Partial molal heat capacity determination

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... 

Both these considerations would be taken into accoimt if the activation process were assumed to occur at a constant pressure, p, such that the partial molar volume of the solvent is independent of the temperature, though this possibility does not appear to have been considered. A full discussion is beyond the scope of this chapter, but the resulting heat capacities of activation are unlikely to differ greatly from those determined at a constant pressme of, say, 1 atm. (see p. 137). Unfortunately, this approach requires the definition of rather clumsy standard states for solutes, e.g., hypothetically ideal, 1 molal, under a pressure such that a given mass of the pure solvent occupies a particular volume. 

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. 

Activity coefficients at temperatures other than that at which they were determined may be obtained using the relative partial molal enthalpy, and heat capacity, /j Differentiation with respect to temperature of the equation (j2 — 2 = In a2 for the partial molal free energy of the... 

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