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Activation Energy

A reaction oc...

Question

A reaction occurs in 3 steps having rate constant $K_{1}, K_{2}, K_{3}$ the overall rate constant of the reaction $1 △$
$K = \frac{K_{1} K_{2}}{K_{3}}$
The $E_{a}$ energies of first, second and third steps are 30, 60, 40 $k J {m o l}^{- 1}$ respectively. Determine activation energy of the reaction.

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Solution

$R_{1} = A_{1} e^{- E_{a_{1}} / R T} = A_{1} e^{- 30 K J / R T}$
$R_{2} = A_{2} e^{- E o R J / R T}$
$R_{3} = A_{3} e^{- 40 K J / R J}$
$K_{3} = A_{3} e^{- 40 K J / R J}$
$K = \frac{K_{1} K_{2}}{K} = \frac{A_{1} e^{- 30 K J / R T} \times A_{2} e^{- 60 K J / R T}}{A_{3} e^{- 40 K J / R T}}$
$= (\frac{A_{1} A_{2}}{A_{3}}) e^{- 50 K J / R T}$
$∴ E_{n e t} = 50 R J$

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