To calculate the standard Gibbs free energy change G for the electrochemical reaction, we can use the following equation:G = -nFEcellwhere n is the number of moles of electrons transferred in the reaction, F is the Faraday constant 96,485 C/mol , and Ecell is the standard cell potential.First, we need to determine the balanced half-reactions for the oxidation of aluminum and the reduction of oxygen:Oxidation half-reaction: 4Al s 4Al aq + 12eReduction half-reaction: 3O aq + 12e 6O aq Now, we can combine these half-reactions to form the overall balanced reaction:4Al s + 3O aq 2AlO s From the balanced reaction, we can see that 12 moles of electrons are transferred n = 12 .Now, we can plug the values into the equation:G = -nFEcellG = - 12 mol 96,485 C/mol 1.66 V G = -1,919,468.52 J/molSince the standard Gibbs free energy change is usually expressed in kJ/mol, we can convert the value:G = -1,919.47 kJ/molSo, the standard Gibbs free energy change for the electrochemical reaction of 2 moles of aluminum being oxidized to form 3 moles of aluminum oxide in a standard state is -1,919.47 kJ/mol.