Kenneth S. Pitzer

Energy Levels and Thermodynamic Functions for Molecules with Internal Rotation I. Rigid Frame with Attached Tops

A general treatment of internal rotation is given for molecules whose moments of inertia for over‐all rotation are independent of internal rotational coordinates. Tables are presented for the various thermodynamic functions which are accurate for molecules with one internal rotation and for the potential energy (V/2) (1 — cos nφ). The tables are shown to be a good approximation for molecules with several internal rotational coordinates, provided the potential energy can be expressed as a sum of terms of this type. Methods are suggested for treating problems where cross terms involving more than one internal coordinate are present in the potential energy. The energy level expressions are developed for the more general case with the potential energy expressed by a Fourier series. Although a few specific cases were worked out with different shape potential barriers, it appears that the simple form assumed above will be satisfactory for many purposes.

Thermodynamic Properties of Aqueous Sodium Chloride Solutions

Experimental measurements of the osmotic and activity coefficients, the enthalpy, and the heat capacity were used to derive a semiempirical equation for the thermodynamic properties of NaCl(aq) at constant pressure. This equation may be combined with results contained in the previous paper on the volumetric properties to yield a complete equation of state valid in the region 273 K≤T≤573 K, saturation pressure ≤P≤1 kbar, 0≤m≤6.0 mol kg−1. It is shown that this equation may be extrapolated to higher solute molalities at lower pressures. An estimation of uncertainties in various quantities is given. Tables of values for various thermodynamic properties are presented in the appendix.

Thermodynamics of electrolytes. III. Activity and osmotic coefficients for 2–2 electrolytes

The peculiar behavior of 2–2 and higher valence type electrolytes is discussed in terms of various theories some of which assume, while others do not, an equilibrium between separated ions and ion pairs as distinct chemical species. It is recognized that in some case a distinct species of inner-shell ion pairs is indicated by spectroscopic or ultrasonic data. Nevertheless, there are many advantages in representing, if possible, the properties of these electrolytes by appropriate virial coefficients and without chemical association equilibria. It is shown that this is possible and is conveniently accomplished by the addition of one term to the equations of Parts I and II of this series. The coefficients of these equations are given for nine solutes. It is also noted that these equations have been successfully applied to mixed electrolytes involving one component of the 2–2-type.

Thermodynamics of electrolytes. V. effects of higher-order electrostatic terms

The contribution of higher-order electrostatic terms (beyond the Debye-Hückel approximation) to the thermodynamic properties of mixed and pure electrolytes is investigated. It is found that these effects are important for cases of unsymmetrical mixing, especially when one ion has a charge of three units or more. The appropriate correction can be made by a purely electrostatic function since the mutual repulsion of ions of the same sign keeps them far enough apart that short-range forces have little effect. This function is evaluated, and several convenient approximations are also given. Application is made to systems mixing ions of the type 1–2 and 1–3. Higher-order limiting laws exist for symmetrical mixtures and for pure, unsymmetrical solutes, but these effects were not found to be significant in relationship to existing activity or osmotic-coefficient data.

The Free Energy of Hydration of Gaseous Ions, and the Absolute Potential of the Normal Calomel Electrode

The free energies of hydration of the alkali and halide ions are found to agree reasonably well with the simple expression of Born (—ΔF=(1–1/D)Ne2/2re) for solution of charged spheres in a dielectric medium, provided the crystal radii are suitably modified so as to correspond to the radii of the cavities in the dielectric medium. The results show that the dielectric constant of water remains large even in the intense field next to the ion. The entropies of hydration are also found to be consistent with these radii. Because of the simplicity of this calculation, the resulting free energies of solution of individual ions are considered to be a priori the most probable and are used to calculate a value of —0.50 volt for the absolute potential of the calomel half‐cell.

