An isomer of the complex `Co(en)_(2)(H_(2)O)IC l_(2)`, on reaction with concentrated `H_(2)SO_(4)`, it suffers loss in weight and on reaction with `AgNO_(3)` solution gives a yellow precipitated which is isoluble in `NH_(3)` solution.
Q. Total number of space isomers of the formula of the above complex is:

Options

A. 2
B. 3
C. 4
D. 1

Answer

To solve the problem of finding the total number of space isomers of the complex \( \text{Co(en)}_2(\text{H}_2\text{O})\text{ICl}_2 \), we can follow these steps:

### Step 1: Identify the ligands and coordination sphere
The complex consists of cobalt (Co) as the central metal ion, ethylenediamine (en) as a bidentate ligand, water (H2O) as a monodentate ligand, and two chloride ions (Cl) as monodentate ligands.

### Step 2: Determine the coordination number and geometry
Cobalt typically has a coordination number of 6 in octahedral complexes. In this case, we have:
- 2 ethylenediamine ligands (each bidentate contributes 2)
- 1 water molecule (monodentate)
- 2 chloride ions (monodentate)

This gives a total of 6 coordination sites filled.

### Step 3: Analyze isomerism
Space isomers include both geometric (cis/trans) and optical isomers.

#### Geometric Isomers:
1. **Cis Isomer**: In this arrangement, the two chloride ions are adjacent to each other.
2. **Trans Isomer**: Here, the two chloride ions are opposite each other.

#### Optical Isomers:
- The cis isomer can exhibit optical isomerism because it lacks a plane of symmetry, resulting in non-superimposable mirror images.
- The trans isomer does not exhibit optical isomerism because it has a plane of symmetry.

### Step 4: Count the isomers
- **Cis Isomer**: 1 (with optical isomers)
- **Trans Isomer**: 1 (no optical isomers)

Thus, the total number of space isomers is:
- 1 (cis) + 1 (trans) + 1 (optical from cis) = 3 isomers.

### Final Answer
The total number of space isomers of the complex \( \text{Co(en)}_2(\text{H}_2\text{O})\text{ICl}_2 \) is **3**.