For the gas phase decomposition of t-butyl propionate, C2H5COOC(CH3)3 (CH3)2C=CH2 + C2H5COOHthe rate constant at 540 K is 8.90×10-4 s-1 and the rate constant at 578 K is 9.83×10-3 s-1. The activation energy for the gas phase decomposition of t-butyl propionate is kJ/mol.

The activation energy is 164.02 kJ/mol

Explanation:

Log (k2/k1) = Ea/2.303R × [1/T1 - 1/T2]

k1 = 8.9×10^-4 s^-1

k2 = 9.83×10^-3 s^-1

R = 8.314 J/mol.K

T1 = 540 K

T2 = 578 K

Log (9.83×10^-3/8.9×10^-4) = Ea/2.303×8.314 × [1/540 - 1/578]

1.043 = 6.359×10^-6Ea

Ea = 1.043/6.359×10^-6 = 164020 J/mol = 164020/1000 = 164.02 kJ/mol