Equation-of-state representation of phase equilibria and volumetric properties of the system NaCl-H2O above 573 K

Abstract A comprehensive equation of state has been developed for the system NaCl-H 2 O at high temperatures and pressures. The equation consists of a reference part and a perturbation contribution. The reference part represents the properties of a mixture of hard-sphere ion pairs and dipolar solvent molecules. The perturbation part arises from all other interactions and comprises a virial-type expansion truncated after the fifth virial coefficient. Mixing rules for the perturbation part are guided by the composition dependence of virial coefficients and contain empirically determined terms for unlike-molecule interactions. The equation has been fitted to extensive experimental data in the temperature range 573–773 K and to more limited data above 773 K. In both temperature regions, the equation reproduces vapor-liquid equilibria, volumetric properties, and solubilities of solid NaCl essentially within experimental uncertainty. It is valid at temperatures between 573 K and ca. 1200 K and pressures up to 5 kbar.

Energy Levels and Thermodynamic Functions for Molecules with Internal Rotation: II. Unsymmetrical Tops Attached to a Rigid Frame

Formulas are derived which make the tables and equations of the first paper of this series applicable to this more general class molecules. Additional approximations are involved and these are examined carefully.

Thermodynamics of concentrated electrolyte mixtures and the prediction of mineral solubilities to high temperatures for mixtures in the system Na-K-Mg-Cl-SO4-OH-H2O

Mineral solubilities in binary and ternary electrolyte mixtures in the system Na-K-Mg-Cl-SO4-OH-H2O are calculated to high temperatures using available thermodynamic data for solids and for aqueous electrolyte solutions. Activity and osmotic coefficients are derived from the ion-interaction model of Pitzer (1973, 1979) and co-workers, the parameters of which are evaluated from experimentally determined solution properties or from solubility data in binary and ternary mixtures. Excellent to good agreement with experimental solubilities for binary and ternary mixtures indicate that the model can be successfully used to predict mineral-solution equilibria to high temperatures. Although there are currently no theoretical forms for the temperature dependencies of the various model parameters, the solubility data in ternary mixtures can be adequately represented by constant values of the mixing term θij and values of ψijk which are either constant or have a simple temperature dependence. Since no additional parameters are needed to describe the thermodynamic properties of more complex electrolyte mixtures, the calculations can be extended to equilibrium studies relevant to natural systems. Examples of predicted solubilities are given for the quaternary system NaCl-KCl-MgCl2-H2O.

Improved ab initio effective core potentials for molecular calculations

We have investigated the sources of error in bond lengths and dissociation energies computed from ab initio effective potentials derived from Phillips–Kleinman type pseudo‐orbitals. We propose an alternate pseudo‐orbital, effective potential treatment with the primary objective of agreement with all‐electron molecular calculations. This new treatment forces the pseudo‐orbitals to match precisely the Hartree–Fock orbitals in the valence region and thereby eliminates the major cause of error in the earlier calculations. Effective core potentials derived from these revised pseudo‐orbitals were used to compute potential energy curves for the ground states of F2, Cl2, and LiCl and the results are compared with previous all‐electron and effective potential calculations. Our effective potentials yield dissociation energies and bond lengths which are in excellent agreement with the all‐electron values. Furthermore, in contrast to other procedures, our revised effective potentials result in an excellent descriptio...

The Vibration Frequencies and Thermodynamic Functions of Long Chain Hydrocarbons

A method is developed for calculating thermodynamic functions for long chain molecules with particular attention to normal paraffins. In this connection the infinite chain approximation method for calculating vibration frequencies is considered. Starting with the results of Kirkwood, a modification is made which improves the agreement with the exact values for the simpler cases. In addition this method of attack is extended to out of plane motions. This vibrational analysis shows that all skeletal frequencies for molecules of the normal paraffin type can be put into two groups, one fairly narrow band near 1000 cm—1, and a broader band extending from 0 to 460 cm—1. The partition function is then set up on the assumption that motions in the low frequency group can be treated classically, and that the high frequency band can be replaced by a suitable number of 1000 cm—1 frequencies. Contributions from hydrogen atom vibrations are added on later. A formula is finally obtained which is quite simple, considerin...