3\) hybridization, the geometry is octahedral.

### Conclusion
The correct statements regarding the complex \([Fe(CN)_6]^{3-}\) are:
- The oxidation state of Fe is +3.
- The hybridization is \(d^2sp^3\).
- The geometry is octahedral.