For reaction, `2B+A rarr 2C`
Which of the following is correct ?

Options

A. Rate of disappearance of B is twice that of rate of disappearance of C
B. Rate of disappearance of A is twice that of rate of disappearance of C
C. Rate of appearance of C is twice that of rate of disappearance of A
D. All of these

Answer

To solve the question regarding the reaction \(2B + A \rightarrow 2C\), we need to analyze the rates of disappearance and appearance of the reactants and products involved in the reaction.

### Step-by-Step Solution:

1. **Write the Rate Expression**:
For the reaction \(2B + A \rightarrow 2C\), we can express the rate of the reaction in terms of the change in concentration of the reactants and products:
\[ \text{Rate} = -\frac{1}{2} \frac{d[B]}{dt} = -\frac{d[A]}{dt} = \frac{1}{2} \frac{d[C]}{dt} \]

2. **Analyze the Rate of Disappearance of B**:
From the rate expression, we can see that the rate of disappearance of \(B\) is:
\[ -\frac{d[B]}{dt} = 2 \cdot \frac{d[C]}{dt} \]
This means that the rate of disappearance of \(B\) is equal to the rate of appearance of \(C\), but it is not twice the rate of \(C\).

3. **Analyze the Rate of Disappearance of A**:
The rate of disappearance of \(A\) is:
\[ -\frac{d[A]}{dt} = \frac{d[C]}{dt} \]
This indicates that the rate of disappearance of \(A\) is equal to half the rate of appearance of \(C\).

4. **Analyze the Rate of Appearance of C**:
The rate of appearance of \(C\) can be expressed as:
\[ \frac{d[C]}{dt} = 2 \cdot \left(-\frac{d[A]}{dt}\right) \]
This means that the rate of appearance of \(C\) is twice the rate of disappearance of \(A\).

5. **Conclusion**:
Based on the analysis:
- The rate of disappearance of \(B\) is equal to the rate of appearance of \(C\).
- The rate of disappearance of \(A\) is half the rate of appearance of \(C\).
- The rate of appearance of \(C\) is twice the rate of disappearance of \(A\).

Therefore, the correct statement among the options provided is that the rate of appearance of \(C\) is twice the rate of disappearance of \(A\).

### Final Answer:
The correct option is that the rate of appearance of \(C\) is twice the rate of disappearance of \(A\).

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