Oxygen free energy change

Equation (a) forms the basis removing Ca from sodium. The free-energy change for the reaction is highly favorable, and even at small concentrations of Ca in sodium the addition of oxygen should result in the formation of insoluble CaO. 

When the right-hand side of the above equation is zero, i.e., when either T = 0 or P0j equals one atmosphere, AG° must be zero. The intersection of the standard free energy change versus temperature line with the temperature axis, when AG° = 0, gives the temperature at which the oxygen equilibrium pressure, P0i, is equal to one atmosphere. This temperature is known as the decomposition temperature of the oxide and is denoted as TD on line 1 in Figure 3.5. 

If the combination of oxygen and carbon at the anode is included in the electrochemical reaction then the free energy change is much smaller. For the reaction... 

These conditions can be satisfied by drawing the common tangent to the G curves of M(O) and MO. As shown in Fig. 1.7, the chemical potentials of M and O for the M(O) phase with the composition x, are equal to those for the MO phase with the composition Xj, and the values correspond to MqMj and OgO, respectively. If the experimental conditions are similar to those described in Section 1.1, the solid phases must coexist with the gas phase. It may be adequate for the gas phase to be pure O2, because the vapour pressure of other species is very low in this case. The chemical potential of O for the gas phase is equal to OgO, which corresponds to the oxygen pressure. Thus we can understand the coexistence of the M(O) phase with Xj and the MO phase with X2 from the free energy change of composition. 

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