Partial molal heat capacity temperature

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. 

Fig. 2.12.3. Partial molal heat capacities of NaC104 in water and methanol as a function of temperature.

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... 

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... 

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)... 

Since temperature, pressure, and composition are the appropriate independent variables for the Gibbs free energy we must now write out the entropy and volume in the form 5 = S(T, P, n, ) and V = V(T, P, , ), take their differential forms, and substitute these in Eq. (1.20.19a). Following the method used in setting up Eq. (1.13.4c), we next introduce the heat capacity at constant pressure, the appropriate Maxwell relation, as well as a and We also introduce the partial molal entropy S, and volume V,- to obtain... 

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. 

In the work presented here, these processes have been studied primarily by calorimetry. Planned measurements of partial specific heat and partial molal volume will give additional thermodynamic data on the structure of micellar systems. Heat capacity measurements will allow "simple" extrapolation of measured enthalpy terms to higher temperatures. In addition, a direct measure of the effect of temperature variation is of interest for solution structure studies. Partial molal volume measurements give information on the packing of surfactant monomers and micelles within the water structure. The effect of cosurfactants on the partial molal volume will be of particular interest. 

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. 

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. 

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... 

Fig. 1. Standard partial molal volumes and isobaric heat capacities of aqueous organic acids and aqueous Na-carboxylate electrolytes as functions of temperature at the vapor-liquid saturation pressure of H2O (Psat)- The symbols represent experimental values from the references indicated in the figure, but the curve corresponds to values calculated with the revised HKF equations of state using data and parameters from Shock (1993a)...

---