Arrhenius Equation

Question

The rate constant for the rate of decomposition of 𝑁2𝑂5 to NO

and 𝑂2 in the gas phase is 1.66 𝑀−1𝑠−1 at 651 K and 7.39

𝑀−1𝑠−1 at 701 K. Calculate the activation energy for this

decomposition in kJ/mol.

Answer 1

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

k1 = 1.66 M-1s-1

k2 =7.39 M-1s-1

T1 = 651K

T2 = 701K

R = 8.314 J/Kmol = 0.008314 kJ/kmol

ln(7.39/1.66) = -Ea/0.008314 (1/701 - 1/651)

1.493 = -Ea/0.008314 (0.001427 - 0.001536)

1.493 = 0.000109 Ea / 0.008314

Ea = 114 kJ/mol

(be sure to check all of the math)