`3A to B + C ` it would be a zero order reaction , when

Options

A. the rate of reaction is proportional to square of concentration of A
B. the rate of reaction remains same at any concentration of A
C. the rate remains unchanged at any concentration of B and C
D. the rate or reaction doubles if concentration of B is increased to double

Explanation

To determine when the reaction \(3A \rightarrow B + C\) would be classified as a zero-order reaction, we need to analyze the relationship between the rate of the reaction and the concentration of the reactant \(A\).

### Step-by-Step Solution:

1. **Understanding Zero-Order Reactions**:
- A zero-order reaction is characterized by a constant reaction rate that does not depend on the concentration of the reactants. This means that the rate of the reaction remains the same regardless of how much reactant is present.

2. **Rate Expression for Zero-Order Reactions**:
- The rate of a zero-order reaction can be expressed mathematically as:
\[ \text{Rate} = k \]
where \(k\) is the rate constant. This indicates that the rate is constant and does not change with the concentration of \(A\).

3. **Analyzing the Given Options**:
- **Option 1**: The rate of reaction is proportional to the square of the concentration of \(A\).
- This describes a second-order reaction, not zero-order.
- **Option 2**: The rate of reaction remains the same at any concentration of \(A\).
- This is consistent with the definition of a zero-order reaction.
- **Option 3**: The rate remains unchanged at any concentration of \(B\) and \(C\).
- This does not directly relate to the zero-order nature of the reactant \(A\).
- **Option 4**: The rate of reaction doubles if the concentration of \(B\) is increased to double.
- This suggests a dependence on the concentration of products, which is not characteristic of zero-order kinetics.

4. **Conclusion**:
- The correct condition for the reaction \(3A \rightarrow B + C\) to be classified as a zero-order reaction is that **the rate of reaction remains the same at any concentration of \(A\)**. Therefore, the answer is **Option 2**.