A coordiantion complex compound of cobalt has the molecular formula containing four ammonia molecules, one nitro group and two chlorine atoms. A solution of this complex was prepared by dissolving 2.44 g of it in water and making the volume to 200 mL. Excess of `AgNO_(3)` solution was then added to it and the precipitate of AgCl formed was filtered and dried. The weight of AgCl thus obtained was found to be 1.435 g (Atomic mass of Co=59, Ag=108)
The type of isomerism shown by the complex will be

Options

A. linkage isomerism
B. Geometrical isomerism
C. Ionization isomerism
D. All the three

Explanation

To determine the type of isomerism shown by the coordination complex of cobalt with the given formula, we will follow these steps:

### Step 1: Identify the Coordination Complex
The coordination complex has the following components:
- 4 ammonia (NH₃) molecules
- 1 nitro group (NO₂)
- 2 chlorine (Cl) atoms

The general formula for the complex can be written as:
\[ \text{[Co(NH}_3\text{)}_4\text{(NO}_2\text{)}\text{Cl}_2] \]

### Step 2: Calculate the Molecular Mass of the Complex
To find the molecular mass, we will sum the atomic masses of all the components:
- Cobalt (Co) = 59 g/mol
- Ammonia (NH₃) = 14 (N) + 3 (H) = 17 g/mol → 4 NH₃ = 4 × 17 = 68 g/mol
- Nitro group (NO₂) = 14 (N) + 2 × 16 (O) = 46 g/mol
- Chlorine (Cl) = 35.5 g/mol → 2 Cl = 2 × 35.5 = 71 g/mol

Now, summing these:
\[ \text{Molecular mass} = 59 + 68 + 46 + 71 = 244 \text{ g/mol} \]

### Step 3: Calculate the Number of Moles of the Complex
Using the mass of the complex dissolved:
\[ \text{Mass of complex} = 2.44 \text{ g} \]
\[ \text{Number of moles} = \frac{\text{Mass}}{\text{Molecular mass}} = \frac{2.44 \text{ g}}{244 \text{ g/mol}} = 0.01 \text{ moles} \]

### Step 4: Determine the Moles of AgCl Formed
Given the mass of AgCl precipitate:
\[ \text{Mass of AgCl} = 1.435 \text{ g} \]
The molar mass of AgCl (Ag = 108 g/mol, Cl = 35.5 g/mol):
\[ \text{Molar mass of AgCl} = 108 + 35.5 = 143.5 \text{ g/mol} \]
Now, calculating the number of moles of AgCl:
\[ \text{Number of moles of AgCl} = \frac{1.435 \text{ g}}{143.5 \text{ g/mol}} = 0.01 \text{ moles} \]

### Step 5: Relate Moles of Complex to Moles of Cl⁻
From the reaction, we see that:
1 mole of the complex produces 1 mole of Cl⁻ ions.
Since we have 0.01 moles of AgCl, we also have 0.01 moles of Cl⁻ ions, confirming the stoichiometry.

### Step 6: Identify the Types of Isomerism
1. **Geometrical Isomerism**: The complex can exhibit cis and trans isomerism due to the arrangement of the ligands around the cobalt center.
2. **Ionization Isomerism**: The presence of Cl⁻ ions can lead to different isomers depending on whether Cl is inside or outside the coordination sphere.

### Conclusion
The complex can show both geometrical and ionization isomerism. Therefore, the answer is that the type of isomerism shown by the complex will be **all three types of isomerism** (geometrical, ionization, and linkage).