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. Calculate the activation energy for the reaction in kJ/mol

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Alleei Alleei · Answer 1 · 2019-07-18T07:59:05+02:00

Answer : The activation energy for the reaction is, 1.151 KJ

Explanation :

According to the Arrhenius equation,

[tex]K=A\times e^{\frac{-Ea}{RT}}[/tex]

or,

[tex]\log (\frac{K_2}{K_1})=\frac{Ea}{2.303\times R}[\frac{1}{T_1}-\frac{1}{T_2}][/tex]

where,

[tex]K_1[/tex] = rate constant at [tex]737^oC[/tex] = [tex]0.0796M^{-1}s^{-1}[/tex]

[tex]K_2[/tex] = rate constant at [tex]947^oC[/tex] = [tex]0.0815M^{-1}s^{-1}[/tex]

[tex]Ea[/tex] = activation energy for the reaction = ?

R = gas constant = 8.314 J/mole.K

[tex]T_1[/tex] = initial temperature = [tex]737^oC=273+737=1010K[/tex]

[tex]T_2[/tex] = final temperature = [tex]947^oC=273+947=1220K[/tex]

Now put all the given values in this formula, we get:

[tex]\log (\frac{0.0815M^{-1}s^{-1}}{0.0796M^{-1}s^{-1}})=\frac{Ea}{2.303\times 8.314J/mole.K}[\frac{1}{1010K}-\frac{1}{1220K}][/tex]

[tex]Ea=1151.072J/mole=1.151KJ[/tex]

Therefore, the activation energy for the reaction is, 1.151 KJ