Partial molar volume of NaCl

Question. How does the partial molar volume of NaCl(aq) in this solution compare to molar volume of pure solid NaCI ... 

Tube. showing total volume of fluid / AV is partial molar volume of NaCl 1 mole NaCl added... 

The revised HKF model is constructed such that the non-solvation contribution to V° and C° dominates at low temperatures and becomes -oo at 228 K, and the solvation contribution dominates at high temperatures. The contributions of the solvation and non-solvation parts of the partial molar volume of NaCl are compared in Figure 17.11, and in Figure 17.12 the solvation and non-solvation contributions to the partial molar heat capacity of NaCl are shown as a function of temperature. This illustrates quite nicely how the two contributions combine to produce a maximiun, 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 Figure 17.13 we show the two contributions to the partial molar volume of HCl as a function of temperature the same features are present, but the relative contributions of the two parts of the model are quite different. 

The densities of aqueous NaCl solutions at 25°C are given as a function of NaCl molality in Table P.5, (a) Obtain a graph for the partial molar volumes of both water V, and NaCl V2, as a function of NaCl molality. Compare the limiting cases V, (m 0), (m sat) with those of pure water and pure NaCl molar volumes, Vj and V, respectively, (b) Calculate Vj for m = 0.5 and m = 2. (Mussini)... 

Various Systems. 3.3.1. Water (l)-Malate Dehydrogenase (Hm MalDH) (2)—NaCl (3). For water (1)—Hm MalDH (2)—NaCl (3), experimental data for both F and OSVC are available. 3,44 -pbe partial molar volumes of the components of the protein-free mixed solvent (Vi and V3) were calculated from the densities of the water—NaCl... 

Malate dehydrogenase. " 2 was taken equal to the partial molar volume of the protein in a 1 M NaCl solution. 

A single homogeneous phase such as an aqueous salt (say NaCl) solution has a large number of properties, such as temperature, density, NaCl molality, refractive index, heat capacity, absorption spectra, vapor pressure, conductivity, partial molar entropy of water, partial molar enthalpy of NaCl, ionization constant, osmotic coefficient, ionic strength, and so on. We know however that these properties are not all independent of one another. Most chemists know instinctively that a solution of NaCl in water will have all its properties fixed if temperature, pressure, and salt concentration are fixed. In other words, there are apparently three independent variables for this two-component system, or three variables which must be fixed before all variables are fixed. Furthermore, there seems to be no fundamental reason for singling out temperature, pressure, and salt concentration from the dozens of properties available, it s just more convenient any three would do. In saying this we have made the usual assumption that properties means intensive variables, or that the size of the system is irrelevant. If extensive variables are included, one extra variable is needed to fix all variables. This could be the system volume, or any other extensive parameter. 

In Figure 17.14 we show the HKF representation of the partial molar volumes of Na", Cl, and NaCl, together with the exjrerimental data. The data shown for the... 

Fig. 17.13. The standard partial molar volume of aqueous NaCl as a function of temperature. Squares are experimental data, and the solvation and non-solvation contributions are from the HKF model for Cr.

In solutions, particularly electrolyte solutions, the standard state for the solvent is always the pure phase (pure water), so that, for example, refers to the molar volume of pure component 1, that is, pure water. For the solute, the standard state for most properties is, as just mentioned, the state of infinite dilution, so we could use for tho partial molar volume of the solute in the standard state. However, this proves a bit confusing, so for clarity we introduce superscript °° to indicate the infinite dilution state (1 ), and we understand that this is also the standard state for most properties. This raises the question of what symbol to use for the solute in its pure state. The lUPAC recommends the use of for pure substances, but our examples involve only minerals so we will just use the mineral name. Thus we use for the molar volume of pure NaCl. 

This very extensive (99 pages) chapter (no. 2 in Volume II) contains a general discussion of the effects of temperature and pressure on activity coefficients for both binary and mixed electrolyte solutions. Properties of interest are the partial molar volume, expansibility, compressibility, heat capacity, and enthalpy. There is also an excellent discussion of methods of estimating partial molar properties in mixed electrolyte solutions. There are 226 references to the literature. Tables of data are presented for Debye-HUckel limiting law slopes for the afJ parent molar volume, enthalpy, heat capacity, expansibility, and compressibility as a function of temperature parameters for the partial molar volumes of 30 aqueous electrolyes at 25 °C parameters for the partial molar expansibility of ten electrolytes at 25 C parameters for the partial molar compressibilities of 33 electrolytes at 25 °C values of the activity coefficients of aqueous NaCl solutions at 25 C as a function of pressure (up to 1000 bars) parameters for the partial molar enthalpies of 59 electrolytes at 25 C parameters for the partial molar heat capacities of 140 electrolytes at 25 °C and tables giving compositions and the partial molar properties of average seawater. 

Fig. 17.10. The standard partial molar volume and standard partial molar heat capacity of aqueous NaCl as represented by the HKF model, showing the characteristic inverted-U shape and steep negative slopes at high and low temperatures.

FIGURE 8.11 Behavior of A 2,ex(SR) and p" (Ci2 - C°j) for an infinitely dilute CsBr aqueous solution as a function of the solvent density along three supercritical isotherms in comparison with experimental data. (Data from J. Sedlbauer, E. M. Yezdimer, and R. H. Wood, 1998, Partial Molar Volumes at Infinite Dilution in Aqueous Solutions of NaCl, LiCl, NaBr, and CsBr at Temperatures from 550 K to 725 K, Journal of Chemical Thermodynamics, 30, 3.) Vertical arrow indicates the estimated critical density of the model solvent... 

Sedlbauer, J., E. M. Yezdimer, and R. H. Wood. 1998. Partial molar volumes at infinite dilution in aqueous solutions of NaCl, LiCl, NaBr, and CsBr at temperatures from 550 K to 725 K. Journal of Chemical Thermodynamics. 30, 3. 

A striking feature of the 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 oo at these limits, and therefore reasonable that they should exhibit extrema (or inflection points) between these temperatures. ... 

Sedlbauer and Wood (2004) used the MSA model to describe the tiiermodynamics properties of NaCl near the critical point. In this case the crystallographic diameters of the ions were used along with a model (Sedlbauer et al, 2000) for the standard state term. The MSA model without adjustable parameters provides a better fit of the partial molar volume than the Pitzer model. 

Figure 2.14 show the density dependencies of the partial molar volumes at infinite dilution for HjO + NaCl solutions along the supercritical isotherms calculated with the crossover model (Belyakov et al., 1997 and Kiselev and Rainwater, 1997) and the semiempirical equation developed by Sedlbauer et al (1998). 

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