Activity coefficient temperatures with enthalpy

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

For positive deviations from Raoult s law (g >0,y > 1), depending on the sign of the excess enthalpy two cases can be distinguished. In the case of endothermic behavior (h > 0), the excess Gibbs energy and therewith, the values of the activity coefficient decrease with increasing temperature. 

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

The rates of decarboxylation of a range of 3-substituted mesitoic acids in 82.1 wt. % phosphoric and 83.0 wt. % sulphuric acids have been measured636 over a range of temperatures as indicated in Table 209, which gives the first-order rate coefficients together with the log A values and the energies, enthalpies, and entropies of activation calculated at 80 °C for sulphuric acid, and 119 °C for phosphoric acid these kinetic parameters are somewhat different from those... 

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 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 ... 

Figure 18.6 Thermal properties of aqueous NaCl solutions as a function of temperature, pressure and concentration, (a) activity coefficient (b) osmotic coefficient (c) relative apparent molar enthalpy and (d) apparent molar heat capacity. The effect of pressure is shown as alternating grey and white isobaric surfaces of 7 , , L, and Cp at p = 0.1 or saturation, 20, 30, 40, 50, 70, and 100 MPa, that increase with increasing p in (a), (b), and (d), and decrease with increasing P in (c).

For the species in solution (SOLUTIONSPECIES, Table 23), listed in the top row with current number, solubility constant log k and enthalpy delta h are given in kcal/mol or kJ/mol at a temperature of 25 °C. Using the sub-key-word gamma parameters for the calculation of the activity coefficient y according the WATEQ-DEBYE-HUCKEL ion dissociation theory (compare to chapter 1.1.2.6.1) are given. With the sub-key-word analytical , coefficients At to A5 are defined to calculate the temperature dependence of the solubility-product constant. 

Schnitzer M (1986) Binding of humic substances by soil mineral colloids. In Interactions of soil Minerals With Natural Organics and Microbes. In HUANG P M, SCHNITZER M (Eds).-Soil. Sci. Soc. Am. Publ. No. 17, Madison, WI Sigg L, Stumm W (1994) Aquatische Chemie.-B G Teubner Verlag Stuttgart Silvester KS, Pitzer KS (1978) Thermodynamics of electrolytes. X. Enthalpy and the effect of temperature on the activity coefficients.-Jour, of Solution Chemistry, 7 pp 327-337 Sparks DL (1986) Soil Physical Chemistry.- CRC Press Inc., Boca Raton FL Stumm W, Morgan JJ (1996) Aquatic Chemistry, 3rd edition.-John Wiley Sons New York... 

Electromotive force measurements of the cell Pt, H2 HBr(m), X% alcohol, Y% water AgBr-Ag were made at 25°, 35°, and 45°C in the following solvent systems (1) water, (2) water-ethanol (30%, 60%, 90%, 99% ethanol), (3) anhydrous ethanol, (4) water-tert-butanol (30%, 60%, 91% and 99% tert-butanol), and (5) anhydrous tert-butanol. Calculations of standard cell potential were made using the Debye-Huckel theory as extended by Gronwall, LaMer, and Sandved. Gibbs free energy, enthalpy, entropy changes, and mean ionic activity coefficients were calculated for each solvent mixture and temperature. Relationships of the stand-ard potentials and thermodynamic functons with respect to solvent compositions in the two mixed-solvent systems and the pure solvents were discussed. 

Inverse gas chromatography, IGC, has been used to study water sorption of two poly (vinylidene chloride-vinyl chloride) and poly (vinylidene chloride-acrylonitrile) copolymers, at temperatures between 20 and 50°C and low water uptakes. It was found that the specific retention volume of water increases with decreasing amount of water injected, increases dramatically with decreasing temperature and strongly depends on the type of copolymer. Thermodynamic parameters of sorption namely free energy, entropy, enthalpy of sorption and activity coefficient were calculated. 

An approximate relationship between the Arrhenius activation energy a and the standard enthalpy of activation A H° can be found by taking the derivative of Inkp with respect to l/T at constant pressure using equation (7.4.15). Neglecting the temperature derivatives of the activity coefficients, one obtains... 

