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. $\left(5.6 \times 10^{5}\right)$
Solution:
- $k _{500}=A e^{-E _1 / R T _1}$
$$ \begin{array}{rlrl} & & k _{400} & =A e^{-E _2 / R T _2} \ & \because & k _{500} & =k _{400} \ \Rightarrow & & \frac{E _1}{R T _1} & =\frac{E _2}{R T _2} \Rightarrow \frac{E _2}{E _1}=\frac{T _2}{T _1}=\frac{400}{500}=\frac{4}{5} \ & \text { Also } & E _1 & =E _2+20000 J \ \Rightarrow & \frac{E _1-20,000}{E _1} & =\frac{4}{5} \Rightarrow E _1=100,000 J=100 kJ mol^{-1} \end{array} $$
