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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3)can someone explain the question
![### Chemical Kinetics Problem
**Problem Statement:**
"A reaction has a rate constant of 0.0117 M/s at 400.0 K and 0.689 M/s at 450.0 K. What is the activation energy of the reaction?"
**Graphical Explanation (if applicable):**
To calculate the activation energy, you can use the Arrhenius equation:
\[ k = A e^{-\frac{E_a}{RT}} \]
where:
- \( k \) is the rate constant,
- \( A \) is the pre-exponential factor,
- \( E_a \) is the activation energy,
- \( R \) is the universal gas constant (8.314 J/(mol·K)),
- \( T \) is the temperature in Kelvin.
Taking the natural logarithm of both sides gives:
\[ \ln(k) = \ln(A) - \frac{E_a}{RT} \]
For two different temperatures, the equation becomes:
\[ \ln\left(\frac{k_2}{k_1}\right) = -\frac{E_a}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right) \]
Given:
- \( k_{1} = 0.0117 \, \text{M/s} \) at \( T_{1} = 400.0 \, \text{K} \)
- \( k_{2} = 0.689 \, \text{M/s} \) at \( T_{2} = 450.0 \, \text{K} \)
We can solve for \( E_a \):
\[ \ln\left(\frac{0.689}{0.0117}\right) = -\frac{E_a}{8.314} \left( \frac{1}{450.0} - \frac{1}{400.0} \right) \]
Calculating the left side:
\[ \ln\left(\frac{0.689}{0.0117}\right) = \ln(58.8034) \approx 4.0732 \]
Calculating the right side:
\[ \frac{1}{450.0} - \frac{1}{400.0} = 0.002222 - 0.0025 = -0.000278 \]
Then:
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Transcribed Image Text:### Chemical Kinetics Problem
**Problem Statement:**
"A reaction has a rate constant of 0.0117 M/s at 400.0 K and 0.689 M/s at 450.0 K. What is the activation energy of the reaction?"
**Graphical Explanation (if applicable):**
To calculate the activation energy, you can use the Arrhenius equation:
\[ k = A e^{-\frac{E_a}{RT}} \]
where:
- \( k \) is the rate constant,
- \( A \) is the pre-exponential factor,
- \( E_a \) is the activation energy,
- \( R \) is the universal gas constant (8.314 J/(mol·K)),
- \( T \) is the temperature in Kelvin.
Taking the natural logarithm of both sides gives:
\[ \ln(k) = \ln(A) - \frac{E_a}{RT} \]
For two different temperatures, the equation becomes:
\[ \ln\left(\frac{k_2}{k_1}\right) = -\frac{E_a}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right) \]
Given:
- \( k_{1} = 0.0117 \, \text{M/s} \) at \( T_{1} = 400.0 \, \text{K} \)
- \( k_{2} = 0.689 \, \text{M/s} \) at \( T_{2} = 450.0 \, \text{K} \)
We can solve for \( E_a \):
\[ \ln\left(\frac{0.689}{0.0117}\right) = -\frac{E_a}{8.314} \left( \frac{1}{450.0} - \frac{1}{400.0} \right) \]
Calculating the left side:
\[ \ln\left(\frac{0.689}{0.0117}\right) = \ln(58.8034) \approx 4.0732 \]
Calculating the right side:
\[ \frac{1}{450.0} - \frac{1}{400.0} = 0.002222 - 0.0025 = -0.000278 \]
Then:
\[
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