The cis–trans isomerization of 2-butene can be modeled as a reversible elementary process at high temperature:
cis-2-butene ⇌ trans-2-butene
Let k_f be the forward rate constant (cis → trans) and k_r the reverse rate constant (trans → cis).
(a) Write separate differential rate expressions for the forward reaction rate and the reverse reaction rate in terms of the appropriate rate constants and concentrations.
(b) Combine your results from part (a) to obtain an expression for the net rate of change of [cis-2-butene].
(c) Identify the overall reaction order for the forward direction and for the reverse direction, and explain your reasoning.
(d) If [cis-2-butene]₀ = 0.300 M, [trans-2-butene]₀ = 0.100 M, k_f = 2.5 × 10⁻³ s⁻¹, and k_r = 1.8 × 10⁻³ s⁻¹, calculate the initial net rate of conversion of cis-2-butene to trans-2-butene, stating the correct units.
(e) Determine the units of k_f when concentrations are expressed in mol L⁻¹ and time in seconds.