A compound is made by mixing cobalt (III) nitrite and potassium nitrite solution in the ratio of 1 : 3. The aqueous solution of the compound showed 4 particles per molecule whereas molar conductivity reaveals the presence of six electrical charges. The formula of the compound is

Options

A. `Co(NO_(2))_(3). 2KNO_(2)`
B. `Co(NO_(2))_(3). 3KNO_(2)`
C. `K_(3)[Co(NO_(2))_(6)]`
D. `K[Co(NO_(2))_(4)]`

Explanation

To solve the problem, we need to analyze the information given about the compound formed by mixing cobalt (III) nitrite and potassium nitrite.

### Step-by-step Solution:

1. **Identify the Reactants:**
- Cobalt (III) nitrite has the formula \( \text{Co(NO}_2\text{)}_3 \).
- Potassium nitrite has the formula \( \text{KNO}_2 \).

2. **Determine the Ratio of Mixing:**
- The problem states that cobalt (III) nitrite and potassium nitrite are mixed in a ratio of 1:3. This means for every 1 mole of cobalt (III) nitrite, we are using 3 moles of potassium nitrite.

3. **Write the Reaction:**
- When these two compounds are mixed, they form a complex compound. The reaction can be represented as:
\[ \text{Co(NO}_2\text{)}_3 + 3 \text{KNO}_2 \rightarrow \text{K}_3\text{Co(NO}_2\text{)}_6 \]
- Here, the cobalt (III) nitrite forms a complex with the nitrite ions from potassium nitrite.

4. **Analyze the Aqueous Solution:**
- The problem states that the aqueous solution of the compound shows 4 particles per molecule. This means that when the compound dissolves in water, it dissociates into 4 ions.
- The complex ion \( \text{Co(NO}_2\text{)}_6^{3-} \) remains intact, while the potassium ions dissociate.

5. **Determine the Number of Ions:**
- The dissociation of the complex compound \( \text{K}_3\text{Co(NO}_2\text{)}_6 \) in water can be represented as:
\[ \text{K}_3\text{Co(NO}_2\text{)}_6 \rightarrow 3 \text{K}^+ + \text{Co(NO}_2\text{)}_6^{3-} \]
- This results in a total of 4 particles: 3 potassium ions and 1 complex ion.

6. **Molar Conductivity and Charge:**
- The problem mentions that the molar conductivity reveals the presence of six electrical charges. This is consistent with the dissociation of the compound:
- The 3 potassium ions contribute +3 charge.
- The complex ion \( \text{Co(NO}_2\text{)}_6^{3-} \) contributes -3 charge.
- Therefore, the total charge is 3 positive from potassium and 3 negative from the complex, giving a net charge of 0, but the total number of charges is 6.

7. **Final Formula of the Compound:**
- Based on the analysis, the formula of the compound formed is:
\[ \text{K}_3\text{Co(NO}_2\text{)}_6 \]

### Conclusion:
The formula of the compound is \( \text{K}_3\text{Co(NO}_2\text{)}_6 \).