The rate constant for zero order reaction is

Options

A. `A. k = (c_(0))/(2t)`
B. `B..k = ((c_(0)-c_(t)))/(t)`
C. `C. k = ln((c_(0)-c_(t))/(2t))`
D. `D. k = (c_(0))/(c_(t))`

Explanation

To find the rate constant for a zero-order reaction, we can follow these steps:

### Step-by-Step Solution:

1. **Write the Rate Expression**:
For a zero-order reaction, the rate of reaction can be expressed as:
\[ -\frac{d[A]}{dt} = k \]
where \( k \) is the rate constant.

2. **Rearranging the Equation**:
Rearranging the equation gives:
\[ -d[A] = k \, dt \]

3. **Integrate Both Sides**:
We will integrate both sides. The left side will be integrated with respect to concentration \( [A] \) and the right side with respect to time \( t \):
\[ \int_{[A]_0}^{[A]_t} -d[A] = \int_{0}^{t} k \, dt \]

4. **Setting Up the Limits**:
Here, \( [A]_0 \) is the initial concentration at time \( t = 0 \) and \( [A]_t \) is the concentration at time \( t \). The limits for the left side will be from \( [A]_0 \) to \( [A]_t \) and for the right side from \( 0 \) to \( t \).

5. **Performing the Integration**:
The integration results in:
\[ -[A]_t + [A]_0 = kt \]
Rearranging gives:
\[ [A]_0 - [A]_t = kt \]

6. **Expressing the Rate Constant**:
To find the rate constant \( k \), we rearrange the equation:
\[ k = \frac{[A]_0 - [A]_t}{t} \]

### Conclusion:
The rate constant \( k \) for a zero-order reaction is given by:
\[ k = \frac{[A]_0 - [A]_t}{t} \]