The reaction `2X to Y + Z` would be zero order reaction when

Options

A. rate remains unchanged at any concentration of Y and Z
B. rate of reaction doubles if concentration of Y is doubled
C. rate of reaction remains same at any concentration of X
D. rate of reaction is directly proportional to square of concentration of X

Explanation

To determine when the reaction \(2X \rightarrow Y + Z\) would be classified as a zero-order reaction, we can follow these steps:

### Step 1: Understand Zero-Order Reactions
A zero-order reaction is characterized by a rate that is constant and does not depend on the concentration of the reactants. This means that the rate of the reaction remains unchanged regardless of the concentration of the reactant.

### Step 2: Write the Rate Law
For a zero-order reaction, the rate law can be expressed as:
\[ \text{Rate} = k[X]^0 \]
Since any number raised to the power of zero is 1, this simplifies to:
\[ \text{Rate} = k \]
Here, \(k\) is the rate constant.

### Step 3: Analyze the Given Reaction
In the reaction \(2X \rightarrow Y + Z\), we are interested in the concentration of the reactant \(X\). For the reaction to be zero-order, the rate must remain constant regardless of the concentration of \(X\).

### Step 4: Evaluate the Options
1. **Rate remains unchanged at any concentration of Y and Z**: This is incorrect because the rate of a reaction is dependent on the concentration of reactants, not products.

2. **Rate of reaction doubles if the concentration of Y is doubled**: This is also incorrect since the rate of reaction for zero-order does not depend on the concentration of products.

3. **Rate of reaction remains the same at any concentration of X**: This is the correct statement. In a zero-order reaction, the rate is independent of the concentration of the reactant \(X\).

4. **Rate of reaction is directly proportional to the square of concentration of X**: This is incorrect for a zero-order reaction, as this would imply a second-order reaction.

### Conclusion
The reaction \(2X \rightarrow Y + Z\) would be classified as a zero-order reaction when the rate of reaction remains the same at any concentration of \(X\). Therefore, the correct option is that the rate remains unchanged at any concentration of \(X\).

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