Answer: The activation energy for the reaction is 40.143 kJ/mol
Explanation:
To calculate activation energy of the reaction, we use Arrhenius equation for two different temperatures, which is:
[tex]\ln(\frac{K_{317K}}{K_{278K}})=\frac{E_a}{R}[\frac{1}{T_1}-\frac{1}{T_2}][/tex]
where,
[tex]K_{317K}[/tex] = equilibrium constant at 317 K = [tex]3.050\times 10^{8}M^{-1}s^{-1}[/tex]
[tex]K_{278K}[/tex] = equilibrium constant at 278 K = [tex]3.600\times 10^{7}M^{-1}s^{-1}[/tex]
[tex]E_a[/tex] = Activation energy = ?
R = Gas constant = 8.314 J/mol K
[tex]T_1[/tex] = initial temperature = 278 K
[tex]T_2[/tex] = final temperature = 317 K
Putting values in above equation, we get:
[tex]\ln(\frac{3.050\times 10^8}{3.600\times 10^{7}})=\frac{E_a}{8.314J/mol.K}[\frac{1}{278}-\frac{1}{317}]\\\\E_a=40143.3J/mol=40.143kJ/mol[/tex]
Hence, the activation energy for the reaction is 40.143 kJ/mol
