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 for diammine dichlorodicyanochromate(III), we will follow these steps:

### Step 1: Identify the ligands and their quantities
- **Diammine** indicates there are two amine ligands (NH3).
- **Dichlorido** indicates there are two chloride ligands (Cl).
- **Dicyano** indicates there are two cyanide ligands (CN).

### Step 2: Identify the central metal and its oxidation state
- The central metal is **chromate**, which refers to chromium (Cr).
- The oxidation state given is **(III)**, meaning chromium is in the +3 oxidation state.

### Step 3: Write down the ligands and their charges
- **Amine (NH3)** is a neutral ligand with a charge of 0.
- **Chloride (Cl)** has a charge of -1.
- **Cyanide (CN)** has a charge of -1.

### Step 4: Calculate the overall charge of the coordination complex
Using the information from the ligands:
- Total charge from amines: \(2 \times 0 = 0\)
- Total charge from chlorides: \(2 \times (-1) = -2\)
- Total charge from cyanides: \(2 \times (-1) = -2\)

Now, we can sum these charges:
- Total charge = \(0 + (-2) + (-2) = -4\)

### Step 5: Set up the equation for the overall charge
The overall charge of the coordination complex can be represented as:
\[ \text{Charge of metal} + \text{Total charge from ligands} = \text{Overall charge} \]
Given that the oxidation state of chromium is +3:
\[ 3 + (-4) = -1 \]

### Step 6: Write the final formula
Since the overall charge of the coordination complex is -1, we can write the formula as:
\[ \text{[Cr(NH}_3\text{)}_2\text{Cl}_2\text{(CN)}_2]^{-1} \]

### Step 7: Combine all components into the final formula
The final formula can be structured as:
\[ \text{[Cr(NH}_3\text{)}_2\text{Cl}_2\text{(CN)}_2]^{-1} \]

### 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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