Answer : a) 40075.14 J/mol
Explanation :
According to the Arrhenius equation,
[tex]K=A\times e^{\frac{-Ea}{RT}}[/tex]
or,
[tex]\log (\frac{K_2}{K_1})=\frac{Ea}{2.303\times R}[\frac{1}{T_1}-\frac{1}{T_2}][/tex]
where,
[tex]K_1[/tex] = rate constant at [tex]440K[/tex] = k
[tex]K_2[/tex] = rate constant at [tex]550K[/tex] = 10 k
[tex]Ea[/tex] = activation energy for the reaction = ?
R = gas constant = 8.314 J/mole.K
[tex]T_1[/tex] = initial temperature = 440 K
[tex]T_2[/tex] = final temperature = 550 K
Now put all the given values in this formula, we get :
[tex]\log (\frac{10k}{k})=\frac{Ea}{2.303\times 8.314J/mole.K}[\frac{1}{440K}-\frac{1}{550K}][/tex]
[tex]Ea=40075.14J/mol [/tex]
Therefore, the activation energy for the reaction is 40075.14J/mol.
