Table of contents

1. Intro to General Chemistry3h 48m
2. Atoms & Elements4h 16m
3. Chemical Reactions4h 10m
4. BONUS: Lab Techniques and Procedures1h 38m
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

A reaction has a rate constant of 1.21×10⁻⁴ s⁻¹ at 25 °C and 0.225 s⁻¹ at 75 °C. What is the value of the rate constant at 17 °C when the activation energy (Ea) is 130 kJ/mol? Express your answer in units of inverse seconds (s⁻¹) and with 3 significant figures.

8.50×10⁻⁵ s⁻¹

1.50×10⁻⁴ s⁻¹

2.00×10⁻⁴ s⁻¹

5.00×10⁻⁵ s⁻¹

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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.

Use the Arrhenius equation in its logarithmic form to compare the rate constants at two different temperatures: \( \ln\left(\frac{k_2}{k_1}\right) = \frac{E_a}{R} \left(\frac{1}{T_1} - \frac{1}{T_2}\right) \). Here, \( k_1 = 1.21 \times 10^{-4} \) s⁻¹ at \( T_1 = 25 \degree C \) and \( k_2 = 0.225 \) s⁻¹ at \( T_2 = 75 \degree C \).

Convert the temperatures from Celsius to Kelvin by adding 273.15: \( T_1 = 25 + 273.15 = 298.15 \) K and \( T_2 = 75 + 273.15 = 348.15 \) K.

Calculate \( \ln\left(\frac{k_2}{k_1}\right) \) using the given rate constants and the activation energy \( E_a = 130 \) kJ/mol (convert to J/mol by multiplying by 1000).

Use the calculated \( \ln\left(\frac{k_2}{k_1}\right) \) to find the rate constant \( k_3 \) at \( T_3 = 17 \degree C \) (convert to Kelvin: \( T_3 = 17 + 273.15 = 290.15 \) K) using the rearranged Arrhenius equation: \( \ln\left(\frac{k_3}{k_1}\right) = \frac{E_a}{R} \left(\frac{1}{T_1} - \frac{1}{T_3}\right) \).