The reaction `A+2Bto` product, is first order in A and second order in B. If `t_(1//2)` w.r.t. A is same as the `t_(1//2)` of the reaction.

Options

A. `[A]_("Initial")gt[B]_("Initial")`
B. `[A]_("Initial")=[B]_("Initial")`
C. A is the limiting reactant
D. B is the limiting reactant

Answer

To solve the given problem, we need to analyze the reaction and the information provided about its order and half-life.

### Step-by-Step Solution:

1. **Understanding the Reaction**:
The reaction given is:
\[ A + 2B \rightarrow \text{Products} \]
It is stated that this reaction is first order in A and second order in B.

2. **Order of Reaction**:
- The overall order of the reaction can be calculated by adding the orders with respect to each reactant:
- Order with respect to A = 1 (first order)
- Order with respect to B = 2 (second order)
- Therefore, the overall order of the reaction is:
\[ \text{Overall Order} = 1 + 2 = 3 \]

3. **Half-Life of the Reaction**:
The half-life (\(t_{1/2}\)) of a reaction is the time required for the concentration of a reactant to decrease to half of its initial concentration.

For a reaction that is first order in A and second order in B, the half-life expressions are different:
- For a first-order reaction, the half-life is given by:
\[ t_{1/2} = \frac{0.693}{k[A]_0} \]
- For a second-order reaction, the half-life is given by:
\[ t_{1/2} = \frac{1}{k[B]_0} \]

4. **Condition Given in the Question**:
The question states that the half-life with respect to A is the same as the half-life of the reaction. This implies:
\[ t_{1/2} \text{ (with respect to A)} = t_{1/2} \text{ (overall reaction)} \]

5. **Implications of the Condition**:
For the half-lives to be equal, it suggests that the concentration of A is very low compared to B. This means that A is the limiting reactant. As A is consumed, the reaction stops, and thus the rate of reaction is primarily dependent on the concentration of B.

6. **Conclusion**:
Therefore, the condition where the half-life of A equals the half-life of the overall reaction occurs when A is the limiting reagent. This leads us to conclude that the correct option is that A is in excess or limiting.

### Final Answer:
The correct option is that A is a limiting reactant.