For the reaction `A_(2)(g)+(1)/(8)B_(8)(g)rarrA_(2)B(g)` following data was obtained for a large concentration of `B_(8)` . What is the reaction order with respect to `A_(2)` ?
`{:("Time (min)",,[A_(2)]("moles"//L)xx10^(4)),(60,,292),(120,,198),(180,,104),(240,,010):}`

Options

A. Zero
B. One
C. Two
D. Indeterminate

Explanation

To determine the reaction order with respect to \( A_2 \) for the reaction \( A_2(g) + \frac{1}{8}B_8(g) \rightarrow A_2B(g) \), we will analyze the provided data on the concentration of \( A_2 \) over time.

### Step-by-Step Solution:

1. **Data Interpretation**:
We have the following data for the concentration of \( A_2 \) (in moles per liter multiplied by \( 10^4 \)) at different time intervals:
- At 60 min: \( [A_2] = 292 \times 10^{-4} \)
- At 120 min: \( [A_2] = 198 \times 10^{-4} \)
- At 180 min: \( [A_2] = 104 \times 10^{-4} \)
- At 240 min: \( [A_2] = 10 \times 10^{-4} \)

2. **Calculate the Change in Concentration**:
We will calculate the change in concentration of \( A_2 \) over equal time intervals (60 minutes):
- From 60 to 120 min:
\[ \Delta [A_2] = 198 - 292 = -94 \times 10^{-4} \]
- From 120 to 180 min:
\[ \Delta [A_2] = 104 - 198 = -94 \times 10^{-4} \]
- From 180 to 240 min:
\[ \Delta [A_2] = 10 - 104 = -94 \times 10^{-4} \]

3. **Observation of Rate of Reaction**:
The change in concentration \( \Delta [A_2] \) is constant (-94) over equal time intervals (60 minutes). This indicates that the rate of reaction is constant.

4. **Determining Reaction Order**:
Since the concentration of \( A_2 \) decreases by a constant amount in equal time intervals, we can conclude that the reaction is zero-order with respect to \( A_2 \). In a zero-order reaction, the rate of reaction is independent of the concentration of the reactant.

5. **Conclusion**:
Therefore, the reaction order with respect to \( A_2 \) is **0**.

### Final Answer:
The reaction order with respect to \( A_2 \) is **0**.