Hildebrand-Scatchard equation

Real solutions are rarely completely athermal, even when there is considerable similarity between the nature of the molecules. For cases in which some energy effects must be taken into account, Flory introduced an additional term into the expression for excess Gibbs free energy. Adapting the format of the Scatchard-Hildebrand equation, the additional contribution to the excess Gibbs free energy is assumed to be of the form ... 

Scatchard-Hildebrand equation, 173-175 Separation-process, 203 Solubility parameters, 174 Sorbital, 76 State, equation of empirical... 

It is advantageous with a new drug substance to be able to estimate what its solubility will be prior to carrying out dissolution experiments. There are several systems of solubility prediction, most notably those published by Amidon and Yalkowsky [14-16] in the 1970s. Their equation for solubility of p-aminobenzo-ates in polar and mixed solvents is a simplified two-dimensional analog of the Scatchard-Hildebrand equation and is based on the product of the interfacial tension and the molecular surface area of the hydrocarbon portion of a molecule. 

Because of the need for better predictability in more aqueous cosolvent systems, the Scatchard-Hildebrand equation was modiLed into the Extended Hildebrand equation [40,41] ... 

Acree and Rytting [54,55] developed the nearly ideal binary solvent (NIBS) approach to predict solubilities. NIBS did show an increased ability to predict solubilities versus the Scatchard-Hildebrand equation. However, it is limited to use in systems only involving nonspeciLc interactions. 

The Xh term quantifies the nonideal heat of mixing between the HOC and DOM phase and is typically quantified using the one-solubility parameter Scatchard-Hildebrand equation... 

ACTIVITY COEFFICIENTS FROM THE SCATCHARD-HILDEBRAND EQUATION 1.40... 

Scatchard-Hildebrand equation, 374 Schacham equation, friction factor, 94 Scheibel extractor, 483,487 Schildknecht column, 543,544,546 Screens, separating, 335, 337 capacity, 335, 340 flat, 335... 

Scatchard-Hildebrand Equation, Chao-Seader method Solubility parameters and partial molar volumes are referred to 25 °C, suitable for hydrocarbon systems Chao, K.C., and Seader, J.D., AIChE. J. 7 (1961) 4, 598. 

Chao-Seader Correlation. Reference was made earlier to the well known and much used Chao-Seader correlation for the prediction of vapor-liquid equilibrium for principally hydrogen-hydrocarbon systems with small amounts of CO2, H2S, O2, N2, etc. The heart of the correlation consists of several equations to represent liquid fugacity. The other two constituents, the Scatchard-Hildebrand equation for activity coefficients and the Redllch-Kwong equation for the vapor-phase nonideality, were already well established. 

The parameter Ajj has the units of energy per unit volume and is analogous to the square of the solubility parameter in the Scatchard-Hildebrand equation. Numerous tests of the Scatchard-Hilderbrand equation have shown that there is significance to the solubility parameter. Previously, there has been no way to interpret this type of parameter from an equation of state. This new M-VDW equation could provide this opportunity. 

Note A more complete table of this type, showing more details is in Walas [ 1, Chapter 4]. Most of the coefficients in these tables, A B, etc. are data-fitdng values, obtained from experimental VLE measurements. Some have semi-theoretical bases. The constants in the Scatchard-Hildebrand equation are based on the Regular Solution theory, and are calculable from pure species properties, without any data for tha mixture. Many authors replace all the symbols for the coefficients with a universal set, A j and Aba, etc. Here the originally used symbols are shown. 

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