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Arrhenius Equation

At 380 o C,...

Question

At $380^{o} C$ , the half life period for the first order decomposition of $H_{2} O_{2}$ is $360$ $m i n$ . The energy of activation of the reaction is $200$ $k J$ ${m o l}^{- 1}$ . Calculate the time required for $75$ % decomposition at $450^{o} C$ .

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Solution

We have, $K 1 = \frac{0.693}{360} m i n^{- 1}$ at 653 K, $E_{a} = 200 \times 103 J$ ,
$K 2 = ?$ at $723 K, R = 8.314 J$
$∴$ from $2.303 l o g_{10} (\frac{K 2}{K 1}) = (\frac{E a}{R}) [\frac{(T 2 - T 1)}{T 1 T 2}]$
$K 2 = 0.068 m i n^{- 1}$
Now, $t = (\frac{2.303}{0.068}) l o g_{10} (\frac{100}{25})$
$⟹ t = 20.39$ minutes

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