The correct formula of diammine dichlorodicyano chromate (III) is :-

Options

A. `[CrCl_(2)(CN)_(2)(NH_(3))_(2)]^(3+)`
B. `[CrCl_(2)(CN)_(2)(NH_(3))_(2)]^(3-)`
C. `[CrCl_(2)(CN)_(2)(NH_(3))_(2)]`
D. `[CrCl_(2)(CN)_(2)(NH_(3))_(2)]^(-)`

Answer

To determine the correct formula of diammine dichlorodicyanochromate (III), we will follow these steps:

### Step 1: Identify the Ligands
- The name "diammine" indicates that there are two ammonia (NH3) ligands.
- The term "dichloro" indicates that there are two chloride (Cl) ligands.
- The term "dicyano" indicates that there are two cyanide (CN) ligands.

### Step 2: Write the Ligands in the Formula
- From the above, we can write the ligands as:
- Diammine: NH3 (2 times) → NH3\(_2\)
- Dichloro: Cl (2 times) → Cl\(_2\)
- Dicyano: CN (2 times) → CN\(_2\)

### Step 3: Identify the Central Metal Ion and its Oxidation State
- The name "chromate (III)" indicates that the central metal ion is chromium (Cr) and its oxidation state is +3 (Cr\(^{3+}\)).

### Step 4: Calculate the Overall Charge of the Complex
- Each ligand has a specific charge:
- NH3 is a neutral ligand (0 charge).
- Cl has a charge of -1, so Cl\(_2\) contributes -2.
- CN has a charge of -1, so CN\(_2\) contributes -2.

Now, let's calculate the overall charge:
- Charge from Cr: +3
- Charge from Cl\(_2\): -2
- Charge from CN\(_2\): -2
- Charge from NH3\(_2\): 0

Total charge = +3 (from Cr) - 2 (from Cl\(_2\)) - 2 (from CN\(_2\)) + 0 (from NH3\(_2\)) = -1

### Step 5: Write the Final Formula
- The overall charge of the complex is -1. Therefore, we will place the ligands and the central metal ion in the correct order:

The formula is: [Cr(NH3)2Cl2(CN)2]^{−1}

### Final Answer
The correct formula of diammine dichlorodicyanochromate (III) is:
\[ \text{[Cr(NH}_3\text{)}_2\text{Cl}_2\text{(CN)}_2]^{-1} \]

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