Partial Molar Thermal Properties

The accuracy of equation (43.11) may be tested by plotting the experimental values of V29 the partial molar volume of the solute, at various concentrations against Vc the results should approach a straight line of slope 0.99 in 

If the expression for Vt given by equation (43.11) is now introduced, it follows directly that 

The verification of this equation requires accurate measurements of density of aqueous solutions at high dilutions, and so not many data are available for the purpose. From such information as is available, however, it appears that the limiting slope of the plot of the apparent molar volume of an electrol3rte solute against the square root of the molar concentration is approximately equal to 0.66(21 as required by equation (43.13).  

Relative Partial Molar Heat Contents.—The partial molar thermal properties, namely, heat content and heat capacity, are of particular interest, as well as of practical importance, as will be seen from some of the examples to be given below. In accordance with the general definition ( 26a), the partial molar heat content of any constituent of a solution is represented by 

For the solvent, the standard state and the reference state are identical, on the basis of the usual convention, and consequently the molar heat content in the reference state may be represented by The partial molar heat content of the solvent in a solution relative to the heat content in the reference state is then 5 i — /u this quantity is called the relative partial molar heat content of the solvent, and is represented by the symbol ii, so that in any solution 

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Relative Partial Molar and Apparent Relative Partial Molar Thermal Properties... 

Table 7.2 Partial molar thermal properties for aqueous sulfuric acid solutions at T = 298.15 K. m is the molality of the H1SO4 and A is the ratio (moles FFO/moles...

The energy of a system can be changed by means of thermal energy or work energy, but a further possibility is to add or subtract moles of various substances to or from the system. The free energy of a pure substance depends upon its chemical nature, its quantity (AG is an extensive property), its state (solid, liquid or gas), and temperature and pressure. Gibbs called the partial molar free heat content (free energy) of the component of a system its chemical potential... 

Thermal Properties Pitzer s equations for ln7 and 4> [equations (18.18) to (18.26)] can be used to obtain relative partial molar enthalpies L and L2, and relative partial molar heat capacities8 7j and J2, by taking derivatives. For... 

The first part of the right side of Eq. (1) gives the portion of the H-bonded OH groups with the concentration (1-Of) the second part gives the portion of the non H-bonded OH groups with the concentration 0F. The partial molar volume of H-bonded groups and the coefficient of thermal expansion is taken as ice like datas. Both properties of the orientation defects are adjusted. Spectroscopy cannot give informations on these constants. Therefore, the proof of the orientation defects assumption by the density is not very accurate. 

Several methods involve a study of the properties of solutions in equilibrium and are hence reasonably described as thermodynamic. These methods usually involve thermal measurements, as with the heat and entropy of solvation. Partial molar volume, compressibility, ionic activity, and dielectric measurements can make contributions to solvation studies and are in this group. 

It is important to note that the above formulas represent fluctuations (8X=X - (X)) in the properties of the whole system, that is, bulk fluctuations. They are useful expressions but provide no information concerning fluctuations in the local vicinity of atoms or molecules. These latter quantities will prove to be most useful and informative. One can also derive expressions for partial molar quantities by taking appropriate first (to give the chemical potential) and second (to give partial molar volume and enthalpy) derivatives of the expressions presented in Equation 1.28. However, these do not typically lead to useful simple formulas that can be applied directly to theory or simulation. For instance, while it is straightforward to calculate the compressibility, thermal expansion, and heat capacity from simulation, the determination of chemical potentials is much more involved (especially for large molecules and high densities). 

ELDAR contains data for more than 2000 electrolytes in more than 750 different solvents with a total of 56,000 chemical systems, 15,000 hterature references, 45,730 data tables, and 595,000 data points. ELDAR contains data on physical properties such as densities, dielectric coefficients, thermal expansion, compressibihty, p-V-T data, state diagrams and critical data. The thermodynamic properties include solvation and dilution heats, phase transition values (enthalpies, entropies and Gibbs free energies), phase equilibrium data, solubilities, vapor pressures, solvation data, standard and reference values, activities and activity coefficients, excess values, osmotic coefficients, specific heats, partial molar values and apparent partial molar values. Transport properties such as electrical conductivities, transference numbers, single ion conductivities, viscosities, thermal conductivities, and diffusion coefficients are also included. 

As we have seen from our previous discussions of heat capacities, thermal expansion coefficients, and compressibilities, partial derivatives are the key to discussing changes in thermodynamic systems. In a single-component system of fixed size, the specification of two state variables completely determines the state of the system. Calling one of the molar energy quantities Z, we can write Z = Z(X, Y), where Xand Tare any two state variables, such as Tand I] or Tand V. Using the general mathematical properties of functions of two variables that are discussed in Appendix A,... 

In general, this approach may be used in the evaluation of those properties for which the ideal behavior of the system is physically defined, e.g. for Gibbs energy of mixing and the molar volume. The procedure can be demonstrated by means of the calculation of equilibrium composition based on the measurement of density in the system A-B in which the intermediate compound AB is formed. The compound AB undergoes at melting a partial thermal dissociation. 

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