A complex compound of chromium chromium contains five `NH_(3)` molecules, one nitro group and two chloride ions for one `Cr^(3+)` cation. One molecule of this compound produces three ions in aq. Solution, on reacting with excess of `AgNO_(3)` solution, two moles of `AgCl` get precipitated ltBrgt Q. The formula of the complex compound is:

Options

A. `[CrCl(NO_2)(NH_(3))_(4)]NH_(3)*Cl`
B. `[CrCl(NH_(3))_(5)]Cl*NO_(2)`
C. `[Cr(NO_(2))(NH_(3))_(5)]Cl_(2)`
D. `[Cr(NH_(3))_(5)]NO_(2)*Cl_(2)`

Answer

To determine the formula of the complex compound of chromium, we will analyze the information given step by step.

### Step 1: Identify the components of the complex
The complex contains:
- 1 chromium ion (Cr³⁺)
- 5 ammonia (NH₃) molecules
- 1 nitro group (NO₂⁻)
- 2 chloride ions (Cl⁻)

### Step 2: Write the basic structure of the complex
The basic structure can be represented as:
\[ \text{[Cr(NH}_3\text{)}_5\text{(NO}_2\text{)}]\text{Cl}_2 \]
This indicates that the chromium ion is coordinated with 5 ammonia molecules and 1 nitro group, while the 2 chloride ions are outside the coordination sphere.

### Step 3: Determine the charge balance
- The charge of Cr³⁺ is +3.
- Each NH₃ is neutral (0 charge).
- The nitro group (NO₂) has a charge of -1.
- Each Cl⁻ has a charge of -1.

Now, let's calculate the total charge:
- Total positive charge = +3 (from Cr³⁺)
- Total negative charge = -1 (from NO₂) + 2 × (-1) (from 2 Cl⁻) = -1 - 2 = -3

Thus, the overall charge from the ligands is -3, which balances the +3 charge from Cr³⁺.

### Step 4: Count the total number of ions produced
The problem states that one molecule of this compound produces three ions in aqueous solution. The ions produced are:
- 1 cationic complex ion: [Cr(NH₃)₅(NO₂)]²⁺
- 2 chloride ions (Cl⁻)

This gives a total of 3 ions:
1. [Cr(NH₃)₅(NO₂)]²⁺
2. Cl⁻
3. Cl⁻

### Step 5: Reaction with AgNO₃
When this complex reacts with excess AgNO₃, it produces 2 moles of AgCl. Since AgCl precipitates from the chloride ions, the presence of 2 Cl⁻ ions confirms that there are indeed 2 chloride ions outside the coordination sphere.

### Conclusion: Write the final formula
Combining all the information, the formula of the complex compound is:
\[ \text{[Cr(NH}_3\text{)}_5\text{(NO}_2\text{)}]\text{Cl}_2 \]

### Final Answer:
The formula of the complex compound is \[ \text{[Cr(NH}_3\text{)}_5\text{(NO}_2\text{)}]\text{Cl}_2 \].

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