The Thermodynamic Properties of Mixtures of Small, Nonpolar Molecules

Abstract

45)a1 is the thermal expansion coefficient of pure component 1 (see eq. 41). If s1 = s2, the coefficients simplify in eq. 43-45.Series expansions for the partial molar enthalpy and entropy may be obtained from eq. 43 by differentiation. Concluding RemarksAdaptation of the reduced partition function expressed by eq. 7 to mixtures and adoption of eq. 20 for the intermolecular energy on the assumption of random mixing underlies the theory developed above.The expressions derived for the various residual (or excess) properties of a binary mixture involve a single parameter, X12, beyond those furnished by the properties of the two pure components. The thermodynamic properties (e.g., H , Y , and S ) are thus related explicitly to one another in terms of this parameter characterizing the given mixture. Treatment of mixtures of small, nonpolar molecules on this basis is demonstrated in the following paper.I4 Application to polymer solutions will be presented in a future communication.Acknowledgment. The excess enthalpies, volumes, and entropies of 23 equimolar binary liquid mixtures f o r which necessary data are available in the literature are interpreted according to the relationships presented in the preceding paper. Most of the mixtures comprise pairs of small globular molecules from the group c-CsHlz, C 6 H 6 , C(CH3)4, CCI4, SiCI4, TiCI4, and SnCl, or f r o m the condensed gases CH4, Ar, 0 2 , and N2. Also included are mixtures of C6H6 and of c-csH,2 with n-hexane and n-heptane, the benzenediphenyl system, and two hydrocarbon-fluorocarbon mixtures. Previously unaccounted equation of state terms, which depend on properties of the pure components, make important contributions to each of the excess quantities. Through use oj pair interaction parameters chosen to achieve agreement with the observed excess enthalpies, excess volumes are calculated which agree in nearly all cases with those observed within limits set b y experimental errors. Although excess entropies calculated on the same basis tend to be somewhat lower than those observed, the agreement is favorable f o r most systems. Exceptions involve benzene as one component or cyclohexane in admixture with n-alkanes. Because account was taken of equation of state contributions, the present interaction parameters differ f r o m those deduced from experimental results b y previous procedures. Departures from the Berthelot geometric mean rule are discussed. (1) P. J. Flory, J . A m . Chem.Analysis of the dependence of the various excess quantities on composition has not been undertaken for the reason that comparison of theoretical prediction with the observed compositional dependence would be indecisive for the mixtures of nonpolar, small molecules considered. Hence, results are quoted only for

Excess volumes and excess viscosities of binary liquid mixtures: methylisobutylketone + benzene, toluene, chlorobenzene, bromobenzene, and nitrobenzene

“…[5] have their usual significance as described by Patterson and Delmas (5). The site fraction 02, and the interchange energy parameter X I 2 are obtained on the basis of Flory's relation (13,14) using experimental heat of mixing data. The results of excess enthalpy are reported in Table 4.…”

Thermal Expansivity of Ternary Liquid Mixtures: Application of Hard-Sphere Models and Flory's Statistical Theory

“…The expression of thermal expansivity obtained from Flory's statistical theory [10][11][12][13] is given by…”

“…Segment fraction (Ψ ), site fraction (θ) interaction parameter (X ij ), characteristic temperature (T * ), characteristic pressure (P * ) and the reduced temperature (T ) of the liquid mixture have been computed by the earlier suggested methods [10][11][12][13]:…”

“…In recent years, Flory's statistical theory [10][11][12][13] was successfully applied to binary and multicomponent liquid mixtures for estimating various thermodynamic and transport properties. Pandey et al [14] applied Flory's statistical theory with modified expression of characteristic pressure to discuss the thermodynamic behaviour of ternary liquid mixtures.…”

Structure of Carbon Tetrachloride + t-Butanol Mixtures from Positron Annihilation and Ultrasonic Velocity Measurements

“…An approximate but satisfactory representation of liquid state properties was proposed by Flory [5] and applied to the interpretation of thermodynamic properties of mixtures of small non-polar molecules by Abe and Flory [6]. However, most of the authors dealing with the dependence of ultrasonic velocity, compressibility, and molar volume on the composition of binary mixtures have interpreted the experimental results phenomenologically, i.e.…”