## Ellingham Diagram Fig. 9.8 Ellingham diagram for the free energy of formation of oxides v

Fig. 9.8 Ellingham diagram for the free energy of formation of oxides

From Fig. 9.8, AG^/Cu0 = -48 kcal /mole (-203 kJ/mole) . However, this reaction does not represent an equilibrium situation; Cu and CuO can never coexist because the lower oxide Cu2O intervenes. Nonetheless, the standard free energy change for the Cu2O/CuO equilibrium can be obtained from:

AGC^o/cuo = 2AGCu/cuo - AGC^o = 2x (-203 ) -(-230) = -176 kJ/mole so that:

Cu20/Cu0 8.314 x 673 J

Therefore, at 400oC, Cu2O is the sole oxide present in atmospheres with oxygen pressures between 1.4x10-18 and 2.2x10-14 atm. In O2 pressures larger than the upper limit of this interval, only CuO exists.

The lines in Fig. 9.3 are straight. The absence of curvature indicates that AHo and ASo are approximately constant. The effect of the different values of the specific heats of the products and reactants (ACP) discussed in Sects. 9.2 and 9.3 have either been neglected or are too small to cause appreciable nonlinearity in the Ellingham lines. This effect is included in the next subsection.

The effect of a phase change of the metal is to make ASo more negative by adding entropy to the reactant side of the reaction (see the M curve in Fig. 9.2). Since the slope of an Ellingham line is -ASo, the slopes increase discontinuously at the melting point TM and at the boiling point TB (i.e., when the vapor pressure equals 1 atm). The magnitude of the increase in the slope at the melting point is AhM/TM. Because AhM is small, the change in slope at TM is not noticeable at the plus signs on the lines in Fig. 9.8.

Two metals, Li and Mg, have boiling points that fall within the temperature range of Fig. 9.8. When the metals vaporize, the entropy change is Ahvap/TB. Since Ahvap is typically an order of magnitude larger than AhM, the slope change due to the entropy of vaporization is clearly visible on the lines for these two metals.

Figure 9.8 includes lines for the CO/CO2 equilibrium (Eq (9.26)) and the analogous equilibrium for H2/H2O mixtures. These reactions differ from the metal-metal oxide lines in one important aspect. The latter give the oxygen potentials of the M/MaOb couples by Eq (9.56). The oxygen potentials of the two all-gas reactions, on the other hand, also depend on the molar ratio CO2/CO (or H2O/H2), as shown in the example in Sect. 9.6.2. The lines for these two systems are

AG° ,„„ and AGo Vs T. The two all-gas reactions are included in the Ellingham

CO/CO2 h2/h2o diagram because they are often needed in conjunction with the metal-metal oxide data in practical applications.

this to the value obtained from the Ellingham diagram.

At 2000K on the CO/CO2 line, AG°Q/ = 43 kcal/mole; Using Eq (9.52) gives Kp = 6x104, which is a factor of 8 lower than the value used in the example in Sect. 9.9.4. The discrepancy is probably due to the linear approximation for the CO/CO2 data in Fig. 9.8.

Example: In Sect. 9.9.4, the example gave KP = 4.4x105 at 2000 K for the CO/CO2 equilibrium. Compare 