Answer: The activation energy of the reaction is 122.007 kJ.
Explanation:
Rate constant at [tex]T_1,K_1=0.0117 s^{-1}[/tex]
[tex]T_1=400 K[/tex]
Rate constant at [tex]T_2,K_2=0.689 s^{-1}[/tex]
[tex]T_2=450 K[/tex]
Activation of the energy is given by formula:
[tex]\log\frac{K_2}{K_1}=\frac{E_a}{2.303\times R}\times \frac{T_2-T_1}{T_1T_2}[/tex]
[tex]\log\frac{0.689 s^{-1}}{0.0117 s^{-1}}=\frac{E_a}{2.303\times 8.314 J/K mol}}\times \frac{450 K-400 K}{450 K\times 400 K}[/tex]
On solving for [tex]E_a[/tex]
[tex]E_a=122,007.88 Joules=122.007 kilo-Joules (1000 J = 1kJ)[/tex]
The activation energy of the reaction is 122.007 kJ.
