Chemistry
Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
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Question
### Second Order Reaction Kinetics #### Problem Statement The rate constant for this second-order reaction is \(0.780 \, \text{M}^{-1} \cdot \text{s}^{-1}\) at 300 °C. \[ \text{A} \rightarrow \text{products} \] How long, in seconds, would it take for the concentration of A to decrease from 0.740 M to 0.260 M? --- #### Incorrect Attempt \[ t = \textbf{1.28} \quad \text{(Incorrect)} \] --- ### Explanation To solve this problem, we use the integrated rate law for a second-order reaction, which is given by: \[ \frac{1}{[A]} = \frac{1}{[A]_0} + kt \] where: - \([A]_0\) is the initial concentration of A. - \([A]\) is the concentration of A at time \( t \). - \( k \) is the rate constant. Given data: - \([A]_0\) = 0.740 M - \([A]\) = 0.260 M - \( k \) = 0.780 M\(^{-1}\) s\(^{-1}\) Substitute these values into the integrated rate law formula to solve for \( t \): \[ \frac{1}{0.260} - \frac{1}{0.740} = 0.780 \cdot t \] --- By solving the equation, you can find the correct time \( t \) that it takes for the concentration of A to decrease to the given value.
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Transcribed Image Text:### Second Order Reaction Kinetics #### Problem Statement The rate constant for this second-order reaction is \(0.780 \, \text{M}^{-1} \cdot \text{s}^{-1}\) at 300 °C. \[ \text{A} \rightarrow \text{products} \] How long, in seconds, would it take for the concentration of A to decrease from 0.740 M to 0.260 M? --- #### Incorrect Attempt \[ t = \textbf{1.28} \quad \text{(Incorrect)} \] --- ### Explanation To solve this problem, we use the integrated rate law for a second-order reaction, which is given by: \[ \frac{1}{[A]} = \frac{1}{[A]_0} + kt \] where: - \([A]_0\) is the initial concentration of A. - \([A]\) is the concentration of A at time \( t \). - \( k \) is the rate constant. Given data: - \([A]_0\) = 0.740 M - \([A]\) = 0.260 M - \( k \) = 0.780 M\(^{-1}\) s\(^{-1}\) Substitute these values into the integrated rate law formula to solve for \( t \): \[ \frac{1}{0.260} - \frac{1}{0.740} = 0.780 \cdot t \] --- By solving the equation, you can find the correct time \( t \) that it takes for the concentration of A to decrease to the given value.
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