The rate constant for a chemical reaction taking place at $500 k$ is expressed as $k = A . e^{- 1000}$ . The activation energy $(E a)$ of the reaction is:

$100 K c a l$

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$1000 K c a l$

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$10000 K c a l$

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$100000 K c a l$

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Solution

The correct option is B
$1000 K c a l$

Explanation for the correct option:
(B) $1000 K c a l$
$K = A e^{- E a / R T}$
According to the question, $\frac{E a}{R T} = 1000$
Therefore, $E a = 1000 \times 2 \times 500 E a = {(1000)}^{2} cal E a = 1000 Kcal$ $(T = 500 K)$
Explanation for the incorrect options:
Since, the correct value of activation energy is $1000 Kcal$ . Therefore, options (A), (C) and (D) stand incorrect.
Hence, the correct option is (B) $1000 Kcal$

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