For the zero order reaction `A rarr B+C,` initial concentration of A is `0.1A`. If `A=0.08M` after 10 minutes, then it's half`-` life and completion time are respectively `:`

Options

A. 10 min, 20 min
B. `2xx10^(-3)` min, `10^(-3)` min
C. 25 min, 50 min
D. 250 min, 500 min

Explanation

To solve the problem, we need to find the half-life and completion time for the zero-order reaction \( A \rightarrow B + C \) given the initial concentration of \( A \) and its concentration after a certain time.

### Step-by-Step Solution:

1. **Identify the given data:**
- Initial concentration of \( A \) (\( [A]_0 \)) = 0.1 M
- Concentration of \( A \) after 10 minutes (\( [A]_t \)) = 0.08 M
- Time (\( t \)) = 10 minutes

2. **Calculate the change in concentration of \( A \):**
\[ \Delta [A] = [A]_0 - [A]_t = 0.1 \, \text{M} - 0.08 \, \text{M} = 0.02 \, \text{M} \]

3. **Use the formula for the rate constant \( k \) for a zero-order reaction:**
\[ k = \frac{\Delta [A]}{t} = \frac{0.02 \, \text{M}}{10 \, \text{min}} = 0.002 \, \text{M/min} \]

4. **Calculate the completion time:**
- The completion time (\( t_{completion} \)) for a zero-order reaction can be calculated using:
\[ t_{completion} = \frac{[A]_0}{k} = \frac{0.1 \, \text{M}}{0.002 \, \text{M/min}} = 50 \, \text{minutes} \]

5. **Calculate the half-life (\( t_{1/2} \)) for a zero-order reaction:**
- The half-life for a zero-order reaction is given by:
\[ t_{1/2} = \frac{t_{completion}}{2} = \frac{50 \, \text{minutes}}{2} = 25 \, \text{minutes} \]

### Final Results:
- Half-life (\( t_{1/2} \)) = 25 minutes
- Completion time (\( t_{completion} \)) = 50 minutes