Which of the following statement is correct for a reaction X + 2Y —> prodcuts

Options

A. The rate of disappearance of X = twice the rate of disappearance of Y
B. The rate of disappearance of X = 1/2 rate of appearance of products
C. The rate of appearance of products =1/2 the rate of disappearance of Y
D. The rate of appearance of products =1/2 the rate of disappearance of X

Answer

To determine which statement is correct for the reaction \( X + 2Y \rightarrow \text{products} \), we need to analyze the rates of disappearance of the reactants and the rate of appearance of the products based on the stoichiometry of the reaction.

### Step-by-Step Solution:

1. **Write the Rate Law Expression**:
For the reaction \( X + 2Y \rightarrow \text{products} \), we can express the rates of disappearance of the reactants and the rate of appearance of the products as follows:
\[ -\frac{dx}{dt} = \frac{1}{2} \left(-\frac{dy}{dt}\right) = \frac{dP}{dt} \]
Here, \( P \) represents the concentration of the products formed.

2. **Analyze the Stoichiometry**:
From the balanced equation, we see that:
- 1 mole of \( X \) reacts with 2 moles of \( Y \).
- Therefore, for every 1 mole of \( X \) that disappears, 2 moles of \( Y \) disappear.

3. **Relate the Rates**:
Based on the stoichiometric coefficients:
- The rate of disappearance of \( X \) is half the rate of disappearance of \( Y \):
\[ -\frac{dx}{dt} = \frac{1}{2} \left(-\frac{dy}{dt}\right) \]
- The rate of appearance of products is equal to the rate of disappearance of \( X \):
\[ \frac{dP}{dt} = -\frac{dx}{dt} \]

4. **Evaluate the Statements**:
Now let's evaluate the given options:
- **Option 1**: The rate of disappearance of \( X \) is twice the rate of disappearance of \( Y \) (Incorrect).
- **Option 2**: The rate of disappearance of \( X \) is half the rate of disappearance of \( Y \) (Correct).
- **Option 3**: The rate of appearance of products is half the rate of disappearance of \( Y \) (Incorrect).
- **Option 4**: The rate of appearance of products is half the rate of disappearance of \( X \) (Incorrect).

5. **Conclusion**:
The correct statement is that the rate of disappearance of \( X \) is half the rate of disappearance of \( Y \).

### Final Answer:
The correct statement for the reaction \( X + 2Y \rightarrow \text{products} \) is that the rate of disappearance of \( X \) is half the rate of disappearance of \( Y \).

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