Which of the following graphs represents zero order if
`A rarr P` At `t = 0 rArr [A]_(0)` At `t = t rArr [A]_(t)`

Options

A.
B.
C.
D.

Explanation

To determine which graph represents a zero-order reaction for the reaction \( A \rightarrow P \), we need to analyze the characteristics of zero-order kinetics.

### Step-by-Step Solution:

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

2. **Mathematical Representation:**
- For a zero-order reaction, the relationship between the concentration of reactant \( [A] \) and time \( t \) can be described by the equation:
\[ [A]_0 - [A]_t = kt \]
- Rearranging this gives:
\[ [A]_t = [A]_0 - kt \]
- This equation indicates that a plot of \( [A]_t \) versus time \( t \) will yield a straight line with a negative slope of \( -k \) and an intercept of \( [A]_0 \).

3. **Graphical Representation:**
- The graph of \( [A]_t \) versus time \( t \) will be a straight line that starts at \( [A]_0 \) and decreases linearly over time.
- The slope of the line will be negative, indicating that the concentration of \( A \) decreases as time increases.

4. **Identifying the Correct Graph:**
- Among the given options, we need to look for a graph that shows a linear decrease in concentration over time, which corresponds to the equation derived above.

5. **Conclusion:**
- The correct graph that represents a zero-order reaction will be a straight line with a negative slope, indicating a constant rate of reaction over time.