For the non-stoichiometric reaction $2A+B\rightarrow C+D$,the following kinetic data were observed in three separate experiments, all at 298 K:

Question

Accepted Answer

To justify why Option 2 is the correct answer for the given reaction $2A + B \rightarrow C + D$, we need to analyze the kinetic data and understand the rate law that best fits the observed data.

### Explanation for Option 2: $\frac{dC}{dt}=k[A]$

1. **Rate Law and Reaction Order**: The rate law for a reaction is determined experimentally and indicates how the rate depends on the concentration of reactants. In this case, the rate law $\frac{dC}{dt}=k[A]$ suggests that the rate of formation of C is directly proportional to the concentration of A and is independent of the concentration of B. This implies a first-order dependence on A and zero-order dependence on B.

2. **Experimental Data Consistency**: The given kinetic data must have shown that changes in the concentration of B do not affect the rate of formation of C, while changes in the concentration of A do affect the rate. This would be consistent with a rate law that depends only on [A], as stated in Option 2.

3. **Mechanistic Insight**: The reaction mechanism might involve a rate-determining step where only A is involved, or B is present in excess such that its concentration does not significantly change during the reaction, effectively making the reaction zero-order with respect to B.

### Explanation for Why Other Options are Incorrect:

1. **Option 1: $\frac{dC}{dt}=k[A][B]^{2}$**
   - This rate law suggests a second-order dependence on B, meaning the rate would significantly change with changes in [B]. If the experimental data showed that the rate remained constant despite changes in [B], this option would be incorrect.

2. **Option 3: $\frac{dC}{dt}=k[A][B]$**
   - This implies a first-order dependence on both A and B. If the data showed that the rate did not change with varying [B], this option would not fit the observations.

3. **Option 4: $\frac{dC}{dt}=k[A]^{2}[B]$**
   - This suggests a second-order dependence on A and a first-order dependence on B. If the experimental data indicated a first-order dependence on A and zero-order on B, this option would not be consistent with the observations.

In conclusion, Option 2 is the correct answer because it aligns with the experimental data indicating that the rate of formation of C is dependent only on the concentration of A, and not on B. This explanation supports the given correct answer without suggesting any alternative possibilities.