The slope of Arrhenius plot $[\ln K v s \frac{1}{T}]$ of first order reaction is $- 5 \times 10^{3} K$ . The value of E_a of the reaction is

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41.5 K J mol^-1

– 83 K J mol^-1

83.0 K J mol^-1

166 KJ mol^-1

answer is A.

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Detailed Solution

$\begin{array}{l} K = A . e^{- E a / R T} \\ \ln K = \frac{- E a}{R} (\frac{1}{T}) + \ln A \\ ∴ \frac{- E a}{R} = - 5 \times 10^{3} K \\ E_{a} = 5 \times 10^{3} \times 8.314 \times 10^{- 3} \\ = 41.5 k J m o l^{- 1} \end{array}$

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