For the first order reaction A -> P, the rate constant follows log10 k = -(2000)(1/T) + 6. Find the activation energy in kJ/mol. (Use ln x = 2.3 log x, R = 8.314 J/mol/K.)

38.29 kJ/mol
30.8 kJ/mol
19.15 kJ/mol
16.6 kJ/mol

Correct answer: 38.29 kJ/mol

Solution

Matching the given equation to the Arrhenius log form, the slope -2000 = -Ea/(2.303 R), giving Ea = 2000 * 2.303 * 8.314 = 38290 J/mol ~ 38.29 kJ/mol.

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