A compound is made by mixing cobalt (III) nitrite and potassium nitrite solutions in the ratio of 1:3. The aqueous solution of the compound showed 4 particles per molecules whereas molar conductivity reveals 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)]`

Answer

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 Components**:
- Cobalt (III) nitrite has the formula \( \text{Co(NO}_2)_3 \).
- 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.

3. **Calculate the Total Number of Particles**:
- When cobalt (III) nitrite dissociates in solution, it produces one cobalt ion (\( \text{Co}^{3+} \)) and three nitrite ions (\( \text{NO}_2^{-} \)).
- Therefore, \( \text{Co(NO}_2)_3 \) produces a total of \( 1 + 3 = 4 \) particles.
- Potassium nitrite dissociates into one potassium ion (\( \text{K}^{+} \)) and one nitrite ion (\( \text{NO}_2^{-} \)). Thus, \( \text{KNO}_2 \) produces \( 1 + 1 = 2 \) particles.

4. **Calculate the Total Contribution from Potassium Nitrite**:
- Since we are mixing in a ratio of 1:3, for every 1 mole of \( \text{Co(NO}_2)_3 \), we have 3 moles of \( \text{KNO}_2 \).
- The total number of particles from 3 moles of \( \text{KNO}_2 \) is \( 3 \times 2 = 6 \) particles.

5. **Total Particles in the Solution**:
- The total number of particles from the mixture is \( 4 \) (from \( \text{Co(NO}_2)_3 \)) + \( 6 \) (from \( 3 \times \text{KNO}_2 \)) = \( 10 \) particles.

6. **Analyze Molar Conductivity**:
- The molar conductivity indicates the presence of 6 electrical charges. This suggests that the compound dissociates in such a way that it contributes 6 ions to the solution.

7. **Formulate the Compound**:
- The compound formed can be represented as \( \text{Co(NO}_2)_3 \cdot 3\text{KNO}_2 \).
- This compound can be simplified to \( \text{K}_3\text{Co(NO}_2)_3 \) to show that it contains 3 potassium ions and one cobalt nitrite complex.

8. **Final Formula**:
- The final formula of the compound is \( \text{K}_3\text{Co(NO}_2)_3 \).

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