Apparent molal heat capacities

Figure 6. Apparent molal heat capacity of aqueous NaCl at 177 bars as a function of molality and temperature...

The apparent molal heat capacity of DEC was measured in BE-H2O mixtures with a flow microcalorimeter following the usual... 

The specific heats of dilute electrolyte solutions can be expressed in terms of the so-called partial molal heat capacities ( 63.11). If c is the specific heat of a solution of molality m mols of solute of mol. wt. M2 in 1000 g. water, the apparent molal heat capacity of the solute is ... 

The properties selected for evaluation include most of the thermodynamic properties which we normally evaluate in the course of our work in the data centers. They include enthalpies of formation, solution, and dilution Gibbs energies of formation and solution entropies of formation and solution heat capacities and equilibrium constants (solubility, ionization, etc) as well as activity and osmotic coefficients, relative apparent molal enthalpies and apparent molal heat capacities. 

Pure electrolyte parameter viues (p( ), C l ) at 25°C for each acid, together with first derivatives with respect to temperature (p ) ", 0 5 4, and second derivatives (3p( )B/3T, 3C B/3x) given in Table I for the volatile strong electrolytes being treated here. Superscript L is used to denote 3p( )/3T and 3C /3T because these derivatives are obtained from apparent relative molal enthalpy data ( L). Values of the second derivatives are determined from apparent molal heat capacities, e.g. (12). 

The traditional method of obtaining Cp for electrolytic solutions makes use of the apparent molal heat capacity... 

APPARENT MOLAL HEAT CAPACITIES OF AQUEOUS SOLUTIONS OF ALKALI HALIDES AND ALKYLAMMONIUM SALTS. 

J.T. Edsall, Apparent Molal Heat Capacities of Amino Acids and Other Organic Compounds. J. Am. Chem. Soc., 57,1506-1507,1935. 

Volumetric specific heats and densities have been measured for several alditols in water and in salt solutions. " The lower apparent molal heat capacities of d-glucitol and xylitol suggest that alditols which adopt a bent conformation in solution are relatively more disruptive of the solvent structure than those which adopt a planar zig-zag conformation. 

E5.4 The apparent molar heat capacity of sucrose (2) in water (1) is given as a function of the molality, m by the expression... 

Similarly the temperature dependencies of the relative apparent molal heat content can be determined from the heat capacity by ... 

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... 

By plotting the observed values of the apparent molar heat capacity against the molality, it is possible to determine d4>c/dm at any molality, and hence Cp2 at that molality can be obtained from equation (44.49). This procedure is satisfactory for nonelectrolytes, but for electrolytes it is preferable to plot 0c as a function of as in 44f thus, equation (44.49) may be writt ... 

Apparent molar heat capacities were determined for nickel sulphate solutions at 50, 70 and 90°C. The lowest molalities used were 0.3 mol kg, and the extrapolation to / = 0 is problematic, especially if a model that invokes association between nickel and sulphate ions is to be used. The values from this study are not used in the present assessment. 

This is probably the most comprehensive set of heat capacity results available for any nickel salt in aqueous solution. Apparent molar heat capacities of aqueous Ni(C104)2 were measured calorimetrically from 25 to 85°C over a molality range of 0.02 to 0.80 moFkg. Standard molar heat capacities of Ni for the same temperature range were obtained by using the additivity rule and data for HC104(aq), given in literature. The results for C° (Ni " ) can be fitted with a conventional heat capacity model valid from... 

Evaluation of partial molal volumes of electrolytes, and in particular the standard partial molal volume, Fg, is similar to the determination of partial molal heat capacities. As in the case of heat capacities, the apparent molal quantity is of interest. Corresponding to eqns. 2.3.52, 2.3.54 and 2.3.55 we have... 

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 apparent molal volumes and heat capacities were calculated from the relations... 

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). 

What Gucker and Rubin called the apparent molal isochoric heat capacity of an electrolyte is (P(Co2), and the corresponding isopiestic heat capacity is 0(Cp2), where ... 

Enthalpy, Entropy, and Heat Capacity of Protein—Water Systems Below 0°C. A number of investigators have reported the apparent enthalpy of fusion as a function of temperature and composition for several hydrated proteins. MacKenzie and coworkers (10) determined absorption isotherms at low temperatures and found that 1) these absorption isotherms have essentially the same sigmoidal shapes as those observed above zero degrees 2) the magnitudes of the values for partial molal enthalpy and entropy increase as the content of unfrozen water decreases 3) the heat of fusion decreases as the content of unfrozen water decreases and 4) the heat capacity of the system increases as the content of unfrozen water increases. Taking these findings all together, the thermodynamic properties of unfrozen water are not very different from those of supercooled water at comparable temperatures. 

Several studies of the physical properties of sulphates have been carried out these will not be treated in detail but are listed as follows a determination of the dissociation constants of some univalent sulphate ion-pairs,the electrostriction of ammonium sulphate, dielectric and n.m.r. investigations of phase transitions in lithium ammonium sulphate, the surface structure of barium sulphate crystals in aqueous solution, optical activity and the electro-optical effect in crystals of Cd2(NH4)2(S04)3, apparent molal volumes and heat capacities of Na2S04, K2SO4, and MgS04 in water, and densities, heats of fusion, and refractive indices of double sulphates of univalent metals. ... 

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. 

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