Cyclohexane, C₆H₁₂, undergoes a molecular rearrangement in the presence of AlCl₃ to form methylcyclopentane, CH₃C₅H_9, according to the equation: C₆H₁₂ ⇌ CH₃C₅H₉
If K_c = 0.143 at 25 °C for this reaction, find the equilibrium concentrations of C₆H₁₂ and CH₃C₅H₉ if the initial concentrations are 0.200 mol L^-1 and 0. 075 mol L^-1, respectively.

Question

Quizplus · Accepted Answer

The equilibrium constant expression for the given reaction is: Kc = ([CH3C5H9] [H2] [AlCl3]) / ([C6H12]) At equilibrium, let the moles of cyclohexane be x. Then, according to the balanced equation, the moles of methylcyclopentane will be (0.075 + x) mol. The moles of AlCl3 will be (0.075 + x) mol as it is completely consumed during the reaction. The moles of H2 will remain at 0.2 mol as it is a limiting reagent and does not participate in the reaction. Thus, the concentration of each species at equilibrium will be: [C6H12] = (0.2 - x) M [CH3C5H9] = [(0.075 + x) / V] M, where V is the total volume of the mixture in liters. [H2] = 0.2 M [AlCl3] = [(0.075 + x) / V] M Substituting these values in the expression for Kc and solving for x gives: x = 0.179 mol Substituting this value of x in the equilibrium concentrations gives: [C₆H₁₂] = (0.200 - 0.179) M = 0.021 M [CH₃C₅H₉] = (0.075 + 0.179) / V = 0.254 / V M Hence, the best choice is (C) [C₆H₁₂] = 0.241 mol L^-1, [CH₃C₅H₉] = 0.034 mol L^-1, as it gives the correct equilibrium concentrations of both species.

Cyclohexane, C6H12, Undergoes a Molecular Rearrangement in the Presence of AlCl3

Cyclohexane, C₆H₁₂, Undergoes a Molecular Rearrangement in the Presence of AlCl₃