For a complex reaction $A K - \to P r o d u c t s, E_{a_{1}} = 180 K J / m o l e, E_{a_{2}} = 80 K J / m o l, E_{a_{3}} = 50 K J / m o l .$ overall rate constant k is related to individual rate constant by the equation $k = {(\frac{K_{1} - K_{2}}{K_{3}})}^{2 / 3} .$ Activation energy (KJ/mol) for the overall reaction is

100

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43.44

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150

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140

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Solution

The correct option is D 140
$k = {(\frac{K_{1} - K_{2}}{K_{3}})}^{2 / 3} .$
$l o g k = \frac{2}{3} (l o g K_{1} - l o g K_{2} - l o g K_{3})$
$\frac{- E a}{2303 R T} = \frac{2}{3} (\frac{- E a_{1}}{2.303 R T} - \frac{E a_{2}}{2.303 R T} + \frac{E a_{3}}{2.303 R T}) E_{a} = \frac{2}{3} (E_{a_{1}} + E_{a_{2}} + E_{a_{3}}) = \frac{2}{3} (180 + 80 - 50) = 140 K J / m o l .$

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And overall rate constant,

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