For a zero order reaction, the slope in the plot of [R] vs. time is

Options

A. `(-k)/(2.303)`
B. `-k`
C. `(+k)/(2.303)`
D. `+k`

Explanation

To solve the question regarding the slope in the plot of concentration [R] versus 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 characterized by a constant rate that is independent of the concentration of the reactant. The rate law for a zero-order reaction can be expressed as:
\[ r = -\frac{d[R]}{dt} = k \]
where \( k \) is the rate constant.

**Hint**: Recall that in a zero-order reaction, the rate does not depend on the concentration of the reactant.

2. **Rearranging the Rate Equation**:
From the rate law, we can rearrange it to express the change in concentration over time:
\[ -d[R] = k \, dt \]

**Hint**: Think about how to isolate the concentration change from the rate equation.

3. **Integrating the Equation**:
Integrating both sides from time \( t = 0 \) to \( t = t \) and from concentration \( [R]_0 \) to \( [R] \):
\[ \int_{[R]_0}^{[R]} d[R] = -k \int_{0}^{t} dt \]
This gives:
\[ [R] - [R]_0 = -kt \]

**Hint**: Remember that integration helps us find the relationship between concentration and time.

4. **Rearranging the Integrated Equation**:
Rearranging the equation results in:
\[ [R] = [R]_0 - kt \]
This equation is in the form of a straight line \( y = mx + c \), where:
- \( y \) is the concentration [R],
- \( m \) is the slope,
- \( x \) is time \( t \),
- \( c \) is the y-intercept, which is the initial concentration \([R]_0\).

**Hint**: Identify the components of the linear equation to relate them to the slope.

5. **Identifying the Slope**:
From the equation \( [R] = [R]_0 - kt \), we can see that the slope \( m \) is equal to \(-k\). Therefore, in the plot of concentration [R] versus time, the slope is:
\[ \text{slope} = -k \]

**Hint**: The slope in a linear equation is the coefficient of the variable \( t \).

6. **Conclusion**:
The slope in the plot of [R] versus time for a zero-order reaction is \(-k\).

**Final Answer**: The slope is \(-k\).