Answer: The activation energy Ea for this reaction is 22689.8 J/mol
Explanation:
According to Arrhenius equation with change in temperature, the formula is as follows.
[tex]ln \frac{k_{2}}{k_{1}} = \frac{-E_{a}}{R}[\frac{1}{T_{2}} - \frac{1}{T_{1}}][/tex]
[tex]k_1[/tex] = rate constant at temperature [tex]T_1[/tex] = [tex]2.3\times 10^8[/tex]
[tex]k_2[/tex] = rate constant at temperature [tex]T_2[/tex] = [tex]4.8\times 10^8[/tex]
[tex]E_a[/tex]= activation energy = ?
R= gas constant = 8.314 J/kmol
[tex]T_1[/tex] = temperature = [tex]280.0^0C=(273+280)=553K[/tex]
[tex]T_2[/tex] = temperature = [tex]376.0^0C=(273+376)=649K[/tex]
Putting in the values ::
[tex]ln \frac{4.8\times 10^8}{2.3\times 10^8} = \frac{-E_{a}}{8.314}[\frac{1}{649} - \frac{1}{553}][/tex]
[tex]E_a=22689.8J/mol[/tex]
The activation energy Ea for this reaction is 22689.8 J/mol
