The rate constant for a zero order reaction is `2xx10^(-2) mol L^(-1) sec^(-1)`. If the concentration of the reactant after `25 sec` is `0.5 M`, the initial concentration must have been:

Options

A. `0.5 M`
B. `1.25 M`
C. `12.5 M`
D. `1.0 M`

Explanation

To solve the problem, we will use the formula for a zero-order reaction, which relates the initial concentration, the concentration at a given time, the rate constant, and the time elapsed. The formula is:

\[ C_0 - C_t = k \cdot t \]

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

### Step-by-Step Solution:

1. **Identify the given values:**
- Rate constant \( k = 2 \times 10^{-2} \, \text{mol L}^{-1} \text{sec}^{-1} \)
- Concentration after 25 seconds \( C_t = 0.5 \, \text{M} \)
- Time \( t = 25 \, \text{sec} \)

2. **Substitute the known values into the zero-order reaction formula:**
\[ C_0 - C_t = k \cdot t \]
becomes
\[ C_0 - 0.5 = (2 \times 10^{-2}) \cdot 25 \]

3. **Calculate \( k \cdot t \):**
\[ k \cdot t = (2 \times 10^{-2}) \cdot 25 = 0.5 \]

4. **Rearranging the equation to find \( C_0 \):**
\[ C_0 = C_t + k \cdot t \]
Substitute the values:
\[ C_0 = 0.5 + 0.5 \]

5. **Calculate \( C_0 \):**
\[ C_0 = 1.0 \, \text{M} \]

### Final Answer:
The initial concentration \( C_0 \) must have been **1.0 M**.