For the zero order reaction `AtoB+C`, initial concentration of A is 0.1 M. If [A]=0.08 M after 10 minutes,then its half-life and completion time are respectively :

Options

A. 10 min, 20 min
B. `2xx10^(-3)min,4xx10^(-3)min`
C. 25 min, 50 min
D. 250 min, 500 min

Answer

To solve the problem step by step, we will first determine the rate constant \( k \) for the zero-order reaction and then calculate the half-life and completion time.

### Step 1: Determine the Rate Constant \( k \)

For a zero-order reaction, the relationship between the concentration of reactant \( A \) and time \( t \) is given by the equation:

\[ C_t = C_0 - kt \]

Where:
- \( C_t \) = concentration of \( A \) at time \( t \)
- \( C_0 \) = initial concentration of \( A \)
- \( k \) = rate constant
- \( t \) = time

Given:
- \( C_0 = 0.1 \, \text{M} \)
- \( C_t = 0.08 \, \text{M} \)
- \( t = 10 \, \text{minutes} \)

Substituting the values into the equation:

\[ 0.08 = 0.1 - k \times 10 \]

Rearranging the equation to solve for \( k \):

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

### Step 2: Calculate the Half-Life \( t_{1/2} \)

The half-life for a zero-order reaction is given by the formula:

\[ t_{1/2} = \frac{C_0}{2k} \]

Substituting the values we found:

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

### Step 3: Calculate the Completion Time \( t_c \)

The completion time for a zero-order reaction can be calculated using the formula:

\[ t_c = \frac{C_0}{k} \]

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 \( t_{1/2} = 25 \, \text{minutes} \)
- Completion time \( t_c = 50 \, \text{minutes} \)

### Summary

The final answer is:
- Half-life: 25 minutes
- Completion time: 50 minutes