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

Answer 1

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

Explanation :

According to the Arrhenius equation,

$K=A\times e^{\frac{-Ea}{RT}}$

or,

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

where,

$K_1$ = rate constant at $737^oC$ = $0.0796M^{-1}s^{-1}$

$K_2$ = rate constant at $947^oC$ = $0.0815M^{-1}s^{-1}$

$Ea$ = activation energy for the reaction = ?

R = gas constant = 8.314 J/mole.K

$T_1$ = initial temperature = $737^oC=273+737=1010K$

$T_2$ = final temperature = $947^oC=273+947=1220K$

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

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

$Ea=1151.072J/mole=1.151KJ$

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