For a zero order reaction, the plot of concentration versus time is linear with

Options

A. Positive slope with zero intercept
B. positive slope with non-zero intercept
C. negative slope with non-zero intercept
D. parallel to time axis

Answer

To solve the question about the characteristics of a zero-order reaction, we will follow these steps:

### Step 1: Understand Zero-Order Reactions
A zero-order reaction is defined as a reaction where the rate of reaction is constant and does not depend on the concentration of the reactants. This means that the rate of formation of products is constant over time.

**Hint:** Remember that in a zero-order reaction, the rate is independent of the concentration of the reactants.

### Step 2: Write the Rate Law for a Zero-Order Reaction
The rate law for a zero-order reaction can be expressed as:
\[ \text{Rate} = -\frac{d[A]}{dt} = k \]
where \( k \) is the rate constant.

**Hint:** The rate constant \( k \) is a key feature of zero-order reactions and remains constant.

### Step 3: Integrate the Rate Law
To find the relationship between concentration and time, we can rearrange the rate law:
\[ -d[A] = k \, dt \]
Integrating both sides from the initial concentration \( [A_0] \) at time \( t = 0 \) to the concentration \( [A] \) at time \( t \):
\[ \int_{[A_0]}^{[A]} d[A] = -k \int_{0}^{t} dt \]

This gives us:
\[ [A] - [A_0] = -kt \]
Rearranging this, we find:
\[ [A] = [A_0] - kt \]

**Hint:** The integration shows how the concentration decreases linearly over time.

### Step 4: Identify the Linear Relationship
The equation \( [A] = [A_0] - kt \) can be compared to the equation of a straight line \( y = mx + c \), where:
- \( y \) is the concentration \( [A] \)
- \( m \) is the slope, which is \(-k\)
- \( x \) is time \( t \)
- \( c \) is the y-intercept, which is the initial concentration \( [A_0] \)

**Hint:** Recognize that the slope of the line is negative, indicating a decrease in concentration over time.

### Step 5: Conclusion
From the analysis, we conclude that for a zero-order reaction, the plot of concentration versus time is linear with a negative slope equal to \(-k\) and a y-intercept equal to the initial concentration \( [A_0] \).

**Final Answer:** The plot of concentration versus time for a zero-order reaction is linear with a negative slope.