Answer :
Answer:
The value of activation barrier for the reaction is, 43.374 kJ/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]18.0^oC[/tex] = k
[tex]K_2[/tex] = rate constant at [tex]37.0^oC[/tex] = 3k
[tex]Ea[/tex] = activation energy for the reaction = ?
R = gas constant = 8.314 J/mol.K
[tex]T_1[/tex] = initial temperature = [tex]18.0^oC=273+18.0=291 K[/tex]
[tex]T_2[/tex] = final temperature = [tex]37.0^oC=273+37.0=310 K[/tex]
Now put all the given values in this formula, we get
[tex]\log (\frac{3k}{k})=\frac{Ea}{2.303\times 8.314 J/mol K}[\frac{1}{291 K}-\frac{1}{310 K}][/tex]
[tex]Ea=43,374 J/mol=43.374 KJ/mol[/tex]
Therefore, the activation energy for the reaction is, 43.374 kJ/mol.