For a zero-order reaction with rate constant k, the slope of the plot of reactant concentration against time is

Options

A. `k//2 . 303`
B. `k`
C. `-k//2. 303`
D. `-k`

Explanation

To solve the question regarding the slope of the plot of reactant concentration against time for a zero-order reaction, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Zero-Order Reactions**:
- A zero-order reaction is one where the rate of reaction is constant and does not depend on the concentration of the reactant. The rate law can be expressed as:
\[ \text{Rate} = -\frac{d[A]}{dt} = k \]
- Here, \( k \) is the rate constant.

2. **Integrating the Rate Equation**:
- Rearranging the rate equation gives:
\[ -d[A] = k \, dt \]
- Integrating both sides, we have:
\[ \int_{[A]_0}^{[A]} -d[A] = \int_{0}^{t} k \, dt \]
- This results in:
\[ -[A] + [A]_0 = kt \]
- Rearranging gives:
\[ [A] = [A]_0 - kt \]

3. **Identifying the Slope**:
- The equation \([A] = [A]_0 - kt\) is in the form of a linear equation \(y = mx + b\), where:
- \(y\) is the concentration \([A]\),
- \(m\) is the slope,
- \(x\) is time \(t\),
- \(b\) is the intercept \([A]_0\).
- From this equation, we can see that the slope \(m\) is equal to \(-k\).

4. **Conclusion**:
- Therefore, the slope of the plot of reactant concentration against time for a zero-order reaction is:
\[ \text{slope} = -k \]

### Final Answer:
The slope of the plot of reactant concentration against time for a zero-order reaction is \(-k\).