The oxidation number of Co in `[Co(en)_(3)]_(2)(SO_(4))_(3)` is
`+2`
`+1`
`+3`
`+6` .

Explanation

To determine the oxidation number of cobalt (Co) in the complex `[Co(en)_(3)]_(2)(SO_(4))_(3)`, we can follow these steps:

### Step 1: Identify the components of the complex
The complex consists of cobalt (Co) and ethylene diamine (en) ligands. Ethylene diamine is a neutral ligand, meaning it does not contribute any charge to the complex.

### Step 2: Determine the charge of the sulfate ions
The sulfate ion (SO₄²⁻) has a charge of -2. Since there are three sulfate ions in the formula, the total negative charge contributed by the sulfate ions is:
\[ 3 \times (-2) = -6 \]

### Step 3: Determine the total charge of the complex
The overall charge of the complex `[Co(en)_(3)]_(2)` must balance the total charge from the sulfate ions. Since the sulfate ions contribute a total charge of -6, the complex must have a total charge of +6 to balance it:
\[ \text{Total charge from complex} = +6 \]

### Step 4: Determine the charge of the cobalt complex
The complex `[Co(en)_(3)]_(2)` consists of two `[Co(en)₃]` units. Therefore, we can denote the charge of one `[Co(en)₃]` unit as \( y \). Thus, we have:
\[ 2y = +6 \]
This implies:
\[ y = +3 \]
So, the charge of one `[Co(en)₃]` complex is +3.

### Step 5: Calculate the oxidation number of cobalt
Let the oxidation number of cobalt be \( x \). The ethylene diamine ligands contribute 0 charge (since they are neutral), and we have one cobalt atom in the complex. Therefore, we can set up the equation:
\[ x + 0 = +3 \]
This simplifies to:
\[ x = +3 \]

### Conclusion
The oxidation number of cobalt in the complex `[Co(en)_(3)]_(2)(SO_(4))_(3)` is **+3**.

### Final Answer
**Option C: +3**

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