At \(300^\circ C\), decomposition of azomethane follows first order kinetics. Rate constant for this reaction at this temperature is \(2.5\times10^{-4}\,s^{-1}\). If the activation energy of the reaction is \(42\,kcal\,mol^{-1}\), what is the temperature (in K) at which the half-life of the reaction is \(138.6\) seconds?
\[
(R=2\,cal\,K^{-1}mol^{-1},\; \log20=1.30)
\]