Ss = = Y Gs T 1 in .NET Writer barcode 3/9 in .NET Ss = = Y Gs T 1

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Ss = = Y Gs T 1 use .net ansi/aim code 39 generation toincoporate barcode 3/9 with .net SQL server (15.53). Vs = Gs P = Q+ (15.54). CP s = T Ss pT T T = TX + 2TY (15.55). Note that in regions wher 39 barcode for .NET e g = 0 (essentially where T < 150 C or P > 2000 bars), the T and P derivatives of in these expressions become zero (because re j is independent of T P when g = 0), and the solvation terms resume their original fairly simple forms. The re j term in the HKF model essentially takes the place of the term in the D H model, and because it is different for each ion, the overall model suffers from the problem mentioned in 15.

4, i.e., that dGsolution is not an exact differential.

However, the authors consider that the error introduced is acceptable in view of other sources of uncertainty.. Electrolyte solutions 15.8.4 The empirical part After defining the Born f unction as described above, comparison of experimental values of V and CP with calculated values of V s and CP s showed that the discrepancies could be fitted with functions of the form. V n = a1 + a2 f P + a3 f1 visual .net Code39 T + a4 f P f1 T (15.56).

CP n = c1 + c2 f2 T (15.57). where subscript n stands for nonsolvation, and f1 T = 1/ T f2 T = 1/ T f P = 1/ +P In the original HKF model 3 of 9 barcode for .NET , was a fit parameter for each ion having values usually ranging from about 200 to 260 K. Studies of supercooled water reviewed by Angell (1982, 1983; references in Tanger and Helgeson, 1988) however show that 228 3 K is a singular temperature at which several properties approach , and in the revised model takes on the fixed value of 228 K.

The parameter is also fixed at 2600 bars.. 15.8.5 Expressions for V and Combining the Born and empirical parts of the model gives V = Vn + Vs = a1 + a3 a2 Code39 for .NET + +P T 1 + a4 +P T (15.58).

nonsolvation part Q+ solvation part for the (conventional) st Code 3 of 9 for .NET andard partial molar volume of ion j or electrolyte k as a function of T and P, and. CP = CP n + CP s = c1 + c2 T nonsolvation part (15.59) T T P solvation part + TX + 2TY 15.8 The HKF model for aqueous electrolytes for the (conventional) st andard partial molar heat capacity of ion j or electrolyte k as a function of T only. No extra effort need be expended to determine the effect of pressure on CP because this information is included in the expression for partial molar volume already obtained. That is, because.

S P = V T (15.60). it follows that CP P = T V T2 (15.61). This gives CP P CP Pr = V T2 (15.62). CP P T = CP Pr T + V T2 (15.63). which on integration turns out to be CP P T = CP = c1 + c2 T 2T T a3 P Pr + a4 ln +P + Pr nonsolvation part + TX + 2TY P solvation part (15.64). 15.8.6 Expressions for H and Having expressions for th e temperature and pressure effects on CP and V , straightforward, if somewhat lengthy, integration gives expressions for S , H , and G , which can refer either to an ion j or an electrolyte k, depending on the fit parameters used in the expression. Thus. S P T S P r Tr = T C P P dT Tr T Pr V T 1 T = c1 ln T Tr 1 Tr ln Tr T T Tr Electrolyte solutions 1 T 1. a3 P Pr + a4 ln 1 +P + Pr (15.65). + Y P T YP T r r r r V T +P + Pr +P + Pr T H P T H P r Tr = CP dT + V T 1 T = c1 T Tr c2 1 Tr + a1 P Pr + a2 ln + + 2T T 1 (15.66). a3 P Pr + a4 ln 1 1 1 + TY T 1 Pr Tr P T r r 1 P T Tr YP T r r r r GP T GPr Tr = S Pr Tr T Tr + CP dT P CP dT + V dP T Tr Pr T = S Pr Tr T Tr c1 T ln Tr + a1 P Pr + a2 ln c2 + 1 T 1 T +P + Pr 1 Tr T + Tr T +P + Pr ln 1 Tr T T Tr 1 (15.67). a3 P Pr + a4 ln 1 Pr Tr P T r r 1 + P T YP T T Tr r r r r At this point we have sho Code 3/9 for .NET wn how the HKF model develops expressions for the standard state parameters V and CP and hence S , H , and G at high temperatures and pressures. The standard state universally used is the ideal one molal solution, which means that these parameters refer to the properties of ions or electrolytes in infinitely dilute solutions.

You might suppose that therefore they would not be of much use to geochemists interested in natural solutions, which are often quite concentrated, but you would be wrong. The standard state properties allow the calculation of the equilibrium constant for reactions involving ions at high T P, and thus permit the general nature of many important processes to be understood, even in cases where activity coefficients. 15.8 The HKF model for aqueous electrolytes are unknown. Of course fo barcode code39 for .NET r quantitative calculation of ionic concentrations and mass transfers in such cases, activity coefficients are also required.

. 15.8.7 Contributions of the solvation and nonsolvation terms A striking feature of the Code 3/9 for .NET partial molar volumes and heat capacities of aqueous electrolytes is their inverted-U shape as a function of temperature. Experimental data that cover a sufficiently large range of temperature invariably exhibit a maximum, generally somewhere between 50 and 100 C.

This was illustrated in Figures 10.6 and 10.12, which show data for the partial molar volume and heat capacity of NaCl.

The existence of singular temperatures for water at 45 C (228 K, Angell, 1982, 1983) and 374 C (the critical temperature) makes it seem entirely reasonable that thermodynamic parameters of solutes in water should approach at these limits, and therefore reasonable that they should exhibit extrema (or inflection points) between these temperatures.2 The revised HKF model is constructed such that the nonsolvation contribution to V and CP dominates at low temperatures and becomes at 228 K, and the solvation contribution dominates at high temperatures. The contributions of the solvation and nonsolvation parts of the partial molar volume of Na+ are compared in Figure 15.

9, and in Figure 15.10 the solvation and nonsolvation contributions to the partial molar heat capacity of HCl are shown as a function of temperature. Note how the shapes of the two contributions combine to give the inverted-U shape of the measured heat capacity.

This illustrates quite nicely how the two contributions combine to produce a maximum, and it can easily be imagined how the shape of the combined curve is controlled by the fit parameters of the two contributions. Of course, the two contributions do not always cross in such a pedagogically convenient way. In preparing Figures 15.

9, 15.10 and 15.11, the original (pre-Tanger and Helgeson) equations were used.

For example, the solvation contribution to CP is Equation (15.52), and the nonsolvation contribution is.
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