Equilibrium constants and standard enthalpies have been measured calorimetrically for the formation of complexes of aand ^-cyclodextrins with substituted phenols in aqueous solutions at 298.15 K. The study includes variation of the size and shape of the phenol, the size and degree of methylation of the cyclodextrin, and the effects of pH and ionic strength. Substituent effects were measured for p-chloro-, p-bromo-, p-methyl-, p-hydroxy-, p-nitro-and m-nitrophenols. The effects of ionization were studied with m-and p-nitrophenolate ions. The effects of methyl substitutions of ß-cyclodextrin were investigated with nitrophenol and nitrophenolate ions complexing with heptakis(2,6-di-0-methyl)-/3-cyclodextrin and heptakis(2,3,6-tri-0methyl)-/3-cyclodextrin. All of the effects studied show a substantial amount of entropic-enthalpic compensation, such that free energy effects are relatively small in comparison to enthalpic and/or entropic effects, but there was no simple relationship between the standard enthalpies and entropies of complex formation. However, a linear relationship was observed between the enthalpy and entropy for the transfer of substituted phenols from the complex with -cyclodextrin to the complex with /3-cyclodextrin. This relationship was independent of pH and ionic strength. In general, complex formation of a substituted phenol with -cyclodextrin is more exothermic than with /3-cyclodextrin, but the entropy of complex formation is also more negative.

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The calculation of irreversible thermodynamic work is examined in terms of the presentation in textbooks and in the application to actual and conceptual experiments. The force operating across the boundary between system and surroundings is shown to be dependent on the velocity of the operation. An approximate correction for the effect of velocity on the operating pressure for a perfect gas is suggested as P operating = P gas(1 ± u/vx)2; vx 2 = RT/Mwhere u is the absolute value of the velocity of the piston, v x is the average velocity of the gas molecules moving toward the piston, and M is the molar mass of the gas. The positive sign applies to compressions and the negative sign to expansions.

Publication costs assisted by the University of Missouri-Rolla The simple model which has previously led to successful predictive equations for the partial molar excess enthalpy of a solute in nearly ideal binary solvents has been slightly modified for application to the partial molar excess Gibbs free energy (excess chemical potential) of the solute in these systems. Three predictive equations are derived and tested for their ability to predict solubility in mixed solvents from measurements in the pure solvents. The most successful equation involves volumetrically weighted interaction parameters for the excess Gibbs free energy relative to the Flory-Huggins entropy of mixing, and predicts solubility in 22 systems containing naphthalene, iodine, and stannic iodide as solutes with an average deviation of 1.5% and a maximum deviation of 4%, using no adjustable parameters. IntroductionRecent developments in the investigation of weak association complexes in solution'" have shown a need for improved approximations for the thermochemical properties of a solute or solutes in a binary solvent system, to allow compensation for the effects of solution nonideality, or, from a slightly different viewpoint, to separate "chemical" and "physical" effects on the properties of the complexes. In order to provide a firm thermodynamic basis for these approximations, much simpler systems must be studied, establishing the qualitative and if possible the quantitative trends of behavior of solutes in binary solvent systems of nonspecific (or physical) interactions.This work is a continuation of our search for mixing models and equations which will provide reasonable predictions for the thermochemical properties of a solute at high dilution in a binary solvent. Earlier have been primarily concerned with the partial molar excess enthalpy of the solute. In this work, we extend our previous consideration of the chemical potential or partial molar Gibbs free energy of the solute4 through studies of solubility in binary solvents. Three specific forms of the

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