Given: G ^0 _ f of C ₂ H ₂ is 2.09 10^5 ~J / mol and G _ f ^0 of C ₆ H ₆ is 1.24 10^5 ~J / mol . Calculate the equilibrium constant for the cyclic polymerisation of Ethyne to Benzene at 27^ C . ( R =8.314 JK ⁻¹ ~mol ⁻¹)

Step-by-step solution

The reaction for the cyclic polymerization of ethyne to benzene is given by: 3C₂H₂(g) C₆H₆(l) . The standard Gibbs free energy change for the reaction, G⁰_ rxn , is calculated as: G⁰_ rxn = G⁰_ f (products) - G⁰_ f (reactants) G⁰_ rxn = G⁰_ f (C₆H₆) - 3 G⁰_ f (C₂H₂) G⁰_ rxn = 1.24 10⁵ - 3 (2.09 10⁵) G⁰_ rxn = 1.24 10⁵ - 6.27 10⁵ = -5.03 10⁵ J/mol . The relationship between G⁰ and the equilibrium constant K is given by G⁰ = -RT K . Given T = 27^ C = 300 K and R = 8.314 J K ⁻¹ mol ⁻¹ . -5.03 10⁵ = -8.314 300 K K = 5.