Chemical Kinetics - Result Question 62
62. A hydrogenation reaction is carried out at $500 $ $K$. If the same reaction is carried out in the presence of a catalyst at the same rate, the temperature required is $400 $ $K$. Calculate the activation energy of the reaction if the catalyst lowers the activation barrier by $20$ $ kJ$ $ mol^{-1}$.
$(2000,3 M)$
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Answer:
Correct Answer: 62. $(100$ $ kJ $ $mol^{-1})$
Solution:
- $k _{500}=A e^{-E _a / R T _1}$
$ k _{400} =A e^{-E _2 / R T _2} $
$ \because \quad k _{500} =k _{400} $
$\Rightarrow \quad \dfrac{E _1}{R T _1} =\dfrac{E _2}{R T _2} \Rightarrow \dfrac{E _2}{E _1}=\dfrac{T _2}{T _1}=\dfrac{400}{500}=\dfrac{4}{5}$
Also $ E_1 = E_2 + 20000 , \text{J} $
$\Rightarrow \quad \dfrac{E _1-20,000}{E _1} =\dfrac{4}{5} \Rightarrow E _1=100,000 $ $J=100$ $ kJ $ $mol^{-1}$
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