Chemical Kinetics Question 286

Question: A reaction takes place in various steps. The rate constant for first, second, third and fifth steps are $ k_1,k_2,k_3 $ and $ k_4 $ respectively The overall rate constant is given by $ k=\frac{k_2}{k_3}{{( \frac{k_1}{k_5} )}^{1/2}} $ . If activation energy are 40,60,50 and 10 kJ/mol respectively, the overall energy of activation (kJ/ mol) is:

Options:

A) 10

B) 20

C) 25

D) none of these

Show Answer

Answer:

Correct Answer: C

Solution:

[c] $ k=A.{e^{-E_{a}/}}^{(RT)} $
$ \therefore $ Effective overall energy of activation $ E_{a}=E_{a}(2)-E_{a}(3)+\frac{1}{2}E_{a}(1)-\frac{1}{2}E_{a}(5) $

$ =60-50+\frac{1}{2}\times 40-\frac{1}{2}\times 10=25,kJ/mol $



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