Total number of isomers for the complex \([FeCl_2(C_2O_4)_2]^{4-}\) is:

3

The correct answer is option 2. 3.

Let us delve into the detailed reasoning behind the determination of the number of isomers for the complex \([FeCl_2(C_2O_4)_2]^{4-}\).

Structure of the Complex

The complex \([FeCl_2(C_2O_4)_2]^{4-}\) contains:

\( \text{Fe}^{2+} \) as the central metal ion.

2 chloride ions (\(\text{Cl}^-\)) which are monodentate ligands (each can coordinate through one atom).

2 oxalate ions (\(\text{C}_2\text{O}_4^{2-}\)) which are bidentate ligands (each can coordinate through two oxygen atoms, forming a chelate ring).

The coordination number of iron is 6, leading to an octahedral geometry around the central metal ion.

Geometric (Cis-Trans) Isomerism
In an octahedral complex, when there are two types of ligands (such as \( \text{Cl}^- \) and \( \text{C}_2\text{O}_4^{2-} \)), they can be arranged in different spatial orientations:

Cis Isomer:

The two chloride ligands (\( \text{Cl}^- \)) are adjacent to each other, i.e., they occupy adjacent positions. The two oxalate ligands (\( \text{C}_2\text{O}_4^{2-} \)) also occupy adjacent positions.

Trans Isomer:

The two chloride ligands (\( \text{Cl}^- \)) are opposite each other, i.e., they occupy positions across from each other. The two oxalate ligands (\( \text{C}_2\text{O}_4^{2-} \)) are also opposite each other.

This gives rise to two geometric isomers: cis and trans.

Optical Isomerism

Optical isomerism occurs when a molecule cannot be superimposed on its mirror image (chiral). In the context of coordination complexes:

Cis Isomer:

The cis isomer can be chiral. In this isomer, the spatial arrangement of the ligands allows for the possibility that the complex and its mirror image are non-superimposable. This leads to a pair of enantiomers (optical isomers).

Trans Isomer:

The trans isomer is usually non-chiral because the symmetrical arrangement of the ligands typically makes the complex and its mirror image superimposable. Therefore, the trans isomer does not exhibit optical isomerism.

Total Number of Isomer

Combining geometric and optical isomerism:

Cis Isomer: There are 2 optical isomers (a pair of enantiomers).

Trans Isomer: There is 1 isomer (no optical isomerism).

Thus, the total number of isomers for the complex \([FeCl_2(C_2O_4)_2]^{4-}\) is:

\(\text{2 (cis optical isomers)} + \text{1 (trans isomer)} = 3 \text{ isomers}\)

The complex \([FeCl_2(C_2O_4)_2]^{4-}\) has 3 isomers: 2 optical isomers from the cis form and 1 trans isomer.