Consider the following transformation involvi | vedclass

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(C) The overall rate constant is given by $k = \frac{k_1 k_2}{k_3}$.Using the Arrhenius equation $k = A e^{\frac{-E_a}{RT}}$,we can write:$A e^{\frac{

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(C) The overall rate constant is given by $k = \frac{k_1 k_2}{k_3}$.Using the Arrhenius equation $k = A e^{\frac{-E_a}{RT}}$,we can write:$A e^{\frac{-E_a}{RT}} = \frac{A_1 e^{\frac{-E_{a_1}}{RT}} \cdot A_2 e^{\frac{-E_{a_2}}{RT}}}{A_3 e^{\frac{-E_{a_3}}{RT}}}$$A e^{\frac{-E_a}{RT}} = \frac{A_1 A_2}{A_3} e^{\frac{-(E_{a_1} + E_{a_2} - E_{a_3})}{RT}}$Comparing the exponents,we get the overall activation energy expression:$E_a = E_{a_1} + E_{a_2} - E_{a_3}$Given $E_a = 400 \ kJ \ mol^{-1}$,$E_{a_1} = 300 \ kJ \ mol^{-1}$,and $E_{a_2} = 200 \ kJ \ mol^{-1}$:$400 = 300 + 200 - E_{a_3}$$400 = 500 - E_{a_3}$$E_{a_3} = 500 - 400 = 100 \ kJ \ mol^{-1}$.

Step	Rate constant $(s^{-1})$	Activation energy $(kJ \ mol^{-1})$
$1$	$k_1$	$300$
$2$	$k_2$	$200$
$3$	$k_3$	$Ea_3$

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