Enthalpy, excess

Stokes calculated the activity coefficient of the solute, In fut by defining a mole-fraction osmotic coefficient 

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. 

The enthalpy of melting can be readily determined by non-calorimetric methods. One method involves the determination of the cryoscopic constant of the solvent from the temperature depression observed by the addition of a non-associating solute. The second method, using the Clapeyron equation, involves measuring the volume change on melting for the solvent and the pressure dependence of the melting temperature of the solvent.  

In principle the molar excess enthalpy may be derived from the temperature dependence of the excess Gibbs free energy. 

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In Equation (15), the third term is much more important than the second term. The third term gives the enthalpy of the ideal liquid mixture (corrected to zero pressure) relative to that of the ideal vapor at the same temperature and composition. The second term gives the excess enthalpy, i.e. the liquid-phase enthalpy of mixing often little basis exists for evaluation of this term, but fortunately its contribution to total liquid enthalpy is usually not large. 

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

For many liquid mixtures. Equation (19) can be used to provide a crude estimate of excess enthalpy. A much better estimate is obtained if the UNIQUAC parameters are considered temperature-dependent. For example, suppose Equations (4-9) and (4-10) are modified to = + k /t... 

This chapter presents quantitative methods for calculation of enthalpies of vapor-phase and liquid-phase mixtures. These methods rely primarily on pure-component data, in particular ideal-vapor heat capacities and vapor-pressure data, both as functions of temperature. Vapor-phase corrections for nonideality are usually relatively small. Liquid-phase excess enthalpies are also usually not important. As indicated in Chapter 4, for mixtures containing noncondensable components, we restrict attention to liquid solutions which are dilute with respect to all noncondensable components. 

LIQUID ENTHALPY IS CALCULATED WITH EXCESS ENTHALPY OF MIXING TAKEN... 

GET UNIQUAC INTERACTION TERMS IF EXCESS ENTHALPY IS CALCULATED FOR LIQUID... 

Ott J B and Wormald C J 1994 Excess enthalpy by flow calorimetry Solution Calorimetry, Experimental Thermodynamics vol IV, ed K N Marsh and PAG O Hare (Oxford Blackwell)... 

For cyclohexane the excess enthalpy (H ) is positive and large, whereas for solvent with aromatic character it is low and even negative in the case of pyridine. 

PARTIAL MOLAR EXCESS ENTHALPY AT INFINITE DILUTION OF THIAZOLE IN VARIOUS SOLVENTS AT SIS.IS K... 

The heat of mixing (excess enthalpy) and the excess Gibbs energy are also experimentally accessible, the heat of mixing by direcl measurement and G (or In Yi) indirectly as a prodiicl of the reduction of vapor/hqiiid eqiiihbriiim data. Knowledge of H and G allows calculation of by Eq. (4-13) written for excess properties. 

The methanol(l)/acetone(2) system serves as a specific example in conjunction with the Peng/Robinson equation of state. At a base temperature To of 323.15 K (50°C), both XT E data (Van Ness and Abbott, Jnt. DATA Ser, Ser A, Sel. Data Mixtures, 1978, p. 67 [1978]) and excess enthalpy data (Morris, et al., J. Chem. Eng. Data, 20, pp. 403-405 [1975]) are available. From the former. 

J. B. Ott, K. N. Marsh and R. H. Stokes. "Excess Enthalpies. Excess Gibbs Free Energies, and Excess Volumes for (Cyclohexane + //-Hexane). and Excess Gibbs Free Energies and Excess Volumes for (Cyclohexane + Methylcyclohexane) at 298.15 and 308.15 K". J.Chem. Thermodyn., 12, 1139-1148 (1980). 

For a detailed discussion of the calculation of activities (and excess Gibbs free energies) from freezing point measurements, see R. L. Snow. J. B. Ott. J. R. Goates. K. N. Marsh, S. O Shea, and R. N. Stokes. "(Solid + Liquid) and (Vapor + Liquid) Phase Equilibria and Excess Enthalpies for (Benzene + //-Tetradecane), (Benzene + //-Hexadecane). (Cyclohexane + //-Tetradecane), and (Cyclohexane +//-Hexadecane) at 293.15, 298.15, and... 

