Apparent molar, heat capacity volume

Mixtures of these surfactants with water result in solutions with unique properties that we want to consider. We will use the alkylpyridinium chlorides as examples. Figure 18.11 compares the osmotic coefficient 0, apparent relative molar enthalpy 4>L, apparent molar heat capacity Cp, and apparent molar volumes V as a function of molality for two alkylpyridinium chlorides in water.w19... 

Figure 18.11 (a) Osmotic coefficient (b) apparent relative molar enthalpy (c) apparent molar volume and (d) apparent molar heat capacity, at T = 298.15 K and p = 0.1 MPa, for (1) n-decylpyridinium chloride and (2) n-dodecylpyridinium chloride. 

Figure 18.13 Effect of temperature on (a) apparent relative molar enthalpies (b) apparent molar volumes and (c) apparent molar heat capacities, for n-dodecylpyridinium chloride. The temperatures are (1) 298.15 K (2) 313.15 K and (3) 328.15 K.

Figure 18.15 Surfactant pseudo-phase model prediction for (a) the apparent molar volume and (b) the apparent molar heat capacity. Drawing courtesy of K. Ballerat-Busserolles from the Institut de Chemie des Surfaces et Interfaces, Mulhouse, France.

Figure 18.16 (a) Apparent molar volume and (b) apparent molar heat capacities for aqueous sodium dodecylsulfate at T = 298.15 K and /> = 0.1 MPa, graphed as a function of 1 /m. The insets give the values at low m where a second transition occurs in the micelle. 

PAT/WOO] Patterson, B. A., Woolley, E. M., Thermodynamics of ionization of water at temperatures 278.15 K < T/K < 393.15 K and at the pressure p = 0.35 MPa apparent molar volumes and apparent molar heat capacities of aqueous of potassium and sodium nitrates and nitric acid, J. Chem. Thermodyn., 34, (2002), 535-556. Cited on pages 87, 88. 

HOV/HEP] Hovey, J. K., Hepler, L. G., Apparent and partial molar heat capacities and volumes of aqueous HCIO4 and HNO3 from 10 to 55"C, Can. J. Chem., 67, (1989), 1489-1495. Cited on page 87. 

This series of papers contains an extensive array of correlated data on aqueous electrolyte solutions, much of It having been calculated using the system of equations given In paper I In this series. The contents of these papers have been summarized by Pitzer In a chapter in the book edited by Pytkowicz (see Item [123]). The data Include activity and osmotic coefficients, relative apparent molar enthalpies and heat capacities, excess Gibbs energies, entropies, heat capacities, volumes, and some equilibrium constants and enthalpies. Systems of Interest Include both binary solutions and multi-component mixtures. While most of the data pertain to 25 °C, the papers on sodium chloride, calcium chloride, and sodium carbonate cover the data at the temperatures for which experiments have been performed. Also see Items [48], [104], and [124]. 

The apparent molar volumes and heat capacities, V2. and Cp 2 of NaDec In water and In 0.05 mol kg l BE are shown In figure 1. As expected from the formation of mixed micelles, BE shifts the CMC of NaDec to lower values. 

Figure 1 Apparent molar volumes and heat capacities of sodium deca noate In water (ref. 11) and In 0.05 mol kg of 2-butoxy-ethanol at 25°C.

With most properties (enthalpies, volumes, heat capacities, etc.) the standard state is infinite dilution. It is sometimes possible to obtain directly the function near infinite dilution. For example, enthalpies of solution can be measured in solution where the final concentration is of the order of 10-3 molar. With properties such as volumes and heat capacities this is more difficult, and, to get standard values, it is usually necessary to measure apparent molal quantities 0y at various concentrations and extrapolate to infinite dilution (y° = Y°). Fortunately, it turns out that, at least with volumes and heat capacities, the transfer functions AYe (W — W + N) do not vary significantly with the electrolyte concentration as long as this concentration is relatively low (3). With most of the systems investigated, the transfer functions were calculated from apparent molal quantities at 0.1m and assumed to be equivalent to the standard values. 

The thermodynamic properties at T = 298.15 K shown in Figure 18.11 come from S. Causi, R. De Lisi, and S. Milioto, Thermodynamic properties of N-octyl-, N-decyl- and N-dodecylpyridinium chlorides in water , J. Solution Chem., 20, 1031-1058 (1991). Results at the other two temperatures are courtesy of K. Ballerat-Busserolles, C. Bizzo, L. Pezzimi, K. Sullivan, and E. M. Woolley, Apparent molar volumes and heat capacities at aqueous n-dodecyclpyridium chloride at molalities from 0.003 molkg-1 to 0.15 molkg-1, at temperatures from 283.15 K. to 393.15 K, and at the pressure 0.35 MPa , J. Chem. Thermodyn., 30, 971-983 (1998). 

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. 

The first thing we come across when looking at real data is that quite often the data are reported as apparent molar volumes, enthalpies, entropies or heat capacities. If we call component 1 the solvent (usually water in our cases), component 2 the solute (say, NaCl), Z and Z the total and molar forms of any of these properties, then apparent molar properties are defined as... 

This 268 page article is concerned with the prediction of the thermodynamic properties of aqueous electrolyte solutions at high temperatures and pressures. There is an extensive discussion of the fundamental thermodynamics of. solutions and a discussion of theoretical concepts and models which have been used to describe electrolyte solutions. There is a very extensive bibliography ( 600 citations) which contains valuable references to specific systems of interest. Some specific tables of interest to this bibliography contain Debye-Hiickel parameters at 25 C, standard state partial molar entropies and heat capacities at 25 °C, and parameters for calculating activity coefficients, osmotic coefficients, relative apparent and partial molar enthalpies, heat capacities, and volumes at 25 °C. 

Patterson BA, Wooley EM (2001) Thermodynamics of proton dissociation from aqueous citric acid apparent molar volumes and apparent heat capacities of citric acid and its sodium salts at the pressure of 0 35 MPa and at temperatures from 278.15 K to 393.15 K. J Chem Thermodyn 33 1735-1764... 

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