The activation energy for the gas phase isomerization of methyl cis-cinnamate is__________kJ.

Question

For the gas phase isomerization of methyl cis-cinnamate,

cis-C₆H₅CH = CHCOOCH₃ --> trans-C₆H₅CH = CHCOOCH₃

the rate constant at 648 K is 3.29 x 10^-4s^-1 and the rate constant at 687 K is 2.06 x 10^-3s^-1 .

The activation energy for the gas phase isomerization of methyl cis-cinnamate is__________kJ.

Answer 1

Use the Arrhenius equation:

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

k1 = 3.29x10^-4s^-1

T1 = 648K

k2 = 2.06x10^-3s^-1

T2 = 687K

R = 8.314 J / Kmole

Ea = ?

ln (2.06x10^-3s^-1 / 3.29x10^-4s^-1) = - Ea / 8.314 (1 / 687 - 1 / 648)

1.834 = -Ea / 8.314 (-8.7x10^-5)

Ea = 175263 J/mol = 175 kJ/mol