Oxygen partial molar enthalpy

Figure 11. (a) The calculated partial molar entropy of oxygen (sQJ and (b) the calculated partial molar enthalpy of oxygen (fto2) as a function of 8 for La02Sr08Fe0 55Tio4503 s. Symbols are calculated by the Gibbs-Helmholtz equation. Lines correspond to the partial molar quantities calculated by statistical thermodynamics. 

The partial molar enthalpy (h0 ) and the partial molar entropy ( s0 ) of oxygen can be derived from the chemical potential (p-o2) of oxygen as below... 

Since Roberts has discussed nonstoichiometric fluorite-type oxides in several papers, the thermodynamics need be only briefly summarized. Below 1123° C., the distinct nature of the nonstoichiometric U02 and U409 phases, and the more highly ordered nature of the latter, are shown by the differences in partial molar enthalpy of oxygen in the two phases, and by the considerable decrease in entropy accompanying the U02+a. phase reaction (Table II). 

Figure 4. Partial molar enthalpy and entropy of oxygen in nonstoichiometric phases based on fluorite structure...

A proper description of electronic defects in terms of simple point defect chemistry is even more complicated as the d electrons of the transition metals and their compounds are intermediate between localized and delocalized behaviour. Recent analysis of the redox thermodynamics of Lao.8Sro,2Co03. based upon data from coulometric titration measurements supports itinerant behaviour of the electronic charge carriers in this compound [172]. The analysis was based on the partial molar enthalpy and entropy of the oxygen incorporation reaction, which can be evaluated from changes in emf with temperature at different oxygen (non-)stoichiometries. The experimental value of the partial molar entropy (free formation entropy) of oxygen incorporation, Asq, could be... 

Figure 10.8 Variation of the relative partial molar enthalpy of component oxygen versus oxygen nonstoichiomet7 for nontrapped case — 0 solid curve) and fully trapped case — oo ...

Equation (56) indicates that when an oxygen atom is incorporated into the lattice, it picks up holes [Eq. (52)] and electrons [Eq. (53)] at random, depending on then-availability. It is, therefore, quite natural that the partial molar enthalpy of the component oxygen, AHo is dependent on the relative amount of electrons and holes or the oxygen nonstoichiometry. 

The relative partial molar enthalpy of oxygen is evaluated at different nonstoichiometry values by using the thermodynamic identity... 

Figure 10.10 shows the plotted log Oq versus reciprocal temperature at different nonstoichiometries. As can be seen, this is generally linear for a fixed 5 over the temperature range examined. The relative partial molar enthalpy and entropy of oxygen may then be evaluated from the slope and intercept, respectively. The results of AHo are as shown in Figure 10.11. In agreement with Eq. (50), the partial molar enthalpy variation is best fitted as ...

Figure 10.11 Relative partial molar enthalpy of component oxygen versus nonstoichiometry for undoped BaTiOs. The solid curve is best fitted to Eq. (50). Data from Ref. [19].

Standard enthalpies of formation from oxides (A,JT°) and from elements H°), and partial molar enthalpy of oxygen, evaluated for 298 K and the listed exact compositions, according to drop-calorimetry for units see the... 

Nevertheless, the partial molar values play an important role. The composition w enters the configurational partial molar entropy, and the partial molar enthalpy of oxygen should be rather independent of w and the model adopted. Experimental data at constant w (like in fig. 52) across the homogeneity range give indeed only modestly varying (between 160 and 172 kJ/mol) whereas changes markedly (between some 100 and 210 J/mol K)... 

Consider location 1. The total enthalpy of the mixture is xoj/ JfojHn2, where Hi is the partial molar enthalpy of species i in the mixture. At location A, the enthalpy of pure oxygen is xq Hq since there are Xoj gmols of pure O2, whose molar enthalpy is Hoj. Since we have ideal gas behavior, = Hoz- Similarly, at location C, where the enthalpy of pure N2 is xn /Hn. Note that this O2 semipermeable membrane allows O2 to come through at the feed partial pressure similarly for the N2 semipermeable membrane. Calculate the Gibbs free energy change as follows ... 

Figure 13. Experimental data and calculated partial molar enthalpies of mixing for oxygen in the bcc, hep, and bcc+hcp phase fields for the Zr-O System (Ref 11).

A particular case of dopants is that of Pr and Tb, which have the potential to be in a mixed valence state 3+/4+ at more oxidizing conditions than Ce as X-ray absorption near-edge structure (XANES) and X-ray photoelectron spectroscopy (XPS) measurements have revealed. The partial molar enthalpy of oxygen (Ai/o, ) associated with reduction of Pr or Tb appears to be strongly dependent on doping level, degree of reduction, and co-doping. Knauth and... 

Figure 12.9 Composition dependence of the partial molar enthalpy of oxygen...

Fm is the metal molar volume, which accounts for the steric effects at the interface, and C is a constant fitted to experimental values. This model takes care of the metal-oxygen and the metal-cation pair interactions through the quantities AHq(M) and AH y Neglecting the entropy variations, a partial mixing enthalpy AH Q may be written as a function of the AA, BB and AB pair interactions eAA. and 6ab and as a function of the mean coordination number Z of an atom A dissolved in B, in the following way ... 

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