Answer:
The activation energy of the reaction is 1.152 kJ/mol.
Explanation:
Activation energy is the minimum amount which is absorbed by the reactant molecules to undergo chemical reaction.
Initial temperature of reaction = [tex]T_1=100 K[/tex]
Final temperature of reaction = [tex]T_2=200 K[/tex]
Initial rate of the reaction at 100 k = [tex]K_1=k[/tex]
Final rate of the reaction at 200 k = [tex]K_2=2k[/tex]
Activation energy is calculated from the formula:
[tex]\log\frac{K_2}{K_1}=\frac{E_a}{2.303\times R}(\frac{T_2-T_1}{T_1T_2})[/tex]
R = Universal gas constant = 8.314 J/ K mol
[tex]\log\frac{2k}{k}=\frac{E_a}{2.303\times 8.314 J/K mol}(\frac{200 K-100K}{200 K\times 100K})[/tex]
[tex]E_a=1,152.772 J/mol=1.152 kJ/mol[/tex]
