Cyclopropane ring-opening to propene at 25°C has Arrhenius prefactor $4.3\times10^{15}$ s⁻¹. Find activation entropy in J/(mol K) to 2 decimals. Given $h=6.626\times10^{-34}$ J s, $k_B=1.38\times10^{-23}$ J/K, R = 8.314 J/(mol K).
Combining Eyring theory with $E_a=\Delta H^\ddagger+RT$ gives Arrhenius prefactor $A=e(k_BT/h)e^{\Delta S^\ddagger/R}$. Therefore $\Delta S^\ddagger=R\ln[Ah/(e k_BT)]$. At 298 K this gives about 46.06 J/(mol K). Omitting the factor e would shift the result by R and would not match the specified Arrhenius prefactor convention.
More Kinetics and Reaction Dynamics: Elementary, parallel, opposing, and consecutive reactions. Steady state approximation. Mechanism of complex reactions. Unimolecular reactions. Potential energy surface and classical trajectories, Concept of saddle points, Transition state theory: Eyring equation, thermodynamic aspects. Kinetics of polymerization. Catalysis concepts and enzyme catalysis. Kinetic isotope effects. Fast reaction kinetics: relaxation and flow methods. Diffusion controlled reactions. Kinetics of unimolecular and bimolecular photophysical processes, Quantum yield calculation, static and dynamic quenching. questions
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