Michael I. Davis

Isentropic compressibilities : Experimental origin and the quest for their rigorous estimation in thermodynamically ideal liquid mixtures

In this review, attention is initially focused upon the evolution of the Newton-Laplace Equation, that links the measured speed of sound in a fluid in conjunction with its density, to a reliable estimate of its isentropic compressibility κS. Definitions of ideal and excess isentropic quantities are formulated on the premise that the thermodynamic properties of an ideal mixture are mutually related in the same manner as are those of a real mixture or a pure substance. It is shown that both intensive and extensive properties can be derived from the ideal Gibbs energy. Different approaches previously used to calculate ideal isentropic quantities are examined and some subtle errors are identified. The consequences of using conflicting definitions are pointed out. Isentropic pressure derivatives obtained under different conditions and empirical models for estimating the differences between ultrasonic speeds in real and ideal liquid mixtures are discussed.

Ultrasonic speeds and isentropic functions of (a 2-alkoxyethanol + water) at 298.15 K

Abstract Ultrasonic speeds have been measured in (2-methoxyethanol + water), (2-ethoxyethanol + water), and (2-butoxyethanol + water) at 298.15 K, across their entire composition ranges. Their values have been combined with those of the molar volumes to obtain estimates of the product of the molar volume and the isentropic compressibility. The values that were obtained for the excess molar quantities are analysed using a segmented-composition model.

Ultrasonic speeds and isentropic functions of 2-(2-alkoxyethoxy)ethanol + water at 298.15 K

Abstract Ultrasonic speeds were measured in 2-(2-ethoxyethoxy)ethanol + water and 2-(2-butoxy ethoxy)ethanol +water systems across their entire composition ranges, at the temperature 298.15 K, using a sing-around technique, at a frequency of 1.8 MHz. Measurements were also made of the densities of the two systems. From these measurements, values of the molar and excess molar volumes were obtained together with the values of ⋍ (∂ V m /∂ p ) S,m and the corresponding excess quantities. The various excess quantities were analysed using a segmented-composition model.

Aggregative processes in aqueous solutions of isomeric 2-butoxyethanols at 298.15 K

Ultrasound speed measurements across the entire composition range of aqueous mixtures of both isobutoxyethanol (iC4E1) and tert-butoxyethanol (tC4E1) have been made at 298.15 K with a sonic solution monitor that employs a “pulse–echo–overlap” technique. In addition, densities of aqueous mixtures of tC4E1 were determined using a vibrating tube densimeter. These new data were complemented with literature values for densities of aqueous mixtures of tC4E1 and for densities and sound speeds of aqueous mixtures of n-butoxyethanol (nC4E1). In all cases, density values were converted to molar volumes, Vm, and excess molar volumes, VmE. Estimates of the isentropic molar compression, KS,m [= −(∂Vm/∂p)S], and of its excess counterpart, KS,mE, were obtained from the combination of the ultrasound speeds and density values. Data reduction procedures were used to generate consistent sets of values for thermodynamic properties of isomeric amphiphiles with increasing degree of alkyl branching. The graphs for the composition dependence of excess partial molar volumes and isentropic compressions of water show enhanced visual impact. These graphs are used for presenting evidence for identifying the prevailing patterns of molecular aggregation. Segmented-composition models, including a version onto which a mass action component has been grafted, are employed, together with a simplified pseudo-phase model, to analyse the various excess molar quantities. The experimental evidence thus obtained is used to relate the effect of chain branching with the degree of self-aggregation of amphiphiles in aqueous solution. An unexpectedly low self-aggregation among iC4E1 molecules is found and discussed in terms of vicinity to the lower critical solution temperature.

The concepts of non-Gibbsian and non-Lewisian properties in chemical thermodynamics

The concepts of Gibbsian and non-Gibbsian, Lewisian and non-Lewisian thermodynamic variables are explored with respect to the thermodynamic properties of liquid mixtures and solutions. The general structures of equations for isochoric heat capacities, isentropic compressions and isentropic expansions are compared and contrasted. A simple rule is proposed for transcribing non-Gibbsian equations in terms of non-Lewisian partial molar properties. The bases of equations for partial molar isochoric heat capacities, isentropic compressions and isentropic expansions are examined for (i) components of liquid mixtures, and (ii) solute and solvent in solutions together with the properties of solutes at infinite dilution.