In this equation, H is the enthalpy of pure component i at system temperature and pressure, and is the excess enthalpy. Equation 1.39 together with the equations defining the activity coefficient and the fugacity provide the basis for deriving an expression for the excess enthalpy in terms of the derivatives of the activity coefficients with respect to temperature. The result is... 

The amplitudes of chemical relaxation processes are determined by the equilibrium concentrations (and strictly speaking, associated activity coefficients) and by thermodynamic variables appropriate for the particular perturbation method used. Thus, for example, an analysis of the amplitudes of relaxation processes associated with temperature jump measurements can lead to determination of the equilibrium constants and enthalpies associated with the mechanism under study. As might be anticipated from our previous discussion, the relaxation amplitudes are determined by normal mode thermodynamic variables which are linear combinations of the thermodynamic variables associated with the individual steps in the mechanism. The formal analysis of relaxation amplitudes has been developed in considerable detail [2, 5,7],... 

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... 

This activity coefficient is so defined that it becomes unity at infinite dilution of the solute in the solvent, in contrast to the one commonly used for liquid mixtures, which becomes unity for the pure liquid solute. The pure liquid-solute-based activity coefficient can be calculated by combining the melting data with vapour-liquid equilibria data at the melting temperature of the solvent. When vapour-liquid equilibria data are known only at higher temperatures, it is necessary to know the molar excess enthalpies of the mixture over the temperature range. 

Gas chromatography is primarily an analytical separation technique. However, since the basic process is an equilibration of a solute between two immiscible phases, the chromatographic technique may be used to measure such physical properties as activity coefficients, second virial coefficients of gas mixtures, partition coefficients, adsorption and partition isotherms, and complex formation constants. Other properties which can be measured with less accuracy, from secondary measurements or from temperature variation studies, include surface areas, heats of adsorption, and excess enthalpies and excess entropies of solution. A number of reviews and discussions on these measurements have appeared in the literature. The present work is restricted to a review of activity-coefficient measurements. 

The Bristol group have studied the activity coefficients of benzene and fluorobenzenes in various n-alkane long-chain hydrocarbons with the aim of testing various solution theories. The activity coefficient of benzene at 323 K varies from 0.993 in hexadecane to 0.644 in dotriacontane. The trend in the fluorobenzene systems is for the activity coefficient to increase with increasing fluorocarbon substitution. For example, in the case of n-octadecane systems at 323 K, the activity coefficient for fluorobenzene is 1.130 while for hexafluoro-benzene it is 1.945. In these cases, the temperature variation of the activity coefficients was sufficiently great to warrant the determination of the infinitely dilute excess enthalpies. 

Approximately straight lines are obtained in a plot of the logarithm of the activation coefficient vs. 1/7 or, better, vs. 1 / r, cf Fig. 2.1-25. Figure 2.1-25 shows the activity coefficient vs. the vapor pressure and the respective boihng temperature for the system water/acetic acid. Provided a small variation of the partial molar mixing enthalpy with temperature, the following simple relation is applicable to recalculate the activity coefficient at different temperatures ... 

FIG U RE 10.4 Comparison between experimental (o) and calculated (solid lines) solubilities of phenacetin (S is the mole fraction of phenacetin) in the mixed solvent water/dioxane is the mole fraction of dioxane) at room temperature. The solubility was calculated using Equation 10.29. 1-activity coefficients expressed via the Flory-Huggins equation, 2-activity coefficients expressed via the Wilson equation. (From C. Bustamante, and P. Bustamante, 1996, Nonlinear Enthalpy-Entropy Compensation for the Solubility of Phenacetin in Dioxane-Water Solvent Mixtures, Journal of Pharmaceutical Sciences, 85, 1109. Reprinted from E. Ruckenstein, and I. L. Shulgin, 2003c, Solubility of Drugs in Aqueous Solutions. Part 2 Binary Nonideal Mixed Solvent, International Journal of Pharmaceutics, 260, 283, With permission from Elsevier.)... 

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