**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.

According to Arrhenius equation activation energy is determined by the negative slope of the graph.

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

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

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Question

**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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