Chemical Kinetics Question 56

Question: A hydrogenation reaction is carried out at 500 K. $ CH_2=CH_2+H_2\xrightarrow[no,catalyst]{500k}CH_3-CH_3 $ Activation energy $ -,E_{a},KJ,mo{l^{-1}} $

$ CH_2=CH_2+H_2\xrightarrow{pd,400k}CH_3-CH_3 $ Activation energy = ( $ E_{a}-20 $ ) KJ $ mo{l^{-1}} $ If rate remains constant, then $ E_{a} $ is

Options:

A) $ 120kJmo{l^{-1}} $

B) $ 100kJmo{l^{-1}} $

C) $ 20kJmo{l^{-1}} $

D) $ 80kJmo{l^{-1}} $

Show Answer

Answer:

Correct Answer: B

Solution:

[b] $ k=A{e^{-E_{a}/RT}} $

$ k=A{e^{-E_{a}/R\times 500}} $

$ k’=A{e^{-(E_{a}-20)/R\times 400}} $ Rates are equal, hence
$ \therefore A{e^{-E_{a}/R\times 500}}=A{e^{-(E_{a}-20)/R\times 400}} $
$ \therefore \frac{E_{a}}{500}=\frac{E_{a}-20}{400} $

$ 4E_{a}=5E_{a}-100 $
$ \therefore E_{a}=100KJmo{l^{-1}} $



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