Calculate the equilibrium constant and AG for the oxidation of Mn (II) to manganese oxide by dissolved oxygen. What oxygen concentrations are needed for pH values of 6.0, 7.0, and 8.0 such that the reaction is thermodynamically favorable? Given: [Mn2+] = 10-6 M and the temperature is 298 K.

Half reactions will be used:

Mn²⁺ + 2H₂O= MnO₂ + 4 H⁺ + 2e E_0x =-1.23 V

O₂(aq) +4H⁺ +4e = 2HO E_red =1.27 V