Respuesta :
Answer: The activation energy for the gas phase isomerization of methyl cis-cinnamate is 173.519 kJ
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]637K[/tex] = [tex]1.88\times 10^{-4}s^{-1}[/tex]
[tex]K_2[/tex] = rate constant at [tex]679K[/tex] = [tex]1.43\times 10^{-3}s^{-1}[/tex]
[tex]Ea[/tex] = activation energy for the reaction = ?
R = gas constant = 8.314 J/mole.K
[tex]T_1[/tex] = initial temperature = [tex]637K[/tex]
[tex]T_2[/tex] = final temperature = [tex]679K[/tex]
Now put all the given values in this formula, we get
[tex]\log (\frac{1.43\times 10^{-3}}{1.88\times 10^{-4}})=\frac{Ea}{2.303\times 8.314J/mole.K}[\frac{1}{637}-\frac{1}{679}][/tex]
[tex]0.88=\frac{Ea}{2.303\times 8.314J/mole.K}[\frac{1}{637}-\frac{1}{679}][/tex]
[tex]Ea=173519J/mole=173.519kJ[/tex]
Therefore, the activation energy for the reaction is, 173.519 kJ
