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

Answer

To find the initial concentration of a zero-order reaction given the rate constant and the concentration after a certain time, we can use the formula for zero-order kinetics:

\[ A_0 = kt + A_t \]

Where:
- \( A_0 \) is the initial concentration,
- \( k \) is the rate constant,
- \( t \) is the time,
- \( A_t \) is the concentration at time \( t \).

### Step-by-Step Solution:

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

2. **Substitute the values into the formula:**
\[ A_0 = kt + A_t \]

3. **Calculate \( kt \):**
\[ kt = (2 \times 10^{-2} \, \text{mol L}^{-1} \text{sec}^{-1}) \times (25 \, \text{sec}) = 0.5 \, \text{mol L}^{-1} \]

4. **Now substitute \( kt \) and \( A_t \) into the equation:**
\[ A_0 = 0.5 \, \text{mol L}^{-1} + 0.5 \, \text{mol L}^{-1} \]

5. **Calculate \( A_0 \):**
\[ A_0 = 1.0 \, \text{mol L}^{-1} \]

6. **Conclusion:**
The initial concentration \( A_0 \) is \( 1.0 \, \text{M} \).

### Final Answer:
The initial concentration must have been \( 1.0 \, \text{M} \).

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