Domain: Chemical kinetics

The bimolecular gas-phase reaction between  \({F_2}\) and  \({IF_5}\) follows first-order kinetics in each reactant. The activation energy is \(58.6~\text{kJ mol}^{-1}\). At  \(65^\circ\text{C}\), the rate constant is \(7.84\times10^{-3}~\text{kPa}^{-1}\text{s}^{-1}\). Determine the entropy of activation  at  \(65^\circ\text{C}\).

Grading rubric:
criterion: The solution explicitly identifies the problem as belonging to chemical kinetics and applies transition state theory to a bimolecular gas-phase reaction.
weight: 10
criterion: The solution explicitly writes the bimolecular Eyring equation in the form
k = (k_B T / h)(RT / P°) exp(ΔS‡ / R) exp(−ΔH‡ / (RT))
before any numerical substitution.
weight: 20
criterion: The solution explicitly relates the Arrhenius activation energy to the enthalpy of activation using ΔH‡ = E_a − RT evaluated at 338.15 K.
weight: 10
criterion: The solution explicitly performs an algebraic rearrangement of the written Eyring equation to isolate ΔS‡ prior to inserting numerical values.
weight: 10
criterion: The solution explicitly substitutes the standard-state pressure P° = 101.325 kPa into the rearranged entropy expression.
weight: 10
criterion: The solution explicitly evaluates the enthalpy contribution ΔH‡/(RT) numerically and includes it additively inside the entropy expression.
weight: 20
criterion: The solution explicitly reports the entropy of activation as −83.0 J K⁻¹ mol⁻¹ at 65 °C.
weight: 20

Answer:
-83.0 J K^-1 mol^-1