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* e^{(-Ea)/(RT)}`

or,

`\log ((K_2)/(K_1))=(Ea)/(2.303* R)[(1)/(T_1)-(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 ((0.0815M^(-1)s^(-1))/(0.0796M^(-1)s^(-1)))=(Ea)/(2.303* 8.314J/mole.K)[(1)/(1010K)-(1)/(1220K)]`

`Ea=1151.072J/mole=1.151KJ`

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