Enthalpy activity coefficients

But in spite of the great advantages compared to original UNIFAC (better results for excess enthalpies, activity coefficients at infinite dilution, asymmetric systems) it shows the typical weaknesses of a group contribution approach. Hence, for example... 

In most commercial process simulators, model parameters for pure component properties and binary parameters can be found for a large number of compounds and binary systems. However, the simulator providers repeatedly warn in their software documentations and user manuals that these default parameters should be applied only after careful examination by the company s thermodynamic experts prior to process simulation. For verification of the model parameters again, a large factual data bank like the DDE is the ideal tool. The DDE allows checking all the parameters used for the description of the pure component properties as a function of temperature and of the binary parameters of a multicomponent system by access to the experimental data stored. On the basis of the results for the different pure component properties and phase equilibria, excess enthalpies, activity coefficients at infinite dilution, separation factors, and so on, the experienced chemical engineer can decide whether all the data and parameters are sufficiently reliable for process simulation. 

The molar excess enthalpy h is related to the derivatives of the activity coefficients with respect to temperature according to... 

The computer subroutines for calculation of vapor-phase and liquid-phase fugacity (activity) coefficients, reference fugac-ities, and molar enthalpies, as well as vapor-liquid and liquid-liquid equilibrium ratios, are described and listed in this Appendix. These are source routines written in American National Standard FORTRAN (FORTRAN IV), ANSI X3.9-1978, and, as such, should be compatible with most computer systems with FORTRAN IV compilers. Approximate storage requirements and CDC 6400 execution times for these subroutines are given in Appendix J. 

It is not necessary to limit the model to idealized sites Everett [5] has extended the treatment by incorporating surface activity coefficients as corrections to N and N2. The adsorption enthalpy can be calculated from the temperature dependence of the adsorption isotherm [6]. If the solution is taken to be ideal, then... 

An overview of some basic mathematical techniques for data correlation is to be found herein together with background on several types of physical property correlating techniques and a road map for the use of selected methods. Methods are presented for the correlation of observed experimental data to physical properties such as critical properties, normal boiling point, molar volume, vapor pressure, heats of vaporization and fusion, heat capacity, surface tension, viscosity, thermal conductivity, acentric factor, flammability limits, enthalpy of formation, Gibbs energy, entropy, activity coefficients, Henry s constant, octanol—water partition coefficients, diffusion coefficients, virial coefficients, chemical reactivity, and toxicological parameters. 

Table 7.1 Debye-Hiickel parameters for the activity coefficient, volume, enthalpy, and...

The net retention volume and the specific retention volume, defined in Table 1.1, are important parameters for determining physicochemical constants from gas chromatographic data [9,10,32]. The free energy, enthalpy, and. entropy of nixing or solution, and the infinite dilution solute activity coefficients can be determined from retention measurements. Measurements are usually made at infinite dilution (Henry s law region) in which the value of the activity coefficient (also the gas-liquid partition coefficient) can be assumed to have a constant value. At infinite dilution the solute molecules are not sufficiently close to exert any mutual attractions, and the environment of each may be considered to consist entirely of solvent molecules. The activity... 

Unless liquid phase activity coefficients have been used, it is best to use the same equation of state for excess enthalpy that was selected for the vapour-liquid equilibria. If liquid-phase activity coefficients have been specified, then a correlation appropriate for the activity coefficient method should be used. 

If a2/ax = gim2lgxmx m2/mx (a = activity, g = molal activity coefficient, m = molality) if Henry s law is obeyed and a = gm, mh and m2 are the molal solubilities of the polymorphs, and if the standard molar enthalpies and standard molar entropies of solution are, respectively,... 

In addition to the activity and osmotic coefficients at room temperature, the first temperature derivatives and the related enthalpy of dilution data were considered for over 100 electrolytes (26, 29). The data for electrolytes at higher temperatures become progressively more sparse. Quite a few solutes have been measured up to about 50°C (and down to 0°C). Also, over this range, the equations using just first temperature derivatives have some validity for rough estimates in other cases. But the effects of the second derivative (or the heat capacity) on activity coefficients at higher temperatures is very substantial. 

