Determining Reaction Order from a Concentration vs. Time Plot

Q6. Using the following plot, determine the order of the rate law of this reaction: A (aq) → X (aq) + Y (aq)

Background

Topic: Chemical Kinetics – Reaction Order

This question tests your ability to interpret kinetic data from a plot and relate it to the order of a reaction. The plot shows how the inverse of the concentration of A changes with time.

Key Terms and Formulas

• Reaction Order: The power to which the concentration of a reactant is raised in the rate law.

• Integrated Rate Laws:

  • For a zero-order reaction: $[A] = [A]_0 - kt$

  • For a first-order reaction: $\ln([A]) = \ln([A]_0) - kt$

  • For a second-order reaction: $\frac{1}{[A]} = \frac{1}{[A]_0} + kt$

Step-by-Step Guidance

1. Examine the axes of the plot: the y-axis is $\frac{1}{[A]_0}$ (inverse concentration), and the x-axis is time (s).

2. Recall the integrated rate laws for different reaction orders. For a second-order reaction, plotting $\frac{1}{[A]}$ versus time yields a straight line.

3. Observe that the plot shows a linear relationship between $\frac{1}{[A]_0}$ and time, which matches the second-order integrated rate law.

4. Compare this to the other rate laws: zero-order would be linear in $[A]$ vs. time, and first-order would be linear in $\ln([A])$ vs. time.

Try solving on your own before revealing the answer!