Answer:
The decomposition of ethane is 153.344 times much faster at 625°C than at 525°C.
Explanation:
According to the Arrhenius equation,
[tex]K=A\times e^{\frac{-Ea}{RT}}[/tex]
[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_2[/tex] = rate of reaction at [tex]T_2[/tex]
[tex]K_1[/tex] = rate of reaction at [tex]T_1[/tex]
[tex]Ea[/tex] = activation energy of the reaction
R = gas constant = 8.314 J/K mol
[tex]E_a=300 kJ/mol=300,000 J/mol[/tex]
[tex]T_2=625^oC=898.15 K,T_1=525^oC=798.15 K[/tex]
[tex]\log (\frac{K_2}{K_1})=\frac{300,000 J/mol}{2.303\times 8.314 J/K mol}[\frac{1}{798.15 K}-\frac{1}{898.15 K}][/tex]
[tex]\log (\frac{K_2}{K_1})=2.185666[/tex]
[tex]K_2=153.344\times K_1[/tex]
The decomposition of ethane is 153.344 times much faster at 625°C than at 525°C.
