IUPAC name of the isomer of compound with molecular formula, \(FeCl_3.6H_2O\) having \(i = 3\) is:

Tetraaquachlorido iron (III) dichloride dihydrate

The correct answer is option 3. Tetraaquachlorido iron (III) dichloride dihydrate.

The compound with the molecular formula \( FeCl_3 \cdot 6H_2O \) can exist in different isomeric forms depending on how the water and chloride ions coordinate to the central iron ion. The van't Hoff factor \( i \) indicates the number of particles into which the compound dissociates in solution. The question states that \( i = 3 \), which means the compound dissociates into three particles in solution.

Step-by-step analysis:

Understanding \( i = 3 \) and the dissociation behavior:

The van't Hoff factor, \( i \), represents the number of ions or particles a compound produces upon dissociation in solution. If \( i = 3 \), the compound must dissociate into three particles.

In a coordination complex, chloride ions can be either:

Coordinated to the central metal ion (in this case, iron), where they do not dissociate.

Free as counterions in the solution, which dissociate and contribute to the number of particles.

Interpreting the complex structure:

The formula \( FeCl_3 \cdot 6H_2O \) indicates that iron is in the +3 oxidation state (Fe³⁺) and there are three chloride ions associated with it. Water molecules and chloride ions can be arranged around the central iron ion (Fe³⁺) in different ways. Some of the water molecules can coordinate directly to the iron, while others can remain in the crystal lattice as hydration water. The chloride ions can either coordinate to iron or remain free in solution as dissociable anions.

Coordination possibilities and van't Hoff factor:

If all three chloride ions are coordinated to the iron ion, the complex would not dissociate into free chloride ions, resulting in \( i = 1 \) because it would be a single particle.

If one chloride ion is coordinated to the iron and two chloride ions are free in solution, the complex would dissociate into three particles:

One cationic complex (e.g., \([Fe(H_2O)_4Cl]^+\))

Two free chloride ions (Cl⁻)

This would result in \( i = 3 \).

Examining the options:

Now, let's analyze the given IUPAC names:

Option 1: Tetraaquadichlorido iron (III) chloride dihydrate

Two chloride ions are coordinated to iron, and one chloride ion is free.This would result in 2 particles upon dissociation (one complex cation and one chloride ion).

van't Hoff factor: \( i = 2 \), so this option is incorrect.

Option 2: Triaquatrichlorido iron (III)

All three chloride ions are coordinated to iron. This would result in 1 particle (a neutral complex), and no dissociation of chloride ions.

van't Hoff factor: \( i = 1 \), so this option is incorrect.

Option 3: Tetraaquachlorido iron (III) dichloride dihydrate

One chloride ion is coordinated to iron, and two chloride ions are free.This would result in three particles upon dissociation (one complex cation and two chloride ions).

van't Hoff factor: \( i = 3 \), so this option is correct.

Option 4: Pentaaquachlorido iron (III) chloride monohydrate

One chloride ion is coordinated to iron, and one chloride ion is free. This would result in 2 particles (one complex cation and one chloride ion).

van't Hoff factor: \( i = 2 \), so this option is incorrect.

Conclusion

The correct isomer with \( i = 3 \) is option 3: Tetraaquachlorido iron (III) dichloride dihydrate. In this case:

One chloride ion is bound to the iron, and two chloride ions are free in solution.

The compound dissociates into three particles: one complex cation \([Fe(H_2O)_4Cl]^+\) and two free chloride anions (Cl⁻).