A first order reaction has a rate constant of 4.6x10^-2/sec and 8.10x10^-2/sec at 0°C and 20°C, respectively.

Question

What is the value of the activation energy?

Answer 1

Use the Arrhenius equation:

ln(k2/k1) = -Ea/R (1/T2 - 1/T1)

k1 = 4.6x10-2

k2 = 8.1x10-2

T1 = 273K

T2 = 293K

R = gas constant = 8.314 J/Kmol = 0.008314 kJ/Kmol

Ea = activation energy

ln (8.1x10^-2/4.6x10^-2) = -Ea/0.008314 (1/293 - 1/273)

0.566 = -Ea/0.008314 (-0.00025)

0.566 = 0.00025 Ea / 0.008314

Ea = 18.8 kJ/mol

(be sure to check the math)