Question

The pyrolysis of ethane proceeds with an activation energy of about 300 kJ/mol. How much faster is the decomposition at 625°C than at 525°C?

Answer 1

Answer:

The decomposition of ethane is 153.344 times much faster at 625°C than at 525°C.

Explanation:

According to the Arrhenius equation,

$K=A\times e^{\frac{-Ea}{RT}}$

$\log (\frac{K_2}{K_1})=\frac{Ea}{2.303\times R}[\frac{1}{T_1}-\frac{1}{T_2}]$

where,

$K_2$ = rate of reaction at $T_2$

$K_1$ = rate of reaction at $T_1$

$Ea$ = activation energy of the reaction

R = gas constant = 8.314 J/K mol

$E_a=300 kJ/mol=300,000 J/mol$

$T_2=625^oC=898.15 K,T_1=525^oC=798.15 K$

$\log (\frac{K_2}{K_1})=\frac{300,000 J/mol}{2.303\times 8.314 J/K mol}[\frac{1}{798.15 K}-\frac{1}{898.15 K}]$

$\log (\frac{K_2}{K_1})=2.185666$

$K_2=153.344\times K_1$

The decomposition of ethane is 153.344 times much faster at 625°C than at 525°C.