`2A rarrB +C`
It would be a zero order reaction when

Options

A. The rate of reaction is proportional to sequare of conc of A
B. The rate of reaction remains same at any conc of A
C. The rate remains unchanged at any conc of B and C
D. The rate of reaction doubles if conc of B is increased to double

Answer

To determine when the reaction \( 2A \rightarrow B + C \) is a zero-order reaction, we need to analyze the rate of reaction in relation to the concentration of the reactant \( A \).

### Step-by-Step Solution:

1. **Understanding Zero-Order Reactions**:
- In a zero-order reaction, the rate of reaction is independent of the concentration of the reactants. This means that changes in the concentration of the reactants do not affect the rate of the reaction.

2. **Rate Law Expression**:
- The rate law for a reaction can be expressed as:
\[ \text{Rate} = k [A]^x \]
- Here, \( k \) is the rate constant, \( [A] \) is the concentration of reactant \( A \), and \( x \) is the order of the reaction with respect to \( A \).

3. **Setting the Order to Zero**:
- For a reaction to be zero-order with respect to \( A \), we need to set \( x = 0 \):
\[ \text{Rate} = k [A]^0 = k \]
- Since \( [A]^0 = 1 \), the rate becomes equal to \( k \), which is a constant.

4. **Implications of Zero-Order**:
- This indicates that the rate of reaction does not change with variations in the concentration of \( A \). Therefore, the rate remains constant regardless of the concentration of \( A \).

5. **Evaluating the Options**:
- Now, let's evaluate the given options:
1. The rate of reaction is proportional to the square of the concentration of \( A \) - **Incorrect** (as it contradicts the definition of zero-order).
2. The rate of reaction remains the same at any concentration of \( A \) - **Correct** (this is the defining characteristic of zero-order).
3. The rate remains unchanged at any concentration of \( B \) and \( C \) - **Correct** (the rate does not depend on products).
4. The rate of reaction doubles if the concentration of \( B \) is increased - **Incorrect** (the rate is independent of \( B \)).

6. **Conclusion**:
- The correct answers are options 2 and 3. The reaction \( 2A \rightarrow B + C \) is a zero-order reaction when the rate of reaction remains the same at any concentration of \( A \).