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Multiple Choice
Using the Arrhenius Equation, what is the activation energy (Ea) in kJ/mol for a reaction with a rate constant of 0.000122 s⁻¹ at 27 °C and 0.228 s⁻¹ at 77 °C?
A
68.3 kJ/mol
B
35.4 kJ/mol
C
24.7 kJ/mol
D
52.1 kJ/mol
Verified step by step guidance
1
Start by understanding the Arrhenius Equation, which is: , where is the rate constant, is the pre-exponential factor, is the activation energy, is the gas constant, and is the temperature in Kelvin.
Convert the given temperatures from Celsius to Kelvin. Use the formula: . For 27 °C, K, and for 77 °C, K.
Use the Arrhenius Equation in its logarithmic form to find the activation energy: , where and are the rate constants at temperatures and respectively.
Substitute the known values into the equation: . Use J/mol·K for the gas constant.
Solve for by rearranging the equation and performing the necessary calculations. Remember to convert the final result from J/mol to kJ/mol by dividing by 1000.