Question

5.1. Find the change in free energy for the reactions given below. Are the reactions exer- gonic or endergonic? In what direction will the reaction proceed spontaneously? Which reaction is likely to release the most free energy? Assume a pH of 7 for reac- tions a and c, and a pH of 2 for reaction b. a. CO2 + 4H2 → CH4 + 2H2O AG° : - FAE b. 4Fe2+ + O2 + 4H+ + 4Fe3+ + 2H2O c. 4CO2+8H20 - 4CH40+ 602 use the values!

Answer 1

CO2 + 4H2 - CH, + 2H,0 AG' = n, Gr (products) - En, AG (reactants) AG' = [(-50.75 kJ/mol)+ 2(-237.17 kJ/mol) ]- [(-394.4kJ/mol)+ 4 (0) ] AGE" = (-50.75 kJ/mol- 474.34 kJ/mol) ]- [-394.4kJ/mol ] AG;' = -525.09 kJ/mol + 394.4 kJ/mol AGE' = -130.69 kJ/mol So: AG: < 0 -----> Exergonic reaction (Gº <Gº, ) ---->Energy is released Spontaneous reaction

b) 4Fe2+ + 0, + 4H- 4Fe3+ + 2H,0 Oxide Reaction-Reduction n = 4 e F = 96500 J/mol xn number of moles of electrons that are transferred AGⓇ = n FAE 4Fe2+ — 4Fe + 4e Eoxig=-0.70 v 2 H,0 Ered = +1.23 v 02 + 4H + 4e - AE = E° red - Eºoxid AE = +1.23 v- (-0.70 v ) AE = 1.93 v AG° = - n FAE AGⓇ = - 4 x 96500 J/4 x 1.93 + AG = - 733400 J AG; <0 -----> Exergonic reaction (Gº,<Gº ) ---->Energy is released Spontaneous reaction

400, +8H,0 - > 4CH,0 +602 AG' = I n, Gi (products) - En, AG (reactants) G CH,0 = -175.39 kJ/mol G' 0, = 0 G' H20 = -237.17 kJ/mol G Co, = -394.4 kJ/mol; AG;° = [4(-175.39 kJ/mol)]- [4(-394.4kJ/mol)+ 8 (-237.17 kJ/mol) ] AG,' = (-701.56 kJ/mol- [(1577.6 kJ/mol) - 1897.36 kJ/mol ] AG;' = (-701.56 kJ/mol - 1577.6 kJ/mol )- 1897.36 kJ/mol AG;' = -4176.52 kJ/mol So: AG; <0 -----> Exergonic reaction (Gº <Gº,) ---->Energy is released Spontaneous reaction