Math Problem Statement
Solution
To solve for (activation energy) and using the given Arrhenius equation data:
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The Arrhenius equation is:
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We have two data points for at different temperatures:
- at
- at
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Using the equation: Substitute the known values:
Calculating the terms: Therefore: Rearranging to solve for : Converting to kJ:
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To find , we use: Using the first data point: Calculating the term: So:
Final Answers:
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Relative Questions:
- What is the significance of the activation energy in a chemical reaction?
- How does temperature influence the rate of a reaction according to the Arrhenius equation?
- What other methods can be used to determine activation energy experimentally?
- How does the pre-exponential factor relate to molecular collisions and reaction orientation?
- Can you derive the Arrhenius equation from first principles of kinetics?
Tip:
When calculating activation energy, small changes in temperature can have a significant impact on reaction rates; precise measurements and calculations are key!
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Math Problem Analysis
Mathematical Concepts
Logarithmic Equations
Linear Equations
Chemical Kinetics
Formulas
Arrhenius equation: \(\ln k = \ln A - \frac{E}{R} \times \frac{1}{T}\)
Two-point form of Arrhenius equation: \(\ln k_2 - \ln k_1 = -\frac{E}{R} \left(\frac{1}{T_2} - \frac{1}{T_1}\right)\)
Theorems
Arrhenius Equation
Suitable Grade Level
Undergraduate Chemistry
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