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 follow these steps:

### Step 1: Understand the Zero Order Reaction
For a zero-order reaction, the rate of reaction is constant and the concentration of the reactant decreases linearly over time. The rate law for a zero-order reaction is given by:

\[ [A] = [A]_0 - kt \]

Where:
- \([A]\) is the concentration of A at time \(t\),
- \([A]_0\) is the initial concentration of A,
- \(k\) is the rate constant,
- \(t\) is the time.

### Step 2: Set Up the Equation
Given:
- Initial concentration, \([A]_0 = 0.1 \, M\)
- Concentration after 10 minutes, \([A] = 0.08 \, M\)
- Time, \(t = 10 \, \text{minutes}\)

We can substitute these values into the equation:

\[ 0.08 = 0.1 - k(10) \]

### Step 3: Solve for the Rate Constant \(k\)
Rearranging the equation to solve for \(k\):

\[ k(10) = 0.1 - 0.08 \]
\[ k(10) = 0.02 \]
\[ k = \frac{0.02}{10} = 0.002 \, M/min \]

### Step 4: Calculate Half-Life
The half-life (\(t_{1/2}\)) for a zero-order reaction is given by the formula:

\[ t_{1/2} = \frac{[A]_0}{2k} \]

Substituting the values we have:

\[ t_{1/2} = \frac{0.1}{2 \times 0.002} \]
\[ t_{1/2} = \frac{0.1}{0.004} = 25 \, \text{minutes} \]

### Step 5: Calculate Completion Time
The completion time (\(T_c\)) for a zero-order reaction can be calculated using:

\[ T_c = \frac{[A]_0}{k} \]

Substituting the values:

\[ T_c = \frac{0.1}{0.002} \]
\[ T_c = 50 \, \text{minutes} \]

### Final Answer
Thus, the half-life and completion time are:

- Half-life: **25 minutes**
- Completion time: **50 minutes**

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