Showing papers on "Gibbs–Duhem equation published in 1995"

Global Optimization and Analysis for the Gibbs Free Energy Function Using the UNIFAC, Wilson, and ASOG Equations

Abstract: The Wilson equation for the excess Gibbs energy has found wide use in successfully representing the behavior of polar and nonpolar multicomponent mixtures with only binary parameters but was incapable of predicting more than one liquid phase. The UNIFAC and ASOG group contribution methods do not have this limitation and can predict the presence of multiple liquid phases. The most important area of application of all these equations is in the prediction of phase equilibria. The calculation of phase equilibria involves two important problems: (1) the minimization of the Gibbs free energy and (2) the tangent plane stability criterion. Problem (2), which can be implemented as the minimization of the tangent plane distance function, has found wide application in aiding the search for the global minimum of the Gibbs free energy. However, a drawback of all previous approaches is that they could not provide theoretical guarantees that the true equilibrium solution will be obtained. The goal of the work is to find the equilibrium solution corresponding to the global minimum of the Gibbs free energy. A proof that the Wilson equation leads to a convex formulation for the minimization of the Gibbs energy is provided so that a local optimization technique will always converge to a global minimum. In addition, new expressions are derived for the molar Gibbs free energy function when the UNIFAC, ASOG, and modified Wilson equations are employed. These expressions are then transformed so that application of a branch and bound based global optimization algorithm originally due to Falk and Soland (1969) is possible. This allows global solutions to be obtained for both the minimization of the Gibbs free energy and the minimization of the tangent plane distance function. The algorithm is implemented in C as part of the package GLOPEQ, global optimization for the phase equilibrium problem (McDonald and Floudas, 1994d). Results for several examples are presented

The Equivalence of Ensembles for Classical Systems of Particles

Abstract: For systems of particles in classical phase space with standard Hamiltonian, we consider (spatially averaged) microcanonical Gibbs distributions in finite boxes. We show that infinite-volume limits along suitable subsequences exist and are grand canonical Gibbs measures. On the way, we establish a variational formula for the thermodynamic entropy density, as well as a variational characterization of grand canonical Gibbs measures.

Dielectric constant of a Stockmayer fluid along the vapour-liquid coexistence curve

Abstract: By DEZSO BODA, J,~NOS LISZI and ISTVAN SZALAI Department of Physical Chemistry, University of Veszpr6m, H-8201 Veszpr6m, PO Box 158, HungarY (Received 16 February 1995; revised version accepted 3 April 1995) We have proposed an extension of the NpT plus test particle method (Boda, D., Liszi, J., and Szalai, I., 1995, Chem. Phys. Lett., 235, 140). Here, it is applied to determine the vapour-liquid equilibrium of a Stockmayer fluid with reduced dipole moment #,2 = p2/Eer3 = 1'0. On the basis of this method a procedure is also suggested to calculate the dielectric constant along the coexistence curve. Our phase equilibrium results show good agreement with Gibbs ensemble simulation and perturbation theory data. The predicted dielectric constants are also given along the coexistence curve. There are several methods for the determination of vapour-liquid phase equilibrium (VLE) of pure fluids by simulation. The Gibbs ensemble technique has been proposed by Panagiotopoulos [1 3], while the Gibbs Duhem integration method was recently suggested by Kofke [4]. Fischer et al. [5-7] introduced the NpT plus test particle (NpT+ TP) method an extension of which (extended NpT + TP) was suggested in our previous work [8]. It was employed to deter- mine VLE of the Lennard-Jones (L J) fluid [8], and proved to be very efficient and accurate. Since we described the method in detail in [8] we only outline it here. Prescribing a point (/~o, Po) in the parameter plane of/? (fi = 1/kT, where T is the temperature and k is the Boltzmann constant) and the pressure p, the two-dimensional Taylor series expansion of the function tiff (/i is the density dependent part of the chemical potential) can be rewritten about (fl0, P0) up to third order. A second-order series can be given for the enthalpy h and the volume v, while a first-order series is given for the isobaric heat capacity cp (these quantities refer to one particle: v = V/N etc.). The coefficients of the series can be derived from simple thermodynamic relations on the basis of the derivatives of h and v with respect to fl and p, and can be calculated from fluctuation formulas by performing an NpT + TP Monte Carlo (MC) simula- tion for the raw point. All these derivatives and fluctuation formulas can be found in [8]. Performing this procedure for a gas and a liquid phase point, and rewriting the third-order Taylor series of ~/~ for these points, the vapour pressure curve as well as other equilibrium data (e.g., the vapour and liquid phase densities, enthalpies, heat capacities, etc.) can be obtained fi'om the intersection of these series in a certain temperature range within a given accuracy. This is the main advantage of our method over Fischer's because in the latter the chemical potential is expanded only with respect to the pressure at fixed temperature.

Determination of excess Gibbs free energy of quantum mixtures by path integral Monte Carlo simulations

Abstract: We report a new path integral method for calculating the difference in chemical potentials for a quantum mixture, which is a combination of the difference method and the ‘f-g’ method. The method is based on distribution functions of fictive changes of paths of real particles in the system. We applied the new method to the isotopic mixture, 3He + 4He, at T = 2 K. The excess Gibbs free energy was computed over a range of compositions; the results are in relatively good agreement with experimental data. The method thus shows promise for further applications in the study of thermodynamic properties of dense quantum mixtures.

Chemical Reactions in Phases at Different Electric Potentials

Abstract: When some reactants or products in a chemical reaction are ions that are in a phase at a different electric potential, the equilibrium constant K for the reaction is affected by the difference in the electric potentials. The equilibrium expression can be derived by using the Gibbs energy G(T, P, n[sub i]) or a transformed Gibbs energy G[prime](T, P, n[sub i],[phi][sub i]) defined by subtracting electrical work terms from the Gibbs energy. This terminology is used because such a change in natural variables is referred to as a Legendre transform. The thermodynamics of a simple reaction involving ionic species in two phases at different electric potentials is discussed using the Gibbs energy G and the transformed Gibbs energy G[prime]. In the first case, the thermodynamic behavior is discussed in terms of standard molar enthalpies and entropies of species, and in the second case the thermodynamic behavior is discussed in terms of standard molar transformed enthalpies and standard molar transformed entropies of species. The use of the transformed reaction Gibbs energy leads to the apparent equilibrium constant K[prime] that would be obtained if all the species were in the same phase. The advantages and disadvantages of these different treatments are discussed,more » as well as problems with the current electrochemical nomenclature.« less

A critical assessment of the standard molar gibbs free energy of formation of NiWO4

Abstract: Three independent studies have been reported on the free energy of formation of NiWO4. Results of these measurements are analyzed by the i?½third-lawi?½ method, using thermal functions for NiWO4 derived from both low and high temperature heat capacity measurements. Values for the standard molar enthalpy of formation of NiWO4 at 298·15 K obtained from i?½third-lawi?½ analysis are compared with direct calorimetric determinations. Only one set of free energy measurements is found to be compatible with calorimetric enthalpies of formation. The selected value for ?f H m 0 (NiWO4, cr, 298·15 K) is the average of the three calorimetric measurements, using both high temperature solution and combustion techniques, and the compatible free energy determination. A new set of evaluated data for NiWO4 is presented.