Computer aided packages for the design and simulation of separation processes will contain sub-routines for the estimation of excess enthalpy and liquid and vapour density from the appropriate equation of state. 

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. 

Ways are discussed of measuring both compositions and heats of formation fi.e.. excess enthalpies) of two conjugate phases in model amphiphile/water systems by isoperibol titration calorimetry. Calorimetric and phase-volume data are presented for n-C H OH/water at 30... 

In an earlier study calorimetry achieved this objective for the compositional boundaries between two and three phases (2). Such boundaries are encountered both in "middle-phase microemulsion systems" of low tension flooding, and as the "gas, oil, and water" of multi-contact miscible EOR systems (LZ). The three-phase problem presents by far the most severe experimental and interpretational difficulties. Hence, the earlier results have encouraged us to continue the development of calorimetry for the measurement of phase compositions and excess enthalpies of conjugate phases in amphiphilic EOR systems. 

This paper considers systems of lesser dimensionality than the previous study, namely, systems of two compounds, which (ignoring the vapor) can form only one or two phases. Specifically, excess enthalpies and phase compositions have been measured (at ambient pressure) by isoperibol calorimetry for n-butanol/water at 30.0 and 55.0 °C and for n-butoxyethanol/water at 55.0 and 65.0 °C. (Butanol, or C4E0, is C HgOH butoxyethanol, or C4E1, is C HgCX OH.) The miscibility... 

Figure 2 shows measured excess enthalpies for aqueous phases and two-phase mixtures of n-butoxyethanol/water at 55.0 °C. Data from four replicate additions of 2 cm3 of butoxyethanol to water are shown in Figure 2a Figure 2b shows data from the subsequent addition of an additional 2 cm3 of butoxyethanol to each of the solutions of Figure 2b. 

Figure 3 shows the excess enthalpy v . composition measured for aqueous solutions of n-butanol and water at 30.0 °C Figure 4 shows corresponding results for the amphiphilic side of the miscibility gap at... 

Figure 4. Measured excess enthalpies for the amphiphilic side of the n-butanol/water diagram at 55.0 °C compared to results from the literature.(14,16) (Symbols same as for Fig. 3.)...

Table II shows the "heats of formation" of the conjugate phases, that is, the excess enthalpies for mixing the appropriate amounts of water and amphiphile (at the same initial temperature and pressure as the final system) to make a unit amount of the conjugate phase. Values labeled "calorimeter" and "phase volume," respectively, are based on the same set of calorimetric titrations. In the former case the phase composition was taken from the calorimetric measurements, and in the latter case the composition was taken from our phase-volume compositions. Literature values for the heats of formation are based on data from references 13-16.

Although heat capacities have been reported for the butoxyethanol/ water system, excess enthalpies that could be compared directly with our results apparently have not been measured (12). 

However, the titrations must begin with the neat compound, if one desires to measures excess enthalpies referred to a single-compound standard state. In this case the number of experiments and the data... 

Isoperibolic calorimetry measurements on the n-butanol/water and n-butoxyethanol/water systems have demonstrated the accuracy and convenience of this technique for measuring consolute phase compositions in amphiphile/water systems. Additional advantages of calorimetry over conventional phase diagram methods are that (1) calorimetry yields other useful thermodynamic parameters, such as excess enthalpies (2) calorimetry can be used for dark and opaque samples and (3) calorimetry does not depend on the bulk separation of conjugate fluids. Together, the present study and studies in the literature encompass all of the classes of compounds of the amphiphile/CO ydrocarbon/water systems that are encountered in... 

Horstmann, S., Wilken, M., Fischer, K., Gmehling, J. (2004) Isothermal vapor-liquid equilibrium and excess enthalpy data for the binary systems propylene oxide + 2-methylpentane and difluoromethane (R32) + pentafluoroethane (R125). J. Chem. Eng. Data 49,1504-1507. 

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