Partial enthalpy at infinite dilution

Let us now consider the data obtained in the liquid alloys using calorimetric methods. These data concern only rare-earth-based alloys. The values of the partial enthalpies at infinite dilution of rare earths in liquid Ni, Co, Fe and Mn (tables 17-20) have been plotted as a function of atomic number in figs. 59-62. Even though large discrepancies between values obtained in a same system exist, one may discern a decrease of the partial enthalpy from La to Lu (except with Fe) and from La to Y to Sc. 

Fig. 59. Partial enthalpy at infinite dilution in liquid nickel of rare earth elements. The references of the data are quoted in table 17.

Values of partial and integral enthalpies of mixing have been obtained by calorimetric methods in liquid-phase Cu-R (table 25). The variation of the partial enthalpy at infinite dilution of rare earth elements in liquid copper is displayed in fig. 75 as a function of atomic number. Even though large discrepancies exist between the reported values, one observes a slight decrease of these values from La to Lu. 

There are also only few data obtained by calorimetric methods for the liquid indium alloys. Considering the two values reported in table 39 it seems unlikely that the partial enthalpy at infinite dilution of Eu in indium will be more negative than the value obtained for Ce in liquid indium (see the results obtained in liquid aluminum). 

In the liquid state some values of partial enthalpies at infinite dilution of rare earths in silicon and enthalpies of mixing have been obtained by calorimetric measurements they concern only rare earth elements. Nothing can be deduced from these values. 

In the liquid state a systematic study of the partial enthalpy at infinite dilution of rare earths in liquid germanium has been performed by Nikolaenko et al. (1979a,b, 1980a,b, 1987, 1988). A decrease of the partial enthalpy at infinite dilution from Sc to Y to La and an increase of these values from La to Lu is seen (fig. 116). Figure 117 shows the values of the enthalpy of mixing at equiatomic composition obtained by the same authors, plotted as a function of the atomic number. The same trend as mentioned above is observed. The values of the enthalpies of formation at equiatomic composition (table 46) have also been reported in figure 117. The same trends of the enthalpies of mixing and of the enthalpies of formation at equiatomic composition are observed. 

In liquid alloys of rare earths or actinides with elements of column VB, we may just quote the value of the partial enthalpy at infinite dilution of cerium in liquid bismuth obtained by Yamshchikov et al. (1983) using a calorimetric method. 

Evolution of the partial enthalpy at infinite dilution of rare earths in liquid metallic solvent... 

An accuracy improvement in determining of the chemical potential (AjUi(T, Xt) versus temperature (T) and atomic fraction (xi) from 10 to 50 J/mol not only leads to the various thermodynamic properties of the system (partial entropies (A) and enthalpies (AfHj) of components, phase enthalpies of transformation (A), partial enthalpies at infinite dilution (Aj-H ), thermal capacities (Cp), but also gives a possibility to study the phase diagram in detail (liquidus and solidus, miscibility gaps, invariant points, stoichiometry deviations, ordering, etc...)... 

PARTIAL MOLAR EXCESS ENTHALPY AT INFINITE DILUTION OF THIAZOLE IN VARIOUS SOLVENTS AT SIS.IS K... 

GLC is a well-established and accurate method used to obtain and the partial molar excess enthalpies at infinite dilution values AHf" , which is determined from the Gibbs-Helmholtz equation ... 

The partial molar excess enthalpy at infinite dilution, Hf- " , can be determined by Equation 4.5. 

Table 13 Partial Molal Excess Enthalpy at Infinite Dilution (HE) of Thiazole in Various Solvents at 318.15 K <79HC(34-i)i, p. 88)...

An application of continuum solvation calculations that has not been extensively studied is the effect of temperature. A straightforward way to determine the solvation free energy at different temperatures is to use the known temperature dependence of the solvent properties (dielectric constant, ionization potential, refractive index, and density of the solvent) and do an ab initio solvation calculation at each temperature. Elcock and McCammon (1997) studied the solvation of amino acids in water from 5 to 100°C and found that the scale factor a should increase with temperature to describe correctly the temperature dependence of the solvation free energy. Tawa and Pratt (1995) examined the equilibrium ionization of liquid water and drew similar conclusions. An alternative way to study temperature effect is through the enthalpy of solvation. The temperature dependence of is related to the partial molar excess enthalpy at infinite dilution,... 

