The formula of the complex tris (ethylenediamine) cobalt (III) sulphate is

Options

A. (a) `[Co(en)_2SO_4]`
B. (b) `[Co(en)_3SO_4]`
C. (c) `[Co(en)_3]_2SO_4`
D. (d) `[Co(en)_3]_2(SO_4)_3`

Explanation

To derive the formula of the complex tris(ethylenediamine)cobalt(III) sulfate, we will follow these steps:

### Step 1: Identify the components of the complex
The complex consists of:
- **Cobalt (Co)** as the central metal ion
- **Ethylenediamine (en)** as the ligand
- **Sulfate (SO₄²⁻)** as the anion

### Step 2: Determine the oxidation state of cobalt
In this complex, cobalt is in the +3 oxidation state, which is indicated as cobalt(III).

### Step 3: Count the ligands
The prefix "tris" indicates that there are three ethylenediamine ligands coordinated to the cobalt ion. Therefore, we have:
- 3 ethylenediamine (en) ligands.

### Step 4: Write the cationic part of the complex
The cationic part of the complex will be written first. Since we have one cobalt ion in the +3 oxidation state and three ethylenediamine ligands (which are neutral), the cationic part can be represented as:
\[ \text{[Co(en)₃]}^{3+} \]

### Step 5: Write the anionic part
The anionic part of the complex is the sulfate ion, which has a charge of -2:
\[ \text{SO₄}^{2-} \]

### Step 6: Combine the cationic and anionic parts
To balance the charges, we need to ensure that the overall charge of the complex is neutral. The cationic part has a +3 charge, and the anionic part has a -2 charge. To balance these charges, we need 3 sulfate ions to balance the +3 charge from the cationic part:
\[ \text{SO₄}^{2-} \text{ (3 times)} \]

### Step 7: Write the final formula
Combining the cationic and anionic parts, we write the formula of the complex as:
\[ \text{[Co(en)₃]SO₄} \]

Since we have three sulfate ions to balance the charge, the complete formula becomes:
\[ \text{[Co(en)₃]₂(SO₄)₃} \]

### Final Answer
The formula of the complex tris(ethylenediamine)cobalt(III) sulfate is:
\[ \text{[Co(en)₃]₂(SO₄)₃} \]

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