Understanding the high-temperature behavior of nitrogen oxides is essential for controlling pollution generated in automobile engines. The decomposition of nitric oxide (no) to n2 and o2 is second order with a rate constant of 0.0796 m-1⋅s-1 at 737∘c and 0.0815 m-1⋅s-1 at 947∘c. You may want to reference (page) section 14.5 while completing this problem. Part a calculate the activation energy for the reaction. Express the activation energy in kilojoules per mole to three significant digits.

Question

Chemistry

Molly Fletcher

20 July, 08:48

Understanding the high-temperature behavior of nitrogen oxides is essential for controlling pollution generated in automobile engines. The decomposition of nitric oxide (no) to n2 and o2 is second order with a rate constant of 0.0796 m-1⋅s-1 at 737∘c and 0.0815 m-1⋅s-1 at 947∘c. You may want to reference (page) section 14.5 while completing this problem. Part a calculate the activation energy for the reaction. Express the activation energy in kilojoules per mole to three significant digits.

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Ellen Singleton · Answer 1

Hey there!

Arrhenius equation:

k = A exp (-Ea / RT)

ln (K2 / K1) = (-Ea / R) * (1 / T2 - 1 / T1)

K1 = 0.0796 m⁻¹s⁻¹

K2 = 0.0815 m⁻¹s⁻¹

T1 = 737 ºC = 737 + 273.15 = > 1010.15 K

T2 = 947ºC = 947 + 273.15 = > 1220.15 K

R = 8.314 J / mol*K

ln (0.0815 / 0.0796) = (-Ea / 8.314) * (1 / 1220.15 - 1 / 1010.15)

Activation energy Ea = 1151 J / mol ≈ 1.15 Kj/mol