Hl,i = partial molar enthalpy at infinite dilution for the aqueous molecular species i, cal/gm-mole... 

Equations (8.37) and (8.41) thus give the means to calculate the partial molal enthalpies at infinite dilution for ionic and molecular species. The calculation of the partial molal enthalpy of species i is complete but for the contribution due to the "excess enthalpy term of equation (8.31) ... 

In these equations and again refer to the partial molar enthalpy at infinite dilution and in the solution where the activity coefficient is y< respectively. These quantities can be determined by experiment as discussed in 2-14. It will be noted from (9 26) and (9 28) that the activity coefficients of a solute defined by Conventions n and III both have the same temperature coefficient. 

These correlations make use of the atomic and electronic characteristics of the metal and of the oxide. However, the adhesion energy also depends upon the nature of the chemical bonds formed at the interface. This is the guiding idea of the first thermodynamical models of adhesion (McDonald and Eberhart, 1965), later improved by Chatain et al (1986 1987). The adhesion energy W dh for an XO oxide, is related to the partial mixing enthalpies at infinite dilution of oxygens (O) and cations (X) in the metal... 

FIG. 2-29 Enthalpy-concentration diagram for aqueous sodium hydroxide at 1 atm. Reference states enthalpy of liquid water at 32 F and vapor pressure is zero partial molal enthalpy of infinitely dilute NaOH solution at 64 F and 1 atm is zero. [McCahe, Trans. Am. Inst. Chem. Eng., 31, 129(1935).]... 

Solute. The standard state for the solute is the hypothetical unit mole fraction state (Fig. 16.2) or the hypothetical 1-molal solution (Fig. 16.4). In both cases, the standard state is obtained by extrapolation from the Henry s-Iaw line that describes behavior at infinite dilution. Thus, the partial molar enthalpy of the standard state is not that of the actual pure solute or the actual 1 -molal solution. 

We have pointed out that a concentration m2(o of the solute in the real solution may have an activity of 1, which is equal to the activity of the hypothetical 1-molal standard state. Also, Hm2, the partial molar enthalpy of the solute in the standard state, equals the partial molar enthalpy of the solute at infinite dilution. We might inquire whether the partial molar entropy of the solute in the standard state corresponds to the partial molar entropy in either of these two solutions. 

P-C-T Determinations Low Pressure Studies. Absorption isotherms obtained for the reaction of hydrogen with TiMo are shown in Figure 3 for 590°-392°C. These temperatures are above the decomposition temperature of /J-TiMo (see Figure 2) consequently, decomposition of the solid solution plays no role here. These data follow Sieverts Law only in the very dilute region—to hydrogen-to-metal ratios (H/M) of about 0.02. Thereafter, deviations in the direction of decreased solubility are observed. Data in the region of Sieverts Law can be used to determine the relative partial molar enthalpy and entropy at infinite dilution (47). From Sieverts Law (Equation 1), where Ks is a tempi/2 = Ksn (1)... 

This means that the partial specific enthalpy of NaOH at infinite dilution ( at xN.OH 0) is aibirarily set equal to zero at 68(T). The graphical interpretation that the diagram is constructed in such a way that a tangent drawn to the isotherm at xNaOH = 0 intersects the xn oh = 1 ordinate (not shown) at an entl of zero. The selection of ff ttOH as zero at 68(°F) automatically fixes the values the enthalpy of NaOH in all other states. 

Activity coefficients can be related to the partial enthalpies and partial excess entropies of mixing of A1 and O at infinite dilution in M as follows ... 

Figure 7.3. Calculated values of molar fraction of Si in liquid metal M at the three phase M/SiC/Cg equilibrium (equation 7.4) as a function of the partial enthalpy of mixing of Si at infinite dilution in M. Arrows indicate values of AH (M for some metals M given in Appendix G.

Table G. 1 reproduces values calculated by Miedema s model (Niessen et al. 1983) for the partial enthalpy of solution at infinite dilution of a liquid metal solute i in a liquid metal solvent i, AH, (in kJ/mole). For a i-j alloy, the regular solution parameter k can be approximated by [AHj(j( + AHJ(l)]/2.

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