The standard state for the heat capacity is the same as that for the enthalpy. For a proof of this statement for the solute in a solution, see Exercise 2 in this chapter. This choice of standard state for components of a solution is different fixjm that used by many thermodynamicists. It seems preferable to the choice of a 1-bar standard state, however, because it is more consistent with the extrapolation procedure by which the standard state is determined experimentally, and it leads to a value of the activity coefficient equal to 1 when the solution is ideal or very dilute whatever the pressure. It is also preferable to a choice of the pressure of the solution, because that choice produces a different standard state for each solution. For an alternative point of view, see Ref. 2. 

Once activity coefficients have been determined at one temperature by one of the methods mentioned above, calorimetric measurement of enthalpies of dilution can be used to determine activity coefficients at other temperatures. 

Extension of Activity Coefficient Data to Additionai Temperatures with Enthalpy of Dilution Data... 

As with equilibrium constants [see Equation (10.24)], so it is sometimes convenient to measure activity coefficients at one temperature and to obtain values at other temperatures with the use of enthalpy data. From Equation (16.1)... 

The solubility of pure solid glycine at 25°C in water is 3.33 moles (kg H20). The activity coefficient of glycine in such a saturated solution is 0.729. Data for the relative partial molar enthalpies of glycine in aqueous solution are tabulated in Exercise 15 of Chapter 18. Given AfG and... 

Consideration of the thermodynamics of nonideal mixing provides a way to determine the appropriate form for the activity coefficients and establish a relationship between the measured enthalpies of mixing and the regular solution approximation. For example, the excess free energy of mixing for a binary mixture can be written as... 

Table 6.2 presents data showing the effect of various CMOS on the activity coefficient or mole fraction solubility of naphthalene, for two different solvent/water ratios. To examine the cosolvent effect, Schwarzenbach et al. (2003) compare the Hildebrand solubility parameter (defined as the square root of the ratio of the enthalpy of vaporization and the molar volume of the liquid), which is a measure of the cohesive forces of the molecule in pure solvent. 

Using PCA, Cramer found that more than 95% of the variances in six physical properties (activity coefficient, partition coefficient, boiling point, molar refractivity, molar volume, and molar vaporization enthalpy) of 114 pure liquids can be explained in terms of only two parameters which are characteristic of the solvent molecule (Cramer 111, 1980). These two factors are correlated to the molecular bulk and cohesiveness of the individual solvent molecules, the interaction of which depends mainly upon nonspecific, weak intermolecular forces. 

L. F. Silvester and K. S. Pitzer, Thermodynamics of electrolytes. X. Enthalpy and the effect of temperature on the activity coefficients. J. Solution Chem. 7, 327-337, (1978) and earlier work cited therein. 

The mean ionic activity coefficients of hydrobromic acid at round molalities (calculated by means of Equation 2) are summarized in Tables XI, XII, and XIII for x = 10, 30, and 50 mass percent monoglyme. Values of —logio 7 at round molalities from 0.005 to 0.1 mol-kg-1 were obtained by interpolating a least squares fit to a power series in m which was derived by means of a computer. These values at 298.15° K are compared in Figure 2 with those for hydrochloric acid in the same mixed solvent (I) and that for hydrobromic acid in water (21). The relative partial molal enthalpy (H2 — Hj>) can be calculated from the change in the activity coefficient with temperature, but we have used instead the following equations ... 

A colleague of yours who works in oceanography bets you that both the solubility as well as the activity coefficient of naphthalene are larger in seawater (35%o salinity) at 25°C than in distilled water at 5°C. Is this not a contradiction How much money do you bet Estimate C and for naphthalene in seawater at 25°C and in distilled water at 5°C. Discuss the result. Assume that the average enthalpy of solution (A wsHh Fig. 5.1) of naphthalene is about 30 kJmol-1 over the ambient temperature range. All other data can be found in Tables 5.3 and 5.7 and in Appendix C. 

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