Chemical Thermodynamics of Ultrasound Speed in Solutions and Liquid Mixtures

Abstract

A comprehensive formalism is developed to treat thermodynamically speed of ultrasound data for solutions and liquid mixtures. For solutions, the apparent speed of ultrasound of a solute is introduced and proposed to take the place of empirically defined quantities. The partial speed of ultrasound of a solute is defined and related to the partial molar volume and partial molar isentropic compression. For liquid mixtures, the concept of speed of sound before mixing pure liquids is presented and used to define the change in speed of ultrasound upon ideal mixing, which is predicted to be generally a negative quantity. A new thermodynamic equation is derived linking the values for excess speed of ultrasound, excess molar volume and excess molar isentropic compression of a mixture, and its applications are discussed. Ideal and excess apparent speeds of ultrasound, as well as ideal and excess partial speeds of ultrasound, are defined for substances making up a liquid mixture. Accurate speeds of ultrasound in 31 mixtures of water with the amphiphile 2-(ethylamino)ethanol at 293.15 K are reported. These data are used to demonstrate the ability of the apparent speed of ultrasound to describe the impact of solutes on sonic properties of solutions and the advantages of analysing thermodynamic properties of binary liquid mixtures in terms of the dependence on composition of Balankina's ratios between excess and ideal values. It is concluded that the new thermodynamic functions defined for speeds of ultrasound in solutions and liquid mixtures give, at the least, equivalent information on molecular aspects to the usual functions related to the isentropic compressibility, without needing density data for this purpose.

Refractive Index of Liquid Mixtures: Theory and Experiment

“…A similar situation was recently encountered for the ultrasound speed. [5] By noting that aÀb = (a 2 Àb 2 )/(a+b), it follows from Equations (6), (10) and (11) …”

“…[5] Here, we draw on the fact that both properties are related to the speed of propagation of waves in liquids to describe unmixed refractive indices in close analogy with unmixed ultrasound speeds.…”

“…Thus, we introduce the concept of refractive index before mixing two portions of pure liquid substances. This development is a natural extension of the recently presented idea of speed of sound before mixing, [5] because the refractive index is proportional to the reciprocal of the speed of light. Then, on the basis of other contributions leading to the estimation of relative permittivities of thermodynamically ideal liquid mixtures, [6] we obtain an equation describing the dependence on composition of the ideal refractive index.…”

“…Recently, Balankina [9] has argued that excess volumetric properties of liquid mixtures should be easier to interpret in terms of the dependence on composition of relative excess properties, the latter being defined as the ratio between excess and ideal values. We have already shown [5] that this is a powerful concept that yields a simple thermodynamic equation interrelating the relative excess values for ultrasound speeds, molar volumes and molar isentropic compressions of binary systems.…”

Thermodynamic and acoustic properties of binary mixtures of 1-butanol with 1,2-butanediol. The comparison with the results for 1,3-, and 1,4-butanediol

“…As noted in the previous paper by one of us [36], a similar relationship between u D and K E S was reported for various systems with two selfassociated compounds and it seems to be a general feature for such systems. As reported recently [37], a detailed analysis of the above relation seems promising for better understanding of the information obtained from acoustic experiments.…”