The cis–trans isomerization of 2-butene in the gas phase follows first-order kinetics.
Experimental rate constants are:
k(350 K) = 1.2 × 10⁻⁶ s⁻¹
k(425 K) = 2.8 × 10⁻⁴ s⁻¹
The standard Gibbs free energy change for the isomerization at 298 K is ΔG°298 = −2.7 kJ mol⁻¹.
(a) Using the two rate constants, calculate the activation energy Ea for the isomerization.
(b) Determine the rate constant k at 298 K and estimate the half-life t½ at this temperature. Assume first-order kinetics.
(c) Discuss whether the isomerization would be observable over a typical laboratory time scale (≈1 hour) at 298 K. Base your answer on the values of ΔG°298, Ea, and t½.
(d) The reaction is carried out in the presence of a heterogeneous catalyst that lowers Ea by 60 kJ mol⁻¹. Qualitatively predict how k298 and t½ will change, and explain the expected impact on observability without altering ΔG°298.
(e) Explain why lowering Ea does not affect the position of equilibrium between the cis and trans isomers.