Chemistry
Chemistry
Problem
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.Intuitive explanation
Isomerization is a first-order process where the rate depends only on the concentration of one reactant, and you can use the Arrhenius equation to connect rate constants at different temperatures. The key insight is that two rate constants at different temperatures let you calculate the activation energy , which then reveals how much energy the molecule must overcome to rearrange its structure. Once you have , you can predict rates at any temperature or explore the thermodynamic driving force behind the reaction.
Intuitive explanation
Isomerization is a first-order process where the rate depends only on the concentration of one reactant, and you can use the Arrhenius equation to connect rate constants at different temperatures. The key insight is that two rate constants at different temperatures let you calculate the activation energy , which then reveals how much energy the molecule must overcome to rearrange its structure. Once you have , you can predict rates at any temperature or explore the thermodynamic driving force behind the reaction.