Ultrasonic speeds and volumetric properties of binary mixtures of water with poly(ethylene glycol)s at 298.15 K

Ultrasonic speed measurements have been made by a sonic solution monitor using a ‘pulse–echo–overlap’ technique, for aqueous mixtures of the poly(ethylene glycol)s di-, tri- and tetra(ethylene glycol) at 298.15 K, across the entire composition range. Density values were taken from the literature and readily converted to molar volumes, V, and excess molar volumes, V E . They were combined with the measured values of the ultrasonic speeds to furnish estimates of the isentropic molar quantity, K S , equal to -(∂V/∂p) S , and of its excess counterpart, K S E . The magnitude of K S E decreases with the number of oxyethylene groups, except in the water-rich region. Data reduction procedures were used to calculate several related quantities leading to graphs with enhanced visual impact. Results were compared with those reported earlier for ethane-1,2-diol–water and for 2-[2-methoxy(ethoxy) n ]ethanol–water. Graphs of the data sets are presented to furnish a basis for the discussion of evidence for the prevailing patterns of molecular aggregation. Segmented-composition models were employed to analyse the various excess molar quantities.

Volumetric properties of binary mixtures of water with methoxy(ethoxy)nethanols

Density and ultrasonic speed measurements have been made, respectively, by means of a densimeter operating in a flow mode and by a sonic solution monitor using a ‘sing-around’ technique, for aqueous mixtures of 2-(2-methoxyethoxy)ethanol and 2-[2-methoxy(ethoxy)2]ethanol, at 298.15 K, across the entire composition range. The density values were readily converted to molar volumes, V, and excess molar volumes, VE. Estimates of the isentropic molar quantity, Ks, equal to –(∂V/∂p)s, and of its excess counterpart, KES, have been obtained from the density values, in combination with the ultrasonic speed values. The magnitude of VE increases with the introduction of oxyethylene groups into the molecule of amphiphile. The composition dependence of KES shows a similar increase, but one that is limited to the water-rich region. Data reduction procedures have been used to calculate several related quantities leading to graphs with enhanced visual impact. Our results have been compared with those reported earlier for methanol–water, and 2-methoxyethanol–water. Graphical analyses of the data sets are presented in an effort to find a plausible rationale for the observed trends in terms of prevailing patterns of molecular aggregation, while the various excess quantities considered are analysed using a segmented-composition model.

THERMODYNAMIC PROPERTIES OF (ETHAN-1,2-DIOL + WATER) AT THE TEMPERATURE 298.15 K. I, MOLAR VOLUMES, ISOBARIC MOLAR HEAT CAPACITIES, ULTRASONIC SPEEDS, AND ISENTROPIC FUNCTIONS

Densities have been measured in (ethan-1,2-diol + water) at the temperatures 288.15 K, 298.15 K, 303.15 K, and 308.15 K, across the entire composition range. Isobaric expansivities were derived from the results. Measurements have also been made of the isobaric heat capacities divided by volume and of the ultrasonic speeds, at the temperature 298.15 K, over the whole composition range. The values of these two properties have been combined with the molar volumes to obtain estimates of the products of the molar volume and the isentropic compressibility and of the molar volume and the isentropic expansivity. The values that were obtained for the excess molar quantities have been analysed using a segmented-composition model.

Studies of dielectric properties of some binary hydroorganic systems

Abstract Four alternative hypotheses, for describing the nature of ideal dielectric behavior in binary liquid mixtures, have been explored for the systems acetonitrile-water and tert-butanol-water. The various excess properties have been analysed using the four segment composition model. The estimation and interpretation of correlation factors and dipolar free energies in binary mixtures of associated liquids is discussed.

An analytic model for the excess properties of binary liquid mixtures

Abstract A model has been devised to analyse excess property data for binary liquid mixtures. The model embodies the concept of the segmentation of the total composition range into three distinct regions. Results are given for the analyses of Δ V , Δ H and Δν for the acetonitrile-water and dimethylsulfoxide-water systems.