3. A reaction has a rate constant of 0.000122 s¹ at 27.0°C and 0.228 s'at 77.0°C. a. Determine the activation energy for this reaction. b. What is the value of the rate constant at 17.0°C?
3. A reaction has a rate constant of 0.000122 s¹ at 27.0°C and 0.228 s'at 77.0°C. a. Determine the activation energy for this reaction. b. What is the value of the rate constant at 17.0°C?
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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![**Title: Understanding Chemical Reaction Rates and Activation Energy**
**1. Measuring Reaction Rates as a Function of Temperature**
The rate constant (\(k\)) for a reaction was assessed based on temperature changes. A plot of \(\ln k\) versus \(1/T\) (in Kelvin) is linear with a slope of \(-1.01 \times 10^4\) K. To discover the activation energy for this reaction, the equation:
\[ E_a = -\text{slope} \times R \]
is used, where \(R\) is the gas constant (\(8.314 \text{ J/mol K}\)):
\[ E_a = -(-1.01 \times 10^4 \, \text{K}) \times 8.314 \, \text{J/mol K} \]
\[ E_a \approx 8.39 \times 10^4 \, \text{J/mol} \]
**2. Rate Constant Calculation at Different Temperatures**
For a reaction at 32.0°C with a rate constant of \(0.0550 \, \text{s}^{-1}\) and a frequency factor of \(1.20 \times 10^{13} \, \text{s}^{-1}\), the activation energy is calculated using:
\[ E_a = RT(\ln A - \ln k) \]
Substituting values and calculating energy:
\[ E_a \approx 89372.257 \, \text{J/mol} \]
**3. Calculating Activation Energy and Rate Constants at Various Conditions**
- **Given Conditions:**
- Rate constant at 27.0°C: \(0.000122 \, \text{s}^{-1}\)
- Rate constant at 77.0°C: \(0.228 \, \text{s}^{-1}\)
**a. Determine Activation Energy:**
- Utilize the Arrhenius equation.
**b. Rate Constant at 17.0°C:**
- Once activation energy is known, use it to find \(k\) at 17.0°C.
**4. Activation Energy in Biological Reactions**
An apple rots extensively in about 4.00 days at room temperature (25.0°C). If refrigerated at 5.0°C, rotting requires roughly 16.0 days. To determine activation energy for the rotting process,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a31084d-53de-40ac-8333-22b405fb7df5%2F170f1189-7982-4974-9c39-c9fd1dcbb8cb%2Fbcqqw3ri_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Chemical Reaction Rates and Activation Energy**
**1. Measuring Reaction Rates as a Function of Temperature**
The rate constant (\(k\)) for a reaction was assessed based on temperature changes. A plot of \(\ln k\) versus \(1/T\) (in Kelvin) is linear with a slope of \(-1.01 \times 10^4\) K. To discover the activation energy for this reaction, the equation:
\[ E_a = -\text{slope} \times R \]
is used, where \(R\) is the gas constant (\(8.314 \text{ J/mol K}\)):
\[ E_a = -(-1.01 \times 10^4 \, \text{K}) \times 8.314 \, \text{J/mol K} \]
\[ E_a \approx 8.39 \times 10^4 \, \text{J/mol} \]
**2. Rate Constant Calculation at Different Temperatures**
For a reaction at 32.0°C with a rate constant of \(0.0550 \, \text{s}^{-1}\) and a frequency factor of \(1.20 \times 10^{13} \, \text{s}^{-1}\), the activation energy is calculated using:
\[ E_a = RT(\ln A - \ln k) \]
Substituting values and calculating energy:
\[ E_a \approx 89372.257 \, \text{J/mol} \]
**3. Calculating Activation Energy and Rate Constants at Various Conditions**
- **Given Conditions:**
- Rate constant at 27.0°C: \(0.000122 \, \text{s}^{-1}\)
- Rate constant at 77.0°C: \(0.228 \, \text{s}^{-1}\)
**a. Determine Activation Energy:**
- Utilize the Arrhenius equation.
**b. Rate Constant at 17.0°C:**
- Once activation energy is known, use it to find \(k\) at 17.0°C.
**4. Activation Energy in Biological Reactions**
An apple rots extensively in about 4.00 days at room temperature (25.0°C). If refrigerated at 5.0°C, rotting requires roughly 16.0 days. To determine activation energy for the rotting process,
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