Stability diagram, exercise

STABCAL was also used to construct pE-pH stability fields for chloropyromorphite, hinsdalite, plumbogummite, tricadmium diphosphate, tricopper diphosphate, and hopeite (Fig. 7). These diagrams allow for estimation of stability with respect to pH and to the presence of insoluble sulphides. The NBS thermodynamic database (Wagman et al. 1982) was used as a source of thermodynamic data. The total concentrations chosen for each metal were selected to produce a stability region for the metal phosphate solid. In some cases, this was a very low total concentration (e.g., CTPb =1 x 10 10 M for Pb). In other cases, the total metals concentration was high (e.g., C r.cd— 1 x 10 3 M for Cd). The modelling exercise used typical equilibrium concentrations for MSW bottom ash leachates as shown in Table 2. 

For states at which the equation of state provides only one real root for v, then Kj > 0 and the simplification (8.3.14) is legitimate. But when the equation of state has bifurcated, producing multiple roots for v, then we must exercise care when using (8.3.14) in place of (8.3.13). Some of those volume roots will have Kj < 0 and therefore will be mechanically unstable, even if those roots also have Gn > 0, so they satisfy (8.3.14). Consequently, those fluids are diffusionally unstable because (8.3.13) is violated. For cubic equations of state, it is the "middle" root for v that has Gn > 0, but Kj < 0, as illustrated in Figure 8.11. Equations of state that are higher-order pol)momials in v will have additional roots that behave as in Figure 8.11. So when we test for the observability of proposed states and we do not know where that state lies on a phase diagram, we should apply the complete stability criterion (8.3.13), rather than the abbreviated form (8.3.14). 

Since the key to understanding AG diagrams is the realization that they are relevant only to the standard state, we can ask what will happen if we change our definition of the standard state. This is very seldom done, but it can be quite instructive to do so. During this exercise, it is important to state right up front that any mathematical analysis will not affect the intrinsic stabilities of H, G, and H G. Yet, as you will see, it does effect what we define as an exergonic or endergonic reaction. 

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