Question

Consider a second order reaction, \( 2A \rightarrow \text{Product} \).
The concentration of A is represented as \( [A] \).
Which of the following is the CORRECT plot for determining the rate constant for the above reaction?

• A. ( \log[A] \) vs time
• B. ( [A] \) vs time
• C. ( \frac{1}{[A]} \) vs time
• D. ( \frac{1}{[A]} \) vs time

Hint:

For a second-order reaction, plotting \( \frac{1}{[A]} \) against time gives a straight line with slope \( k \), which allows for the determination of the rate constant.

Answer 1

The Correct Option is C

Step 1: Understand the rate law for second-order reactions.
For a second-order reaction, the rate law is: \[ \text{Rate} = k[A]^2 \] The integrated form of the rate law for a second-order reaction is: \[ \frac{1}{[A]} = kt + \frac{1}{[A_0]} \] where \( [A_0] \) is the initial concentration of \( A \), and \( k \) is the rate constant.
Step 2: Identify the correct plot.
The integrated rate law for a second-order reaction shows that a plot of \( \frac{1}{[A]} \) vs time gives a straight line with slope \( k \).
Step 3: Conclusion.
The correct plot is option (C), where \( \frac{1}{[A]} \) is plotted against time.