Excess molar enthalpies

Here Y denotes a general bulk property, Tw that of pure water and Ys that of the pure co-solvent, and the y, are listed coefficients, generally up to i=3 being required. Annotated data are provided in (Marcus 2002) for the viscosity rj, relative permittivity r, refractive index (at the sodium D-line) d. excess molar Gibbs energy G, excess molar enthalpy excess molar isobaric heat capacity Cp, excess molar volume V, isobaric expansibility ap, adiabatic compressibility ks, and surface tension Y of aqueous mixtures with many co-solvents. These include methanol, ethanol, 1-propanol, 2-propanol, 2-methyl-2-propanol (tert-butanol), 1,2-ethanediol, tetrahydrofuran, 1,4-dioxane, pyridine, acetone, acetonitrile, N, N-dimethylformamide, and dimethylsulfoxide and a few others. 

Roux, A. H. Grolier, J.-P. E. Inglese, A. Wilhelm, E. Excess molar enthalpies, excess molar heat capacities and excess molar volumes of (fluorobenzene + an n-alkane) Ber. Bunsen-Ges. Phys. Chem. 1984,8S, 986-992... 

CALCULATION OF PARTIAL MOLAR QUANTITIES AND EXCESS MOLAR QUANTITIES FROM EXPERIMENTAL DATA VOLUME AND ENTHALPY... 

In this chapter, we shall consider the methods by which values of partial molar quantities and excess molar quantities can be obtained from experimental data. Most of the methods are applicable to any thermodynamic property J, but special emphasis will be placed on the partial molar volume and the partial molar enthalpy, which are needed to determine the pressure and temperature coefficients of the chemical potential, and on the excess molar volume and the excess molar enthalpy, which are needed to determine the pressure and temperature coefficients of the excess Gibbs function. Furthermore, the volume is tangible and easy to visualize hence, it serves well in an initial exposition of partial molar quantities and excess molar quantities. 

Comelli, F. and Francesconi, R. Excess molar enthalpies and excess molar volnmesofpropionic acid + octane + cyclohexane, + 1,3,5-trimethylbenzene, + oxane, or + 1,4-dioxane at 313.15 K, J. Chem. Eng. Data, 41(1) 101-104, 1996. 

Zhao, X., Yu, Z.-Y., Zhou, R., and Eiu, Y. Excess molar enthalpies for binary mixtures of benzyl alcohol and heptanone isomers at different temperatures, J. Chem. Eng. Data, 46(5) 1258-1260, 2001. 

Strong intermolecular interactions between the hydroxyl group and the IL lead to the negative values of excess molar volumes,, and excess molar enthalpies The strongly negative curve for [CiQlm][QS04] + water, ... 

The excess molar enthalpies at 323 K and 1.3 MPa were measured in [64] for hydrocarbons (hex-l-ene, cyclohexane, benzene, and cyclohexene) in the [C2Cilm][Tf2Nj. The negative excess enthalpies were observed (-730 J mol at Xh = 0.63) only in the mixtures with benzene, expected from the discussion about the interactions in the solution. Much more data can be found in the two existing data banks [1,2] for example, in Dortmund Data Bank, 37 systems are accessible. 

From the experimental temperature dependence of A2 (and the corresponding inferred temperature dependence of juE the other basic excess thermodynamic functions can be determined using general thermodynamic relationships. This then provides a complete thermodynamic characterization of the system as a whole. Thus, for the determination of the excess molar enthalpy of the system at constant pressure, the following equation can be used (Prigogine and Defay, 1954) ... 

The excess molar enthalpy hV is simply the heat of mixing at constant pressure related to 1 mole of solution.) And from the excess molar enthalpy and the excess chemical potential, we can obtain the excess molar entropy of the system from the following equation ... 

Figure 17.5 Derived thermodynamic properties at T — 298.15 K and p = 0.1 MPa for (2Cic-CfiHi2 + X2n-CjHi4) (a) excess molar heat capacities obtained from the excess molar enthalpies (b) relative partial molar heat capacities obtained from the excess molar heat capacities (c) change of the excess molar volume with temperature obtained from the excess molar volumes and (d) change of the excess molar enthalpies with pressure obtained from the excess molar volumes.

Figure 17.6 Excess molar properties at p = 0.1 MPa for (X111-C7H16 +X2I-C4H9CI) (a) gives the excess molar enthalpies. The solid line represents values at T= 298.15 K, while the dashed line gives values changed to T = 323.15 K, using the excess molar heat capacities at T = 298.15 K shown in (b). The excess molar volumes at T= 298.15 K are shown in (c).

Once the species present in a solution have been chosen and the values of the various equilibrium constants have been determined to give the best fit to the experimental data, other thermodynamic quantities can be evaluated by use of the usual relations. Thus, the excess molar Gibbs energies can be calculated when the values of the excess chemical potentials have been determined. The molar change of enthalpy on mixing and excess molar entropy can be calculated by the appropriate differentiation of the excess Gibbs energy with respect to temperature. These functions depend upon the temperature dependence of the equilibrium constants. 

For an ideal mixture, the enthalpy of mixing is zero and so a measured molar enthalpy of mixing is the excess value, HE. The literature concerning HE -values is more extensive than for GE-values because calorimetric measurements are more readily made. The dependence of HE on temperature yields the excess molar heat capacity, while combination of HE and GE values yields SE, the molar excess entropy of mixing. The dependences of GE, HE and T- SE on composition are conveniently summarized in the same diagram. The definition of an ideal mixture also requires that the molar volume is given by the sum, Xj V + x2 V2, so that the molar volume of a real mixture can be expressed in terms of an excess molar volume VE (Battino, 1971). 

Experimental determination of excess molar quantities such as excess molar enthalpy and excess molar volume is very important for the discussion of solution properties of binary liquids. Recently, calculation of these thermodynamic quantities becomes possible by computer simulation of molecular dynamics (MD) and Monte Carlo (MC) methods. On the other hand, the integral equation theory has played an essential role in the statistical thermodynamics of solution. The simulation and the integral equation theory may be complementary but the integral equation theory has the great advantage over simulation that it is computationally easier to handle and it permits us to estimate the differential thermodynamic quantities. 

We have calculated enthalpy, internal energy, excess molar enthalpy, and excess molar internal energy based on the integral equation theory. Validity of its use has been confirmed by the comparison of our results with those of MC calculation. Then, we have calculated the differential thermodynamic quantities of the isobaric heat capacity Cp and the excess isobaric molar heat capacity, Cp. ... 

They are used as industrial solvents for small- and large-scale separation processes, and they have unusual thermodynamic properties, which depend in a complicated manner on composition, pressure, and temperature for example, the excess molar enthalpy (fp-) of ethanol + water mixture against concentration exhibits three extrema in its dependence on composition at 333.15 K and 0.4 MPa. The thermodynamic behavior of these systems is particularly intricate in the water-rich region, as illustrated by the dependencies of the molar heat capacity and partial molar volume on composition. This sensitivity of the partial molar properties indicates that structural changes occur in the water-rich region of these mixtures. Of course, the unique structural properties of water are responsible for this behavior. ... 

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