Question

Calculate the standard molar Gibbs free energy change (DeltaG_rxn⁰) at 298 K and at 400 K for the following reaction (the cyclotrimerization of ethene to benzene), assuming that all heat capacities are independent of temperature:

                                    3 C₂H₄(g)   ®   C₆H₆(g) + 3 H₂(g).

Answer 1

Hf = Heat of formation and Sf = Entropy of formation

C2H4 : Hf = 52.26 kJ/mol, Sf = 219.56 J/K.mol and Gf = 68.15 kJ/mol (at 298 K)

C6H6 : Hf = 49 kJJ/mol ; Sf = 173.3 J/K.mol ; Gf = 124.3 kJ/mol (298 K)

H2 : Hf = 0 ; Gf = 0 ; Sf = 130.68 J/K.mol

Delta Hf of reaction = Hf C6H6 - 3* Hf C2H4 = -107.75 kJ/mol

Delta Sf of reaction = Sf C6H6 + 3*Sf H2 - 3*Sf C2H4 = -93.34 J/K.mol

Delta G = Delta Hf - T * delta Sf

At 298 K : Delta G = -79.73 kJ/mol

At 400 K : delta G = -70.4 kJ/mol : Here we have assumed that Hf and Sf do not vary with temperature.

Verify the data for 298 K by using the Gf values at 298 K for 3 gases.

Delta Gf 298 K = Gf C6H6 - 3* C2H4 = -80.15 kJ/mol which is approx same as calculated.