Apparent molar, heat capacity properties

Figure 18.6 Thermal properties of aqueous NaCl solutions as a function of temperature, pressure and concentration, (a) activity coefficient (b) osmotic coefficient (c) relative apparent molar enthalpy and (d) apparent molar heat capacity. The effect of pressure is shown as alternating grey and white isobaric surfaces of 7 , , L, and Cp at p = 0.1 or saturation, 20, 30, 40, 50, 70, and 100 MPa, that increase with increasing p in (a), (b), and (d), and decrease with increasing P in (c).

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... 

Pabalan, R., and Pitzer, K. S. (1988) Apparent Molar Heat Capacity and Other Thermodynamic Properties of Aqueous Potassium Chloride Solutions to High Temperatures and Pressures, J. Chem. Eng. Data 33, 354-362. 

Quite striking extrema are observed in the dependence of apparent partial molar heat capacities on salt concentration for alkylammonium salts and related compounds, e.g. Bu4N+ octanoate, and these can be understood in terms of long-range hydrophobic interactions (Leduc and Desnoyers, 1973). However, the properties of n-alkylamine hydrobromides have indicated that there are still... 

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. 

The tables in this chapter include Debye-HUckel parameters for the osmotic coefficient, enthalpy, and heat capacity as a function of temperature parameters for the activity and osmotic coefficients of approximately 270 aqueous strong electrolytes at 25 C parameters for the relative apparent molar and excess enthalpy of %90 strong electrolytes at 25 C a table of parameters for the activity and osmotic coefficients ofss75 binary mixtures with and without common ions and with up to three solutes present and parameters for the thermodynamic properties of aqueous NaCI and H2SO4 as a function of temperature. The author has included references to his earlier papers ivhich also contain valuable data on electrolyte solutions (also see item [121]). 

Closely related to volnmetric properties are compressibility properties of solntions, and they usually are evaluated from combining sound velocities, densities and heat capacity determinations. Soimd velocity measnrements in aqneons solntions of citric acid were initiated in 1952 by Miyahara [128] who determined at 20 °C, the isentropic (adiabatic) compressibihty coefficients k (7 /w) and hydration numbers h m,T) in dilute solutions, m<025 mol kg . Sonnd velocities u(T m) in the same concentration range were measmed by Tadkalkar et al. [116] from 30 to 45 °C. In very dilute citric acid solutions u T m) and h(nr,T) values are reported by Bura-kowski and Ghhski [129,130]. Parke et al. [131] correlated the taste and properties of solutions, namely the apparent molar compressibihties, hydration numbers, apparent molar volmnes and apparent specific volnmes of 3 % citric acid solution. In moderately concentrated citric acid solutions, m<0.5 mol kg (in water or in the water + DMSO and water + DMF mixtures), measmements were performed by Bhat et al. [132] at 30 °C. Kharat [117] reported a more complete set of speed velocities, the isentropic (adiabatic) compressibihty coefficients and the apparent molar compressibilities for m<235 mol kg citric acid solutions in... 

In spite of a large amount of experimental data, unfortunately due to absence of heat capacities and sometimes viscosities, only restricted compressibility properties can be determined and they are also limited to one temperature. In Table 5.15 are presented values of A m) and u m) at 25 °C (for other temperatures they are available in the original papers) and they permit to evaluate the isentropic compressibility coefficients Kjj -yn) and the apparent molar compressibilities K (T m) using Eqs. (5.52). 

---