7. Consider the following graphs of In k versus 1/T for reactions A, B, C, and D. D In k In k 1 1 I (K-I) T (K-I) Which reaction of the four (A, B, C, or D) would have the largest activation energy? Explain how you know your answer.
7. Consider the following graphs of In k versus 1/T for reactions A, B, C, and D. D In k In k 1 1 I (K-I) T (K-I) Which reaction of the four (A, B, C, or D) would have the largest activation energy? Explain how you know your answer.
Chemistry
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ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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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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![**Title: Understanding Activation Energy from Arrhenius Plots**
**7. Consider the following graphs of ln k versus 1/T for reactions A, B, C, and D:**
- **Graph 1:**
- **Axes:** The x-axis represents \( \frac{1}{T} \) (in \( K^{-1} \)). The y-axis represents \( \ln k \).
- **Lines:**
- Line A: Steepest slope.
- Line B: Less steep compared to A.
- **Graph 2:**
- **Axes:** The x-axis represents \( \frac{1}{T} \) (in \( K^{-1} \)). The y-axis represents \( \ln k \).
- **Lines:**
- Line C: Steep slope.
- Line D: Less steep compared to C.
**Question:** Which reaction of the four (A, B, C, or D) would have the largest activation energy? Explain how you know your answer.
**Explanation:**
The activation energy (Ea) of a reaction can be determined from the slope of the line in an Arrhenius plot (ln k versus \( \frac{1}{T} \)). The slope of the line in these graphs is given by \( -\frac{Ea}{R} \), where \( R \) is the gas constant. A steeper slope indicates a larger magnitude of \( -\frac{Ea}{R} \), and therefore a larger activation energy.
Based on the provided graphs:
- Reaction A has the steepest slope, indicating the largest negative slope.
- Therefore, Reaction A has the largest activation energy, as its slope \( -\frac{Ea}{R} \) has the greatest absolute value.
The relative steepness of the lines indicates the order of activation energies:
- **Largest activation energy:** Reaction A
- **Next largest activation energy:** Reaction B, followed by C, and finally D.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa755e52e-afcf-45db-bf55-07fc4c384d8b%2F118a1eaf-0d0c-41f7-9684-e3f5930a636e%2Fnlu3nxb_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Activation Energy from Arrhenius Plots**
**7. Consider the following graphs of ln k versus 1/T for reactions A, B, C, and D:**
- **Graph 1:**
- **Axes:** The x-axis represents \( \frac{1}{T} \) (in \( K^{-1} \)). The y-axis represents \( \ln k \).
- **Lines:**
- Line A: Steepest slope.
- Line B: Less steep compared to A.
- **Graph 2:**
- **Axes:** The x-axis represents \( \frac{1}{T} \) (in \( K^{-1} \)). The y-axis represents \( \ln k \).
- **Lines:**
- Line C: Steep slope.
- Line D: Less steep compared to C.
**Question:** Which reaction of the four (A, B, C, or D) would have the largest activation energy? Explain how you know your answer.
**Explanation:**
The activation energy (Ea) of a reaction can be determined from the slope of the line in an Arrhenius plot (ln k versus \( \frac{1}{T} \)). The slope of the line in these graphs is given by \( -\frac{Ea}{R} \), where \( R \) is the gas constant. A steeper slope indicates a larger magnitude of \( -\frac{Ea}{R} \), and therefore a larger activation energy.
Based on the provided graphs:
- Reaction A has the steepest slope, indicating the largest negative slope.
- Therefore, Reaction A has the largest activation energy, as its slope \( -\frac{Ea}{R} \) has the greatest absolute value.
The relative steepness of the lines indicates the order of activation energies:
- **Largest activation energy:** Reaction A
- **Next largest activation energy:** Reaction B, followed by C, and finally D.
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