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(A) The Arrhenius equation is $k = A e^{-E_a/RT}$.Given $k = (k_1 k_2 / k_3)^{2/3}$.Substituting the Arrhenius expressions: $A e^{-E_a/RT} = [ (A e^{-

Vedclass · Accepted Answer

$140$

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(A) The Arrhenius equation is $k = A e^{-E_a/RT}$.Given $k = (k_1 k_2 / k_3)^{2/3}$.Substituting the Arrhenius expressions: $A e^{-E_a/RT} = [ (A e^{-E_{a_1}/RT} 	imes A e^{-E_{a_2}/RT}) / (A e^{-E_{a_3}/RT}) ]^{2/3}$.Assuming pre-exponential factors $A$ are approximately equal,we equate the exponents:$-E_a/RT = (2/3) 	imes [(-E_{a_1} - E_{a_2} + E_{a_3})/RT]$.Thus,$E_a = (2/3) 	imes [E_{a_1} + E_{a_2} - E_{a_3}]$.Substituting the values: $E_a = (2/3) 	imes [180 + 80 - 50]$.$E_a = (2/3) 	imes [210] = 140 \ kJ \ mol^{-1}$.

Step	Rate constant and Activation energy
$Step \ 1$	$k_1, E_{a_1} = 180 \ kJ \ mol^{-1}$
$Step \ 2$	$k_2, E_{a_2} = 80 \ kJ \ mol^{-1}$
$Step \ 3$	$k_3, E_{a_3} = 50 \ kJ \ mol^{-1}$

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