Chemistry
Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
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Question
### Kinetics of a Chemical Reaction At a certain temperature, the reaction described below follows first-order kinetics with a rate constant of \(1.54 \, s^{-1}\): \[ \text{H}_2\text{CO}_3 (aq) \rightarrow \text{H}_2\text{O} (aq) + \text{CO}_2 (aq) \] **Problem Statement:** Suppose a vessel contains \(\text{H}_2\text{CO}_3\) at a concentration of \(1.09 \, M\). Calculate the concentration of \(\text{H}_2\text{CO}_3\) in the vessel \(0.390\) seconds later. You may assume no other reaction is important. Round your answer to 2 significant digits. **Solution Box:** \[ \boxed{M} \] --- **Instructions for Calculation:** 1. **Identify Initial Concentration (\([A]_0\))**: \[ [A]_0 = 1.09 \, M \] 2. **Rate Constant (\(k\))**: \[ k = 1.54 \, s^{-1} \] 3. **Time (\(t\))**: \[ t = 0.390 \, s \] 4. **Use the First-Order Kinetics Formula**: \[ [A] = [A]_0 e^{-kt} \] 5. **Calculate Concentration**: \[ [A] = 1.09 \, M \times e^{-1.54 \times 0.390} \] \[ [A] \approx 1.09 \, M \times 0.525 = 0.57 \, M \] **Answer:** \[ \boxed{0.57 \, M} \] --- This calculated value represents the concentration of \(\text{H}_2\text{CO}_3\) in the vessel after \(0.390\) seconds.
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Transcribed Image Text:### Kinetics of a Chemical Reaction At a certain temperature, the reaction described below follows first-order kinetics with a rate constant of \(1.54 \, s^{-1}\): \[ \text{H}_2\text{CO}_3 (aq) \rightarrow \text{H}_2\text{O} (aq) + \text{CO}_2 (aq) \] **Problem Statement:** Suppose a vessel contains \(\text{H}_2\text{CO}_3\) at a concentration of \(1.09 \, M\). Calculate the concentration of \(\text{H}_2\text{CO}_3\) in the vessel \(0.390\) seconds later. You may assume no other reaction is important. Round your answer to 2 significant digits. **Solution Box:** \[ \boxed{M} \] --- **Instructions for Calculation:** 1. **Identify Initial Concentration (\([A]_0\))**: \[ [A]_0 = 1.09 \, M \] 2. **Rate Constant (\(k\))**: \[ k = 1.54 \, s^{-1} \] 3. **Time (\(t\))**: \[ t = 0.390 \, s \] 4. **Use the First-Order Kinetics Formula**: \[ [A] = [A]_0 e^{-kt} \] 5. **Calculate Concentration**: \[ [A] = 1.09 \, M \times e^{-1.54 \times 0.390} \] \[ [A] \approx 1.09 \, M \times 0.525 = 0.57 \, M \] **Answer:** \[ \boxed{0.57 \, M} \] --- This calculated value represents the concentration of \(\text{H}_2\text{CO}_3\) in the vessel after \(0.390\) seconds.
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