The first order reaction

Question

X -> products

has Ea= 2 kcal/mol and a half-life of 257 sec at 300 K. What is the half life at 540K? Answer in units of s

Answer 1

t 1/2 = 0.693 / k

k at 300K = 0.693 / t 1/2 = 0.693 / 257 s = 0.00270s^-1

Ea = 2000 cal / mol

k2 = k at 540K

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

ln k2 = (2000 / 8.31) (1/300 - 1/540) + ln (0.00270)

ln k2 = -5.56

k2 = e^-5.56 = 0.00385 s^-1

Then t 1/2 at 540 = 0.693 / k2 = 0.693 / 0.00385 s^-1 = 180 s