Rate constants of a reaction at 500 K and 700 K are 0.04 and 0.14 , respectively; then, activation energy of the reaction is (Given : log 3.5 = 0.5441, R = 8.31 J ) [2024]

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Solution

Q.
Rate constants of a reaction at 500 K and 700 K are 0.04 $s^{- 1}$ and 0.14 $s^{- 1}$ , respectively; then, activation energy of the reaction is

(Given : log 3.5 = 0.5441, R = 8.31 J $K^{- 1}$ ${mol}^{- 1}$ ) [2024]

1 182310 J

2 18500 J

3 18219 J

4 18030 J

Ans.
(3)

$\log \frac{k_{2}}{k_{1}} = \frac{E_{a}}{2.303 R} [\frac{T_{2} - T_{1}}{T_{1} T_{2}}]$

Given, $k_{1} = 0.04$ $s^{- 1},$ $k_{2} = 0.14$ $s^{- 1},$ $T_{1} = 500$ $K,$ $T_{2} = 700$ $K,$ $R = 8.31$ $J$ $K^{- 1}$ ${mol}^{- 1}$

$\log (3.5) = \frac{E_{a}}{2.303 \times 8.31} [\frac{700 - 500}{700 \times 500}]$

$E_{a} = 0.5441 \times 2.303 \times 8.31 \times \frac{35 \times 10^{4}}{200} = 18222.65$ $J$

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