The rate constants of the above reaction at 200 K and 300 K are 0.03 and 0.05 respectively. The activation energy for the reaction is __________ J (Nearest Integer). (Given: ln 10 = 2.3) R = 8.3 J log 5 = 0.70 log 3 = 0.48 log 2 = 0.30

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Solution

Q.
$A \to B$
The rate constants of the above reaction at 200 K and 300 K are 0.03 $\min^{- 1}$ and 0.05 $\min^{- 1}$ respectively. The activation energy for the reaction is __________ J (Nearest Integer).

(Given: ln 10 = 2.3

R = 8.3 J $K^{- 1} {mol}^{- 1}$

log 5 = 0.70

log 3 = 0.48

log 2 = 0.30) [2023]

Ans.
(2520)

$\log (\frac{K_{2}}{K_{1}}) = \frac{E_{a}}{2.303 \times R} [\frac{1}{T_{1}} - \frac{1}{T_{2}}]$

$\log (\frac{0.05}{0.03}) = \frac{E_{a}}{2.303 \times 8.3} [\frac{1}{200} - \frac{1}{300}]$

$0.22 = \frac{E_{a}}{2.303 \times 8.3} [\frac{100}{300 \times 200}]$

$E_{a} = 0.22 \times 2.303 \times 8.3 \times 300 \times 2 J$

$E_{a} = 2519.88 J$

$E_{a} = 2520 J$

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