Speed of Sound, Isentropic Compressibilities, and Excess Molar Volumes of Binary Mixtures Containing p-Dioxane

The speed of sound u in and densities of eight binary mixtures of p-dioxane (p-C₄H₈O₂) with methylcyclohexane (c-C₆H₁₁CH₃), 1-chlorohexane (C₆H₁₃C1), 1-bromohexane (C₆H₁₃Br), p-xylene [C₆H₄(CH₃)₂], propylbenzene (C₆H₅C₃H₇), methyl acetate CH₃COOCH₃), butyl acetate (CH₃COOC₄H₉), and amyl acetate (CH₃COOC₅H₁₁) were measured over the whole composition range at 30°C. Isentropic compressibilities (K _S), Rao's molar sound functions (R), excess molar volumes (V ^E), excess isentropic compressibilities (K _S ^E ) together with relative change in volume V/₁₂ values, have been obtained for all measured mole fractions. The excess partial molar volume (V₁-V ₁ ⁰ ) of p-dioxane in different solvents have also been estimated. The experimental results have been analyzed in terms of the Prigogine–Flory–Patterson theory of solutions.     

Calorimetric investigation of the adsorption of binary vapour mixtures of tetrahydropyrrol with methanol and cyclopentane on the homogeneous surface

Adsorption isotherms and differential heats of adsorption of tetrahydropyrrol (THP) and cyclopentane CP), as well as THP and methanol mixtures (mole ratio 1∶1, 1∶2 and 1∶4) on the graphitized carbon black Sterling MT surface were determined. The influence of dilution of [THP] on its ability to undergo homomolecular association was tested. Even 1∶4 dilution of THP does not prevent is association. Methanol strongly interacts with THP in the mixed adsorbed layer forming heteromolecular associates.     

Heats of Mixing of Mixed Solvent Solutions of Alkali Metal Salts of Substituted Benzenesulfonic Acids

The enthalpy change on mixing solutions of methyl-substituted benzenesulfonic acids and their salts, with salts having a common cation or anion, at constant ionic strength in mixtures of 1,4-dioxane with water, were measured at 25°C. The heat effects of mixing solutions having a common anion increase almost linearly with the reciprocal value of the dielectric constant of the solvent. The heat effects of mixing solutions having a common cation, which are all negative in water-rich solutions, become endothermic after a certain value of the dielectric constant is passed. The results are discussed in terms of the solute-solvent structural properties. This revised version was published online in July 2006 with corrections to the Cover Date.     

Phase Equilibria and Critical Curves of Binary Ammonia–Hydrocarbon Mixtures

Liquid or dense supercritical ammonia has been suggested as an extraction fluid. It is indeed good solvent for very different classes of compounds, as can be seen from phase diagrams. Such diagrams for binary systems of ammonia and hydrocarbons are presented and discussed on the basis of their critical curves. Apparatus and methods for the measurement of phase equilibria and equation of state data of fluid mixtures at high pressure are described.     

Conductance studies in amide-water mixtures. II. Sodium salts inN,N-dimethylformamide-water mixtures at 35°C

Conductance data for sodium nitrite, chloride, and acetate in water andN,N-dimethylformamide (DMF)-water mixtures (74.82D42.48) for the concentration range 0.001–0.04N, as well as the densities, viscosities, and dielectric constants of the solvent mixtures at 35°C, are reported. The data have been analyzed by the Fuoss (1975) equation. The existence of a maximum in the viscosity at a 13 mole ratio of DMF and water is indicated. The Walden products for all the three salts pass through a maximum while the equivalent conductances show a minimum with increasing DMF content. The maxima in the Walden product are attributed to the dehydration of ions by the cosolvent (DMF).Part I:Indian J. Chem. 14A, 1015 (1976).Deceased.     

Solvent effect on reaction rates: Reaction between sodium ethoxide and methyl iodide in ethanol + cyclohexane solvent systems

The kinetics of the reaction between sodium ethoxide and methyl iodide has been studied at 25°C in various cyclohexane-ethanol solvent mixtures with a cyclohexane content of 10 to 50% per volume. The determination of the rate constants att=0 were carried out by a new iterative method proposed in this investigation. The obtained results show that the reaction rate decreases with the increasing cyclohexane content. This behavior can be attributed to various solute-solvent interactions of electrostatic nature. On the other hand, the variation of ion and ion pairs rate constants with solvent composition permits the various solvation effects to be taken into account.     

