A reaction is `10%` complete in `5min` and `50%` complete in `25 min`. Which of the following is/are correct?

Options

A. a. Order of reaction is one.
B. b. Order of reaction is zero.
C. c. Reaction will be complete in finite time.
D. d. Reaction will be complete in infinite time.

Answer

To solve the problem, we need to analyze the completion percentages of the reaction over time and determine the order of the reaction based on the given data.

### Step-by-Step Solution:

1. **Understanding the Data**:
- The reaction is 10% complete in 5 minutes.
- The reaction is 50% complete in 25 minutes.

2. **Calculating Completion Rates**:
- From 0% to 10% completion takes 5 minutes.
- From 10% to 50% completion takes an additional 20 minutes (from 5 minutes to 25 minutes).
- This indicates that as the reaction progresses, the time taken for each percentage of completion is increasing.

3. **Identifying the Reaction Order**:
- For a zero-order reaction, the rate of reaction is constant, and the time taken for completion is directly proportional to the extent of the reaction.
- In this case, if we observe that the time taken increases linearly with the percentage completion (5 minutes for 10% and 25 minutes for 50%), it suggests that the rate of reaction is constant, which is characteristic of a zero-order reaction.

4. **Conclusion about the Reaction**:
- Since the time taken for the reaction to reach 50% completion is five times that for 10% completion, it indicates that the reaction does not depend on the concentration of the reactants, confirming that it is a zero-order reaction.

5. **Finite Time for Completion**:
- In a zero-order reaction, the reaction will eventually reach completion in a finite amount of time. Therefore, it can be concluded that the reaction will complete in finite time.

### Final Answer:
Based on the analysis, the correct options are:
- Option B: The order of the reaction is zero.
- Option C: The reaction will complete in finite time.