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

Options

A. `[Ce(e n)_(2)SO_(4)]`
B. `[Co(e n)_(3)SO_(4)]`
C. `[Co (e n)_(3)]_(2) SO_(4)`
D. `[Co (e n)_(3)]_(2) (SO_(4))_(3)`

Answer

To determine the formula of the complex tris(ethylenediamine) cobalt(III) sulfate, we can break down the components step by step.

### Step 1: Identify the Cation and Anion
- The cation in the complex is cobalt in the +3 oxidation state, denoted as Co(III).
- The ligand is ethylenediamine (en), which is a neutral bidentate ligand. "Tris" indicates that there are three ethylenediamine ligands attached to the cobalt ion.
- The anion is sulfate, which has a formula of SO₄²⁻ and carries a charge of -2.

### Step 2: Write the Cation Part
- Since we have cobalt with three ethylenediamine ligands, we denote this as:
- Cobalt: Co
- Ethylenediamine: en
- Since there are three ethylenediamine ligands, we write it as en₃.
- Therefore, the cation part becomes: Co(en)₃.

### Step 3: Write the Anion Part
- The anion is sulfate, which is represented as SO₄²⁻.

### Step 4: Combine Cation and Anion
- The overall charge of the cation (Co(en)₃) is +3, and the charge of the sulfate (SO₄) is -2.
- To balance the charges, we need to determine how many sulfate ions are required. Since the cation has a +3 charge and each sulfate has a -2 charge, we can find the least common multiple to balance the charges.
- The least common multiple of +3 and -2 is 6. Therefore, we need 2 sulfate ions to balance the +3 charge from the cobalt complex.

### Step 5: Write the Final Formula
- The final formula combines the cation and the anions:
- Cation: Co(en)₃
- Anions: (SO₄)₂
- Therefore, the complete formula is: Co(en)₃(SO₄)₂.

### Step 6: Adjust for Tris
- Since we have "tris" in the name, it indicates that there are three ethylenediamine ligands, which we have already accounted for.

### Final Answer
The formula of the complex tris(ethylenediamine) cobalt(III) sulfate is:
\[ \text{[Co(en)}_3\text{]}^{3+} \text{[SO}_4\text{]}^{2-} \]

Thus, the final formula is:
\[ \text{[Co(en)}_3\text{]} \text{(SO}_4\text{)}_2 \]