Table of contents

1. Intro to General Chemistry3h 48m
2. Atoms & Elements4h 16m
3. Chemical Reactions4h 10m
4. BONUS: Lab Techniques and Procedures1h 36m
5. BONUS: Mathematical Operations and Functions48m
6. Chemical Quantities & Aqueous Reactions3h 53m
7. Gases3h 49m
8. Thermochemistry2h 37m
9. Quantum Mechanics2h 58m
10. Periodic Properties of the Elements3h 9m
11. Bonding & Molecular Structure3h 29m
12. Molecular Shapes & Valence Bond Theory1h 57m
13. Liquids, Solids & Intermolecular Forces2h 23m
14. Solutions3h 1m
15. Chemical Kinetics2h 53m
16. Chemical Equilibrium2h 29m
17. Acid and Base Equilibrium5h 1m
18. Aqueous Equilibrium4h 47m
19. Chemical Thermodynamics1h 50m
20. Electrochemistry2h 42m
21. Nuclear Chemistry2h 36m
22. Organic Chemistry5h 7m
23. Chemistry of the Nonmetals2h 39m
24. Transition Metals and Coordination Compounds3h 16m

15. Chemical Kinetics

Arrhenius Equation

General Chemistry

15. Chemical Kinetics

Arrhenius Equation

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Multiple Choice

Using the Arrhenius Equation, calculate the activation energy (Ea) in kilojoules per mole for a reaction with rate constants of 0.000116 s⁻¹ at 25 °C and 0.305 s⁻¹ at 85 °C. Express your answer to three significant figures.

102.5 kJ/mol

89.7 kJ/mol

75.3 kJ/mol

50.2 kJ/mol

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Verified step by step guidance

Identify 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 gas constant (8.314 J/mol·K), and \( T \) is the temperature in Kelvin.

Convert the given temperatures from Celsius to Kelvin by adding 273.15. Thus, 25 °C becomes 298.15 K and 85 °C becomes 358.15 K.

Use the two-point form of the Arrhenius Equation: \( \ln\left(\frac{k_2}{k_1}\right) = \frac{E_a}{R} \left(\frac{1}{T_1} - \frac{1}{T_2}\right) \), where \( k_1 = 0.000116 \text{ s}^{-1} \) at \( T_1 = 298.15 \text{ K} \) and \( k_2 = 0.305 \text{ s}^{-1} \) at \( T_2 = 358.15 \text{ K} \).

Calculate \( \ln\left(\frac{k_2}{k_1}\right) \) using the given rate constants.

Rearrange the equation to solve for \( E_a \): \( E_a = R \cdot \ln\left(\frac{k_2}{k_1}\right) \cdot \left(\frac{1}{T_1} - \frac{1}{T_2}\right)^{-1} \). Substitute the values and solve for \( E_a \) in joules per mole, then convert to kilojoules per mole by dividing by 1000.