Excess partial molar enthalpy

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

GLC is a well-established and accurate method used to obtain and the partial molar excess enthalpies at infinite dilution values AHf" , which is determined from the Gibbs-Helmholtz equation ... 

The partial molar excess enthalpy at infinite dilution, Hf- " , can be determined by Equation 4.5. 

The partial molar excess Gibbs free energy and partial molar excess enthalpy of mixing are defined by the following equations ... 

Therefore, Eqs. (1.205) and (1.206) yield partial molar excess enthalpies... 

An application of continuum solvation calculations that has not been extensively studied is the effect of temperature. A straightforward way to determine the solvation free energy at different temperatures is to use the known temperature dependence of the solvent properties (dielectric constant, ionization potential, refractive index, and density of the solvent) and do an ab initio solvation calculation at each temperature. Elcock and McCammon (1997) studied the solvation of amino acids in water from 5 to 100°C and found that the scale factor a should increase with temperature to describe correctly the temperature dependence of the solvation free energy. Tawa and Pratt (1995) examined the equilibrium ionization of liquid water and drew similar conclusions. An alternative way to study temperature effect is through the enthalpy of solvation. The temperature dependence of is related to the partial molar excess enthalpy at infinite dilution,... 

In addition to calculation of the saturation vapor pressure, a model for calculating the activity coefficient is required. The activity coefficient depends on concentration, and also on pressure and temperature. These dependences can be related to partial molar excess enthalpies and partial molar excess volumes ... 

For a mole fraction of Xj = 0.252, the following values for the partial molar excess enthalpy can be read from Figure 5.17 ... 

While for the partial molar excess enthalpy of ethanol (1) a positive value is obtained, a negative value is obtained for water (2) for this composition. Following Eq. (5.26) one obtains with the help of these values... 

It can be recognized that different temperature dependencies are observed for the two compounds involved, caused by the different sign of the partial molar excess enthalpies. While the activity coefficient for ethanol decreases, the activity coefficient for water increases with increasing temperature in the temperature range covered. But as can be seen from Figure 5.17 the temperature dependence of the partial molar excess enthalpies strongly depends on composition. For example, for compositions Xj <0.1 negative partial molar excess enthalpies for ethanol would result. 

Calculation of Vapor-Liquid Equilibria Using g -Models 203 assuming that the value of the partial molar excess enthalpy of ethanol... 

From these results it can be concluded that the temperature dependence cannot be neglected. While positive values of the partial molar excess enthalpies lead to a decrease of the activity coefficients with increasing temperature, negative values of the partial molar excess enthalpies lead to an increase of the activity coefficients with increasing temperature. The variation of the molar excess enthalpy with composition and temperature is often very complex. In the system ethanol-water around 70 °C even the sign changes with composition, as shown in Figure 5.18. 

However, following Eq. 5.26 not the excess enthalpy but the partial molar excess enthalpy is the determining property to describe the temperature dependence of the activity coefficients. Depending on the curvature of h as a function of composition for positive (negative) values of h negative (positive) partial... 

The temperature dependence of the separation factor (see Eq. (5.18)) and of the azeotropic composition of binary systems depends on the type of azeotrope (pressure maximum, pressure minimum), the temperature dependence of the vapor pressures, and the composition and temperature dependence of the activity coefficients. These dependencies can be described with the help of the heats of vaporization and partial molar excess enthalpies following the Clausius-Clapeyron respectively the Gibbs-Helmholtz equation [38] (derivation see Appendix C, B9) ... 

Besides the enthalpies of vaporization additionally the difference of the partial molar excess enthalpies and the slope dyi/Sxi at the azeotropic point at 70 C is required. This information can be derived from Figures 5.17 and 5.30. For the... 

For each injection, the energy necessary to maintain isothermal condition is recorded as Aq over the injection step. This quantity of energy can be either from an electrical heater or a Peltier cooler. It is assumed that for the addition of small volumes of material Av the experimental conditions ate close to those in the definition of the partial molar excess enthalpy H of component 1. To a good approximation ... 

Thus successive injections of component 1 yield excess enthalpies at a series of compositions appropriate to the total amount of material injected. To a good approximation, the change of enthalpy with each injection of material is the partial molar excess enthalpy of component 1 at the middle of the injection. This may be fitted with an appropriate smoothing equation such as ... 

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