Question #44795

For a complex gas-phase reaction, the temperature dependence of the rate constant $k$ deviates from classical Arrhenius behavior and is accurately described by the modified equation $k = A_0 T^m e^{-E_0/RT}$, where $A_0$, $m$, and $E_0$ are temperature-independent constants. A student plots $\ln k$ versus $1/T$ and observes a non-linear curve. By drawing tangents to the curve, the student determines the instantaneous apparent activation energy ($E_{a,app}$) to be $54.98 \text{ kJ mol}^{-1}$ at $300 \text{ K}$ and $62.47 \text{ kJ mol}^{-1}$ at $600 \text{ K}$. Assuming ideal gas behavior, what are the values of the true threshold energy ($E_0$) and the temperature exponent ($m$)? (Given: $R = 8.314 \text{ J K}^{-1} \text{ mol}^{-1}$)