### Example Problem: Second Order Reaction of an Isomer**Problem Statement:**An isomer, A, dimerizes as follows:\[ 2A \rightarrow A_2 \]This process is known to be second order in the reactant, and the rate constant, \(k\), is known to be 0.276 L mol\(^{-1}\)s\(^{-1}\) at 25 °C. In an experiment, A was placed in a container at 25 °C where \([A]_0 = 8.602 \times 10^{-2} \, \text{M}\). Calculate the concentration of \(A_2\) (in units of M) after 3.98 minutes.**Incorrect Student Answer:**\[ \textrm{Answer: } 0.01289 \]This answer was marked incorrect.**Correct Answer:**The correct concentration of \(A_2\) (in units of M) after 3.98 minutes is:\[ 0.0365612 \]### Detailed ExplanationFor a second-order reaction, the rate law is given by:\[ \frac{1}{[A]} = kt + \frac{1}{[A]_0} \]**Where:**- \([A]\) is the concentration of \(A\) at time \(t\)- \(k\) is the rate constant- \([A]_0\) is the initial concentration of \(A\)- \(t\) is the time the reaction has been running**Calculations:**Given data:- Rate constant, \(k = 0.276 \, \text{L mol}^{-1} \text{s}^{-1} \)- Initial concentration, \([A]_0 = 8.602 \times 10^{-2} \, \text{M} \)- Time, \(t = 3.98 \, \text{min} = 3.98 \times 60 \, \text{s} = 238.8 \, \text{s} \)Plugging these values into the second-order rate equation:\[ \frac{1}{[A]} = (0.276 \, \text{L mol}^{-1} \text{s}^{-1})(238.8 \, \text{s}) + \frac{1}{8.602

Answered: Image /qna-images/answer/580bd32c-31cd-42df-b6ac-4d4b062fb811.jpg

An isomer, A, dimerize as follows: 2 A - A2 This process is known to be second order in the reactant, and the rate constant, k, is know to be 0.276 L mol-is-1 at 25 °C. In an experiment, A was placed in a container at 25 °C where [A], = 8.602 x 10-2 M. Calculate the concentration of A2 (in units of M) after 3.98 min. Answer: 0.01289

An isomer, A, dimerize as follows: 2 A - A2 This process is known to be second order in the reactant, and the rate constant, k, is know to be 0.276 L mol-is-1 at 25 °C. In an experiment, A was placed in a container at 25 °C where [A], = 8.602 x 10-2 M. Calculate the concentration of A2 (in units of M) after 3.98 min. Answer: 0.01289

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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