Excess enthalpy interactions

As one would expect from the definition of Xi2 (cf. viewed as the excess enthalpy/interaction between monomers in a mixed pair vs. in their single phase)... 

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

The ideal solution approximation is well suited for systems where the A and B atoms are of similar size and in general have similar properties. In such systems a given atom has nearly the same interaction with its neighbours, whether in a mixture or in the pure state. If the size and/or chemical nature of the atoms or molecules deviate sufficiently from each other, the deviation from the ideal model may be considerable and other models are needed which allow excess enthalpies and possibly excess entropies of mixing. 

The reciprocal lattice model as derived above is the basis for many different variants. For simplicity we have assumed the interactions between the next nearest neighbours A+ -B+ andC- I) to be independent of composition, even though experiments have shown that this is often not the case. It is relatively simple to introduce parameters which allow the interaction energy, for example between A+ and B+, to depend on the concentration of C and D [14], One may also include other terms that take into account excess enthalpies that are asymmetric with regard to composition and the effects of temperature and pressure. 

Flow calorimetric measurements of the excess enthalpy of a steam + n-heptane mixture over the temperature range 373 to 698 K and at pressures up to 12.3 MPa are reported. The low pressure measurements are analysed in terms of the virial equation of state using an association model. An extension of this approach, the Separated Associated Fluid Interaction Model, fits the measurements at high pressures reasonably well. 

Excess enthalpy is parameterized through interaction parameter W ... 

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. 

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... 

The first and most important feature that can be seen from the data (Table 5.3) is that the excess enthalpies of the smaller-sized compounds are close to zero (i.e., between -10 and +10 kJ mol-1). This is even true for apolar compounds such as tetrachloro-ethene or hexane. Hence in these cases, the intermolecular interactions that must be disrupted to remove a small organic molecule from its pure liquid (i.e., the enthalpy... 

Such NACs do not exhibit linear isotherms when they sorb under certain conditions with aluminosilicate clays (Fig. 11.66 Haderlein and Schwarzenbach, 1993 Hader-lein et al., 1996). Rather they show saturation behavior indicating an association with specific sites on the solid surfaces. This specific site interaction is also indicated by the observations of competitive effects among different NACs in sorption experiments. Further, the sorption enthalpies have been found to be much greater than excess enthalpies of aqueous solution of these sorbates (e.g., 4-methyl-2-nitro-phenol exhibits a sorption enthalpy of-41.7 kJ-mol"1). These data all indicate that there is a strong specific interaction of NACs with the aluminosilicate clay surfaces. 

Another very common misinterpretation of experimental results is the following. Suppose we measure deviations from a DI solution in a T, P, NA, NB system. The corresponding activity coefficient is given by (6.34) the same quantity is often referred to as the excess chemical potential of the solute. One then expands the activity coefficient (or the excess chemical potential) to first order in pA and interprets the first coefficient as a measure of the extent of solute-solute interaction. Clearly, such an interpretation is valid for an osmotic system provided we understand interaction in the sense of affinity, as pointed out above. However, in the T, P, NA, NB system, the first-order coefficient depends on the difference — G°B. It is in principle possible that G be, say, positive, whereas the first-order coefficient in (6.34) can be positive, negative, or zero. This clearly invalidates the interpretation of the first-order coefficient in (6.34) in terms of solute-solute correlation. Similar expansions are common for the excess enthalpies and entropies where the first-order coefficient in the density expansion is not known explicitly. 

To calculate the partial molal excess free energies gf and from this the activity coefficients and the excess enthalpy, size parameters for each functional group and binary interaction parameters for each pair of functional groups are required. Size parameters can be calculated from theory. Interaction parameters are back-calculated from existing phase equilibrium data and then used with the size parameters to predict phase equilibrium properties of mixtures for which no data are available. 

J mol ]. The authors suggest that this rise in excess enthalpy must be associated with a considerable increase of the contributions due to n-n interactions or due to interactions of more than one tetrachloromethane molecule with one 3-w-hexyne molecule. The n-n bond, which is very exposed in the structurally simple 3-w-hexyne molecule, could make the last-mentioned mode of interaction possible. The slight shift of i/max towards higher mole fractions of tetrachloromethane can hardly bear out this suggestion. 

D5.5 A regular solution has excess entropy of zero, but an excess enthalpy that is non-zero and dependent on composition, perhaps in the manner of eqn 5.30. We can think of a regular solution as one in which the different molecules of the solution are distributed randomly, as in an ideal solution, but have different energies of interaction with each other. 

Those criteria are met by a cocrystal screening based on COSMO-RS theory, using the mixing enthalpy (or equivalently the excess enthalpy of a supercooled cocrystal mixture [18]. The main reason for the predictive capability of this theory concerning cocrystal formation is its accurate description of intermolecular interactions. The idea behind a COSMO-RS-based screening can be best understood by having a look at the thermodynamic cycle shown in Scheme 9.1. 

P4.5 Calculate the excess enthalpy of the system benzene (l)-cyclohexane (2) at =25 CandP = 1 bar for a mole fraction of benzene of xi =0.5 using the Soave-Redlich-Kwong equation of state. The required values can be taken from Appendix A. The binary interaction parameter is ki2 = 0.0246. 

While linear temperature-dependent group interaction parameters are already required to describe the VLE behavior and excess enthalpies simultaneously, quadratic temperature-dependent parameters are used when the system shows a strong temperature dependence of the excess enthalpies. 

Even at a superficial view, it is rather obvious that the FH theory has limitations, even when all its restrictive assumptions (weak interactions, entropy-independent enthalpy, etc.) are satisfied. For example, the % for polymers, as defined by FH iX = zlAzIkT, z is coordination number and As the excess enthalpy of interaction for one mixed pair) allows for z solvent neighbors around each monomer, neglecting that... 

FIG. 2 Schematic explanation for the dependence of the heat of demicellization on chain length and temperature. The bold arrows represent the overall enthalpy of demicellization, the dotted arrows represent the excess enthalpy of hydration of the hydrophobic moieties of the amphiphiles, and the dashed arrows represent the sum of enthalpies resulting from van der Waals interactions between hydrophobic moieties in the aggregates and from hydrogen bonds between water molecules. 

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