Question

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.

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