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 formula of the complex would be

Options

A. `[Co(NH_(3))_(4)(NO_(2))]Cl_(2)`
B. `[Co(NH_(3))_(4)Cl(NO_(2))]Cl`
C. `[Co(NH_(3))_(4)Cl_(2)]NO_(2)`
D. `[Co(NH_(3))_(4)Cl_(2)(NO_(2))]`

Explanation

To determine the formula of the coordination complex compound of cobalt, we can follow these steps:

### Step 1: Identify the components of the complex
The complex contains:
- 4 ammonia (NH₃) molecules
- 1 nitro (NO₂) group
- 2 chloride (Cl) ions

This suggests a general formula of the complex as [Co(NH₃)₄(NO₂)Cl₂].

### Step 2: Calculate the molar mass of the complex
To find the molar mass, we need to sum the molar masses of all the components:
- Molar mass of Co = 59 g/mol
- Molar mass of NH₃ = 17 g/mol (4 NH₃ = 4 × 17 = 68 g/mol)
- Molar mass of NO₂ = 46 g/mol
- Molar mass of Cl = 35.5 g/mol (2 Cl = 2 × 35.5 = 71 g/mol)

Now, adding these together:
\[ \text{Molar mass of complex} = 59 + 68 + 46 + 71 = 244 \text{ g/mol} \]

### Step 3: Calculate the number of moles of the complex
Using the mass of the complex dissolved (2.44 g) and its molar mass (244 g/mol), we can calculate the number of moles:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{2.44 \text{ g}}{244 \text{ g/mol}} = 0.01 \text{ moles} \]

### Step 4: Determine the amount of AgCl formed
When excess AgNO₃ is added, it reacts with the chloride ions in the complex to form AgCl. The mass of AgCl obtained is 1.435 g.

### Step 5: Calculate the number of moles of AgCl
To find the number of moles of AgCl, we use its molar mass:
- Molar mass of AgCl = 108 + 35.5 = 143.5 g/mol
\[ \text{Number of moles of AgCl} = \frac{1.435 \text{ g}}{143.5 \text{ g/mol}} \approx 0.01 \text{ moles} \]

### Step 6: Relate moles of AgCl to moles of chloride ions
Since 1 mole of the complex produces 2 moles of Cl⁻ ions (because there are 2 Cl in the formula), we can deduce:
- 0.01 moles of AgCl corresponds to 0.01 moles of Cl⁻ ions.

### Step 7: Calculate the number of moles of Cl⁻ ions from the complex
From the stoichiometry of the complex:
- If 0.01 moles of AgCl were formed, this means that 0.01 moles of Cl⁻ ions were present.
- Therefore, the complex must have contained 0.005 moles of the complex (since each complex yields 2 Cl⁻ ions).

### Step 8: Conclusion
Since we started with 0.01 moles of the complex and the calculations are consistent, we confirm that the formula of the complex is indeed:
\[ \text{[Co(NH₃)₄(NO₂)Cl₂]} \]