`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 of reaction doubles if concentration of B is increased to double.

Explanation

To determine when the reaction \(3A \rightarrow B + C\) is a zero-order reaction, we need to analyze the conditions under which the rate of the reaction does not depend on the concentration of the reactant \(A\).

### Step-by-Step Solution:

1. **Understanding Zero-Order Reactions**:
- A zero-order reaction is characterized by a rate that is constant and does not change with varying concentrations of the reactants. Mathematically, the rate law for a zero-order reaction can be expressed as:
\[ \text{Rate} = k[A]^0 = k \]
- Here, \(k\) is the rate constant, and \([A]\) is the concentration of reactant \(A\). Since any number raised to the power of zero is 1, the rate remains constant regardless of the concentration of \(A\).

2. **Analyzing the Given Options**:
- We need to evaluate the options provided in the question:
- **Option A**: The rate of the reaction is proportional to the square of the concentration of \(A\). (This suggests a second-order reaction)
- **Option B**: The rate of the reaction remains the same at any concentration of \(A\). (This suggests a zero-order reaction)
- **Option C**: The rate remains unchanged at any concentration of \(B\) and \(C\). (This does not directly indicate the order with respect to \(A\))
- **Option D**: The rate of the reaction doubles if the concentration of \(B\) is increased to double. (This suggests a dependency on \(B\))

3. **Identifying the Correct Option**:
- From our understanding of zero-order reactions, the correct condition that indicates a zero-order reaction is when the rate remains constant regardless of the concentration of \(A\).
- Therefore, **Option B** is the correct answer: "The rate of the reaction remains the same at any concentration of \(A\)."

### Final Answer:
The reaction \(3A \rightarrow B + C\) would be a zero-order reaction when the rate of the reaction remains the same at any concentration of \(A\) (Option B).

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