Partial molal heat capacity

Khodakovskiy (16) used this assumption to extrapolate dissociation constants for acids, Henry s law constants for gases and solubility products for salts. In a variation of this technique Khodakovskiy (17) has extrapolated partial molal heat capacities of ions and neutral molecules by using C = bT. 

Figure 8.27 Experimental values of standard partial molal heat capacity of sodium acetate (A) and ethylene (B) in water as a function of P(°C) at pressures corresponding to water-vapor equilibrium. Interpolating curves generated by the HKF model equations. Reprinted from E. L. Shock and H. C. Helgeson, Geochimica et Cosmochimica Acta, 54, 915-946, copyright 1990, with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK.

Figure 3. Partial molal heat capacities of triethylamine, 2-hutoxyethanol, and tert-butoxyethanol in water...

The values of (H2 — Hj ) for rounded molalities at 298.15° K were obtained from the plots of (H2 — H >) against ra1/2. The smooth curve was drawn through all the experimental points the average deviation from the smoothed curve was 15 calth mol-1 for 50 mass percent monoglyme. These values are presented in Table XIV and are higher than those found for hydrochloric acid in the same mixed solvents (1). The values of (H2 — H%) in aqueous medium at 298.15° K are given for direct comparison. The relative partial molal heat capacity (Cp — Cp) was calculated by the following formula ... 

Table XIV. Relative Partial Molal Enthalpy (//2 — H°) and Relative Partial Molal Heat Capacity (Cp — Cp°) of HBr in 50 Mass Percent Aqueous Monoglyme and in Water at 298.15°K (cal = 4.184/)...

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 partial molal heat capacity of the solute is (for an electrolyte) ... 

Partial molal heat capacities of salt and water... 

Apelblat, A., Sahar, A., Properties of aqueous thorium nitrate solutions. 3. Partial molal heat capacities and heats of dilution at 30°C, J. Chem. Soc. Faraday Trans., 71, (1975), 1667-1671. Cited on pages 98, 99, 643. 

Thus the partial molal heat capacity at constant pressure of component i in the regular solution is the same as the molal heat capacity of pure liquid /. Differentiation of Eq. (11-118) with respect to p at constant T and X yields... 

The derivative of Ea with respect to temperature has been shown by LaMer (1(X)) in a pioneering paper to be equal to the difference between the partial molal heat capacity of molecules which react, and that of all molecules. Therefore, dEa/rfT has been termed by LaMer heat capacity of activation. Equation 8 shows that this differs only by R from the specific heat of activation of the transition state theory, as defined by Eq. 6—in fact, the difference between the two is often neglected. It seems to us that dEaldT is the more meaningful quantity. 

Standard partial molal heat capacity of component i. Density of solution. 

The standard partial molal heat capacity of electrolytes, is probably the best thermodynamic property for providing information on ion-solvent interactions, but until very recently only two publications reported this quantity for electrolytes in non-aqueous systems. The reasons for the scarcity of data become obvious when one considers the formidable experimental and theoretical problems in obtaining this function. 

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... 

Tungusov and Mishchenko have measured the heat capacities of pure ethylene glycol and solutions of Nal and K1 in ethylene glycol and calculated the partial molal heat capacity from the data. They report a value of 21.5 cal mol for Nal and conclude that Cp is independent... 

These arguments should apply equally well to partial molal heat capacities in organic solvents. Data for Cp of electrolytes in organic solvents are exceedingly rare. " However, Cp for NaC104 and Me4NBr are known as a function of temperature in both methanol and water.The data for NaC104 are shown in Fig. 2.12.3. Any discussion of electrolytic solutions necessarily centres around water, so... 

STANDARD PARTIAL MOLAL HEAT CAPACITIES OF SODIUM TETRAPHENYLBORON AQUEOUS SOLUTION FROM 0 TO 90 DEGREES. EFFECT OF WATER STRUCTURE AND HYDROPHOBIC HYDRATION. 

FIGURE G3. Relative partial molal heat capacity of solute in KCI solutions. (Data from R. Parsons, Handbook of Electrochemical Constants, Academic Press Inc., New York (1959), p. 43.)... 

In testing their theory they experienced the problem of the lack of reliable data at elevated temperatures. They noted that the best thermodynamic function for calculating the partial molal entropies are the partial molal heat capacities, Cp°, and that few systems had been studied at temperatures greater than 100°C. Acceptable estimates of could be obtained given the partial molal heat... 

Since the average value of the partial molal heat capacity between 25 C and tz can be described by ... 

Gardner, W.L. J.W. Cobble, E.C. Jekel, "The thermodynamic properties of high-temperature aqueous solutions. IX. The standard partial molal heat capacities of sodium sulfate and sulfuric acid from 0 to 100"", J. Phys. Chem., v73, 6. p2017 (1969)... 

R. K. Agarwal, D. K. Sahu, and B. Nayak, Ind. J. Chem., 9,978 (1971). Relative partial molal enthalpy and relative partial molal heat capacity of HCl from EMF measurements. 

M. Mastroianni and C. M. Criss, J. Chem. Eng. Data, 17, 222 (1972). Standard partial molal heat capacities of sodium perchlorate in water from 0-90°C and in anhydrous methanol from —5 to 55°C. 

R. K. Mohanty, S. Sunder, and T. C. Ahluwalia, J. Phys. Chem., 76, 2577 (1972). Excess partial molal heat capacities of -tetraamylammonium bromide in water from 10 to 80° and in aqueous terf-butyl alcohol solvent system at 30° and the effects on the water structure. 

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