Answer:
27.77 kJ/mol is the activation energy for the reaction.
Explanation:
Rate of the reaction at 323 K =[tex]k_1=k[/tex]
Rate of the reaction at 373 K =[tex]k_2=4k[/tex]
Activation energy for the reaction is calculated by formula:
[tex]\log \frac{k_2}{k_1}=\frac{E_a}{2.303\times R}[\frac{T_2-T_1}{T_2\times T_1}][/tex]
[tex]E_a[/tex] = Activation energy
[tex]T_1[/tex] = Temperature when rate of the reaction was [tex]k_1[/tex]
[tex]T_2[/tex] = Temperature when rate of the reaction was [tex]k_2[/tex]
Substituting the values:
[tex]\log \frac{4k}{k}=\frac{E_a}{2.303\times 8.314 J /mol K}[\frac{373 K-323K}{373 K\times 323 K}][/tex]
[tex]E_a=27,776.98 J/mol=27.77 kJ/mol[/tex]
27.77 kJ/mol is the activation energy for the reaction.
