The hydrolysis of СІ (CH2)6C CH3 in 80% ethanol follows the first-order rate equation. The values of the specific reaction rate constants are as follows: t°C 0 25 35 45 k/s-1 : 1.06 X 10-5 3.19 x 10-4 9.86 x 10-4 2.92 x 10-3 (a) Plot log k against 1/T. (b) Calculate the activation energy, (c) Calculate the pre-exponential factor
The hydrolysis of СІ (CH2)6C CH3 in 80% ethanol follows the first-order rate equation. The values of the specific reaction rate constants are as follows: t°C 0 25 35 45 k/s-1 : 1.06 X 10-5 3.19 x 10-4 9.86 x 10-4 2.92 x 10-3 (a) Plot log k against 1/T. (b) Calculate the activation energy, (c) Calculate the pre-exponential factor
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ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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Chapter1: Chemical Foundations
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The hydrolysis of СІ (CH2)6C CH3 in 80% ethanol follows the first-order rate equation. The values of the specific reaction rate constants are as follows:
t°C 0 25 35 45
k/s-1 : 1.06 X 10-5 3.19 x 10-4 9.86 x 10-4 2.92 x 10-3
(a) Plot log k against 1/T. (b) Calculate the activation energy, (c) Calculate the pre-exponential factor.
![**The Hydrolysis of (CH2)6C(CH3)Cl in 80% Ethanol**
**Background:**
The hydrolysis reaction follows a first-order rate equation. The specific reaction rate constants for various temperatures are provided below:
| Temperature (°C) | \( k \) (s\(^{-1}\)) |
|------------------|---------------------|
| 0 | \( 1.06 \times 10^{-5} \) |
| 25 | \( 3.19 \times 10^{-4} \) |
| 35 | \( 9.86 \times 10^{-4} \) |
| 45 | \( 2.92 \times 10^{-3} \) |
**Tasks:**
(a) **Plot \( \log k \) against \( 1/T \):**
- Create a plot where the x-axis represents \( 1/T \) (inverse of temperature in Kelvin) and the y-axis represents \( \log k \) (logarithm of the specific reaction rate constant). This plot is used to determine the activation energy graphically using the Arrhenius equation.
(b) **Calculate the Activation Energy:**
- Use the Arrhenius equation:
\[ \log k = \log A - \frac{E_a}{2.303RT} \]
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
- Determine \( E_a \) from the slope of the line in the plot from part (a).
(c) **Calculate the Pre-Exponential Factor:**
- Using the plot data and the calculated \( E_a \), determine the pre-exponential factor \( A \) from the intercept of the plot. This factor represents the frequency of collisions that result in a reaction.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2589f1d7-658f-47e2-bb7c-ee63dc2fc7e0%2Fb7c73e96-8582-4f3c-9955-8c4e6e5837db%2F19rhx0o_processed.png&w=3840&q=75)
Transcribed Image Text:**The Hydrolysis of (CH2)6C(CH3)Cl in 80% Ethanol**
**Background:**
The hydrolysis reaction follows a first-order rate equation. The specific reaction rate constants for various temperatures are provided below:
| Temperature (°C) | \( k \) (s\(^{-1}\)) |
|------------------|---------------------|
| 0 | \( 1.06 \times 10^{-5} \) |
| 25 | \( 3.19 \times 10^{-4} \) |
| 35 | \( 9.86 \times 10^{-4} \) |
| 45 | \( 2.92 \times 10^{-3} \) |
**Tasks:**
(a) **Plot \( \log k \) against \( 1/T \):**
- Create a plot where the x-axis represents \( 1/T \) (inverse of temperature in Kelvin) and the y-axis represents \( \log k \) (logarithm of the specific reaction rate constant). This plot is used to determine the activation energy graphically using the Arrhenius equation.
(b) **Calculate the Activation Energy:**
- Use the Arrhenius equation:
\[ \log k = \log A - \frac{E_a}{2.303RT} \]
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
- Determine \( E_a \) from the slope of the line in the plot from part (a).
(c) **Calculate the Pre-Exponential Factor:**
- Using the plot data and the calculated \( E_a \), determine the pre-exponential factor \( A \) from the intercept of the plot. This factor represents the frequency of collisions that result in a reaction.
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