Transfer activity coefficient of the proton in water-pyridine mixtures. A comparison of some extrathermodynamic assumptions

Various water-pyridine mixtures have been selected in order to compare several of the most popular extrathermodynamic assumptions involved in the determination of the transfer activity coefficient of the proton, _t(H⁺). Two techniques have been utilized for this purpose: voltammetry [study of the ferrocene, ferricyanide, or thallium(1) systems] and potentiometry at equilibrium (emf measurements of various galvanic cells, including liquid junctions and hydrogen electrode or silver electrode as a test electrode). The assumptions have been classified into various groups [e.g., _t(Z^p+)=_t(Z^q+) or _t(X^–)=_t(Y⁺)], and the values of _t(H⁺) have been experimentally determined in each case. The results vary depending upon the basic assumption (several pH units); less important differences (e.g., 0.5 pH unit) occur within a given group, and this may be assigned to the nature of the reference species chosen. A simple model of solvation has been also examined; the application of the law of mass action to the corresponding equilibrium provides results close to the _t(X^–) =_t(Y⁺)type of assumptions which ultimately leads to most self-consistent results.     

Phase separation of symmetrical polymer mixtures in thin-film geometry

Monte Carlo simulations of the bond fluctuation model of symmetrical polymer blends confined between two neutral repulsive walls are presented for chain lengthN _A=N _B=32 and a wide range of film thicknessD (fromD=8 toD=48 in units of the lattice spacing). The critical temperaturesT _c (D) of unmixing are located by finite-size scaling methods, and it is shown that , wherev ₃0.63 is the correlation length exponent of the three-dimensional Ising model universality class. Contrary to this result, it is argued that the critical behavior of the films is ruled by two-dimensional exponents, e.g., the coexistence curve (difference in volume fraction of A-rich and A-poor phases) scales as , where ₂ is the critical exponent of the two-dimensional Ising universality class ( ₂=1/8). Since for largeD this asymptotic critical behavior is confined to an extremely narrow vicinity ofT _c (D), one observes in practice effective exponents which gradually cross over from ₂ to ₃ with increasing film thickness. This anomalous flattening of the coexistence curve should be observable experimentally.     

The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family

We here consider testing the hypothesis ofhomogeneity against the alternative of a two-component mixture of densities. The paper focuses on the asymptotic null distribution of 2 log _n , where _n is the likelihood ratio statistic. The main result, obtained by simulation, is that its limiting distribution appears pivotal (in the sense of constant percentiles over the unknown parameter), but model specific (differs if the model is changed from Poisson to normal, say), and is not at all well approximated by the conventional ₍₂₎ ² -distribution obtained by counting parameters. In Section 3, the binomial with sample size parameter 2 is considered. Via a simple geometric characterization the case for which the likelihood ratio is 1 can easily be identified and the corresponding probability is found. Closed form expressions for the likelihood ratio _n are possible and the asymptotic distribution of 2 log _n is shown to be the mixture giving equal weights to the one point distribution with all its mass equal to zero and the ²-distribution with 1 degree of freedom. A similar result is reached in Section 4 for the Poisson with a small parameter value (0.1), although the geometric characterization is different. In Section 5 we consider the Poisson case in full generality. There is still a positive asymptotic probability that the likelihood ratio is 1. The upper precentiles of the null distribution of 2 log _n are found by simulation for various populations and shown to be nearly independent of the population parameter, and approximately equal to the (1–2)100 percentiles of ₍₁₎ ² . In Sections 6 and 7, we close with a study of two continuous densities, theexponential and thenormal with known variance. In these models the asymptotic distribution of 2 log _n is pivotal. Selected (1–) 100 percentiles are presented and shown to differ between the two models.     

Necessary conditions for characterization of laws via mixed sums

SupposeX andY are independent and identically distributed, and independent ofU which satisfies 0U1. Recent work has centered on finding the lawsL(X) for whichX U(X+Y) where denotes equality in law. We show that this equation corresponds to a certain projective invariance property under random rotations. Implicitly or explicitly, it has been assumed that the characteristic function ofX has an expansion property near the origin. We show that solutions may be admitted in the absence of this condition when –logU has a lattice law. A continuous version of the basic problem replaces sums with a Lévy process. Instead we consider self-similar processes, showing that a solution exists only whenU is constant, and then all processes of a given order are admitted.This research was in part supported by NSERC grant A-8466.