Potassium manganate `(K_2MnO_4)` is formed when

Options

A. Chlorine is passed through aqueous `KMnO_4` solution
B. Manganese dioxide is fused with potassium hydroxide in air.
C. Formaldehyde reacts with potassium permanganate in the presence of a strong alkali.
D. Potassium permanganate reacts with concentrated sulphuric acid.

Explanation

To determine how potassium manganate `(K2MnO4)` is formed, we can analyze the provided information step by step.

### Step-by-Step Solution:

1. **Understanding the Formation of Potassium Manganate**:
Potassium manganate `(K2MnO4)` can be formed through specific reactions involving manganese compounds and potassium hydroxide.

2. **Identifying the Reaction**:
One of the primary reactions that lead to the formation of potassium manganate is:
- **Manganese Dioxide Reaction**:
\[ 2 \text{MnO}_2 + 4 \text{KOH} + \text{O}_2 \rightarrow 2 \text{K}_2\text{MnO}_4 + 2 \text{H}_2\text{O} \]
This reaction indicates that manganese dioxide `(MnO2)` is fused with potassium hydroxide `(KOH)` in the presence of air (oxygen).

3. **Alternative Reaction**:
Another method of forming potassium manganate involves:
- **Formaldehyde Reaction**:
\[ \text{HCHO} + \text{KMnO}_4 \xrightarrow{\text{strong alkali}} \text{K}_2\text{MnO}_4 + \text{HCOOH} \]
In this reaction, formaldehyde `(HCHO)` reacts with potassium permanganate `(KMnO4)` in the presence of a strong alkali, resulting in the formation of potassium manganate.

4. **Evaluating Options**:
Given the options:
- **Option 1**: Chlorine is passed through aqueous KMnO4 solution. (Incorrect)
- **Option 2**: Manganese dioxide is fused with potassium hydroxide in air. (Correct)
- **Option 3**: Formaldehyde reacts with potassium permanganate in the presence of strong alkali. (Correct)
- **Option 4**: Potassium permanganate reacts with concentrated sulfuric acid. (Incorrect)

5. **Conclusion**:
The correct methods for the formation of potassium manganate `(K2MnO4)` are:
- Manganese dioxide fused with potassium hydroxide in air.
- Formaldehyde reacting with potassium permanganate in the presence of a strong alkali.

### Final Answer:
Potassium manganate `(K2MnO4)` is formed when:
- Manganese dioxide is fused with potassium hydroxide in air.
- Formaldehyde reacts with potassium permanganate in the presence of a strong alkali.