At a certain temperature this reaction follows first-order kinetics with a rate constant of 1.54 s ': H,CO, (aq) → H,0 (aq)+ CO, (aq) Suppose a vessel contains H,CO, at a concentration of 1.09M. Calculate the concentration of H,CO, in the vessel 0.390 seconds later. You may assume no other reaction is important. Round your answer to 2 significant digits. | M
At a certain temperature this reaction follows first-order kinetics with a rate constant of 1.54 s ': H,CO, (aq) → H,0 (aq)+ CO, (aq) Suppose a vessel contains H,CO, at a concentration of 1.09M. Calculate the concentration of H,CO, in the vessel 0.390 seconds later. You may assume no other reaction is important. Round your answer to 2 significant digits. | M
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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![### 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F76b6cb9f-216e-4f5f-860c-25f99efb2a99%2Fbe988707-2e3b-4dae-917c-0f8359fa5acf%2Fxznga1q_processed.png&w=3840&q=75)
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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