The reaction A 3 B -> C 2D

Question

has a rate constant k= 1 x 10^-5 s^-1 at 27 deg C. If the activation energy for the reaction is 20,000 cal/mol, what is the value of the rate constant at 0 deg C?

Answer 1

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

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

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

20,000 cal/mol x (4.184 J / cal) = 83,680 J/mol

ln k2 = (83,680 / 8.31)(1/300 - 1/273) + ln (1 x 10^-5)

ln k2 = -14.9

k2 = e^-14.9 = 3.5 x 10^-7 s^-1

Check my math!