Enthalpy of mixing, excess

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

Still, the strain enthalpy is of particular importance. An elastic continuum model for this size mismatch enthalpy shows that, within the limitations of the model, this enthalpy contribution correlates with the square of the volume difference [41,42], The model furthermore predicts what is often observed experimentally for a given size difference it is easier to put a smaller atom in a larger host than vice versa. Both the excess enthalpy of mixing and the solubility limits are often asymmetric with regard to composition. This elastic contribution to the enthalpy of mixing scales with the two-parameter sub-regular solution model described in Chapter 3 (see eq. 3.74) ... 

The regular solution approximation is introduced by assuming definition) that the excess entropy of mixing is zero. This requires that the excess free energy equal the excess enthalpy of mixing. For binary mixtures the excess enthalpy of mixing is ordinarily represented by a function of the form... 

The data are then compared to predictions based on a new model which includes an excess enthalpy of mixing and two contributions to the excess entropy of mixing. 

The relative partial molar enthalpies of the species are obtained by using Eqs. (70) and (75) in Eq. (41). When the interaction coefficients linear functions of T as assumed here, these enthalpies can be written down directly from Eq. (70) since the partial derivatives defining them in Eq. (41) are all taken at constant values for the species mole fractions. Since the concept of excess quantities measures a quantity for a solution relative to its value in an ideal solution, all nonzero enthalpy quantities are excess. The total enthalpy of mixing is then the same as the excess enthalpy of mixing and a relative partial molar enthalpy is the same as the excess relative partial molar enthalpy. Therefore for brevity the adjective excess is not used here in connection with enthalpy quantities. By definition the relation between the relative partial molar entropy of species j, Sj, and the excess relative partial molar entropy sj is... 

A particularly simple approximation known as regular-solution theory was developed by Hildebrand and co-workers [J. H. Hildebrand. /. Am. Chem. Soc. 51, 66-80 (1929)]. The regular-solution model assumes that the excess enthalpy of mixing can be represented as a simple one-parameter correction... 

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

Figure 8.6. Excess enthalpy of mixing in a binary system.

Figure 32. Excess enthalpies of mixing for ethyl alcohol 4- water mixtures at various temperatures T/K = (a) 383-15, (b) 363-15, (c) 343-15, (d) 333-15, (e) 323-15 and (f) 298-15 (Larkin, 1975).

AGme = excess free energy of mixing of water with the co-solvent AHme = excess enthalpy of mixing water with the co-solvent ASme = excess entropy of mixing water with the co-solvent... 

The integral heat of mixing per mole of solution is equal to the excess enthalpy of mixing defined in the previous paragraph ... 

The enthalpy of mixing is also the excess enthalpy of mixing because an ideal solution has zero enthalpy of mixing. Now, the entropy of mixing can be calculated ... 

Most real solutions are neither ideal nor regular. As a result a realistic description of their thermodynamic properties must consider the fact that both the excess enthalpy of mixing, and excess entropy, are non- zero. Wilson... 

The excess enthalpy of mixing (heat of mixing) for carbon tetrachloride + cyclohexane has been determined at several temperatures by Adcock and McGlashan (Proc. Roy. Soc. A. 1964, 226). Their results can be expressed by the relation (compare problem 70)... 

Lipa tov et calculated the excess enthalpy of mixing at the point of... 

Gmehling (1993) measured excess enthalpies of mixing of different liquids in a commercial isothermal flow calorimeter (Hart Scientific 7501) with an uncertainty of less than 1%. The flow mixing tube was thermostatized by constant Peltier cooling and controlled electrical pulse heating to keep the temperature constant. 

Nonideal solutions may be classified into two limiting cases. In one limiting case, called regular solutions,-AGe AHe, i.e. most of the deviation from ideality is due to the excess enthalpy of mixing. Since AGe = AI/e — TASe, it follows that for regular solutions ASe 0. Furthermore, since ASe = —(0AGe/0T), from (8.4.18) it follows that the activity coefficients are given by... 

Tanaka, R. Mnrakami, S. Fujisbiro, R. Excess enthalpies of mixing of a polar liquid + a non-polar liquid at 298.15 K J. Chem. Thermodyn. 1974,6, 209-218... 

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