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The the rate of decomposition for methyl nitrite and ethyl nitrite can be given in terms of rate constant.
$(in \sec^{- 1}) k_{1}$ and $k_{2}$ respectively. The energy of activations for the two reactions are $152.30 kJ {mol}^{- 1}$ and $157.7 kJ {mol}^{- 1}$ as well as frequency factors are $10^{13}$ and $10^{14}$ respectively for the decomposition of methyl and ethyl nitrite. Calculate the approx. temperature at which rate constant will be same for the two reactions.

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answer is 282.

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Detailed Solution

For the equal rate constant,

$k_{1} = k_{2}$

$\begin{array}{l} \Rightarrow A_{1} e^{- \frac{E_{1}}{R T}} = A_{2} e^{- \frac{E_{2}}{R T}} \\ - \frac{152.3 \times 10^{8}}{8.314 \times T} = 2.3 - \frac{157.7 \times 10^{3}}{8.314 \times T} \\ \Rightarrow T = 282 K \end{array}$

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