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Activation Energy

A certain rea...

Question

A certain reaction is $50 %$ complete in $20 m i n u t e s$ at $300 k$ ; the reaction is $50 %$ complete in $5$ minutes at $350 k$ calculate the activeity energy, of it is a first order reaction.

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Solution

$k_{1} = \frac{0.693}{20}$
$k_{2} = \frac{0.693}{5}$
$l o g \frac{k_{2}}{k_{1}}$ = $\frac{E_{a}}{2.303 \times R} (\frac{1}{T_{1}} - \frac{1}{T_{2}})$
$l o g (4) = \frac{E_{a}}{2.303 \times 8.314} (\frac{1}{300} - \frac{1}{350})$
$E_{a} = 24.2 k J {m o l}^{- 1}$

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