In which of the following complex, the oxidation number of Fe is +1?

The correct option is [Fe(H₂O)₅NO]SO₄.

To determine the oxidation number of iron (Fe) in this complex, we can analyze the charges of the coordinating ligands and the counter-ion step-by-step:

1. Charge on the Coordination Sphere:
The sulfate ion (SO₄^2-) outside the coordination sphere carries a charge of -2. Since the entire compound is electrically neutral, the coordination sphere must carry an equal and opposite charge of +2.
This can be represented as: [Fe(H₂O)₅NO]²⁺.

2. Charges of the Ligands:
• Water (H₂O) is a neutral ligand, so its charge is 0.
• In this specific brown ring complex, the nitric oxide ligand is present as a nitrosonium cation (NO⁺), which carries a charge of +1.

3. Calculating the Oxidation Number of Iron (Fe):
Let the oxidation state of Fe be $x$.
The sum of the oxidation states of the metal and ligands must equal the overall charge of the coordination complex (+2):

$x+5\left(0\right)+1(+1)=+2$

Solving for $x$:

$x+1=+2$

$x=+2-1$

$x=+1$

Therefore, the oxidation state of Fe in the complex [Fe(H₂O)₅NO]SO₄ is +1.