In a reaction `2X+Y rarrX_(2),Y` the reactant `X` will disappear at

Options

A. Half the rats as that of disappearance of `Y`
B. The same rate as that of disappearance of `Y`
C. Twice the rate as that of appearance of `X_(2)Y`
D. Twice the rate as that of disappearance of `Y`

Explanation

To solve the question regarding the disappearance of the reactant \(X\) in the reaction \(2X + Y \rightarrow X_2 + Y\), we will analyze the stoichiometry of the reaction and the rates of disappearance and appearance of the species involved.

### Step-by-Step Solution:

1. **Write the balanced chemical equation**:
\[ 2X + Y \rightarrow X_2 + Y \]

2. **Identify the stoichiometric coefficients**:
In the balanced equation, the stoichiometric coefficients are:
- For \(X\): 2
- For \(Y\): 1
- For \(X_2\): 1

3. **Define the rate of reaction**:
The rate of reaction can be expressed in terms of the change in concentration of the reactants and products. The rate of disappearance of \(X\) can be written as:
\[ \text{Rate} = -\frac{1}{2} \frac{d[X]}{dt} \]
Here, the negative sign indicates that the concentration of \(X\) is decreasing, and we divide by the stoichiometric coefficient (2) to account for the fact that 2 moles of \(X\) are consumed for every reaction.

4. **Relate the rates of disappearance and appearance**:
The rate of disappearance of \(Y\) can be expressed as:
\[ \text{Rate} = -\frac{d[Y]}{dt} \]
The rate of formation of \(X_2\) can be expressed as:
\[ \text{Rate} = \frac{d[X_2]}{dt} \]

5. **Establish relationships between the rates**:
From the stoichiometry of the reaction, we can establish the following relationships:
\[ -\frac{1}{2} \frac{d[X]}{dt} = -\frac{d[Y]}{dt} = \frac{d[X_2]}{dt} \]

6. **Express the rate of disappearance of \(X\)**:
Rearranging the equation gives:
\[ \frac{d[X]}{dt} = -2 \frac{d[Y]}{dt} \]
This indicates that the rate of disappearance of \(X\) is twice the rate of disappearance of \(Y\).

7. **Conclusion**:
Therefore, the reactant \(X\) will disappear at twice the rate of the disappearance of \(Y\).

### Final Answer:
The reactant \(X\) will disappear at twice the rate of disappearance of \(Y\).

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