A first order reaction has a rate constant of 0.20287 at 45.5 oC. Given that the Arrhenius constant for the reaction is 2.7 x 1010 sec -1, what is the value of the activation energy (in kJ/mol)?

Question

Enter your value to three significant figures.

Answer 1

k = Ae^-Ea/RT

ln k = -Ea/RT + ln A

k = 0.20287

R = 8.314 J/mol-K = 0.008314 kJ/mol-K

T = 45.5ºC + 273 = 318.5K

A = 2.7x10¹⁰

Ea = ?

ln (0.20287) = [-Ea / (0.008314)(318.5)] + ln 2.7x10¹⁰

-1.596 = (-Ea / 2.648) + 24.02

-25.616 = -Ea / 2.648

Ea = 67.8 kJ/mol

Please be sure to check the math.