Excess apparent molar volume

In the case of aqueous electrolytes the classical Debye-Hiickel theory (Debye and Hiickel, 1923) predicts that the excess apparent molar volume of the solute is given by... 

Xhe excess apparent molar volume of electrolytes solutes in the DH model is given by Equation (2.12), referred to as the Debye-Huckel limiting law (DHLL), which becomes exact in the infinite dilution limit. Beyond the dilute region the short-range interactions among ions, neglected in the DH model, are responsible for the deviation to the DHLL. 

For neutral solutes the concentration dependence of the excess apparent molar volume is fitted to the experimental results using relationships derived from Equation (2.23),... 

Majer and Wood (1994) used this procedure to extrapolate the apparent molar volume of NaCl solution between 548 and 710 K and pressures up to 38 MPa, by assuming that in Equation (2.27) the ion-pairs do not contribute to the excess volume, while the free ions contributions is given by the Pitzer model. Thus,... 

Since the amount of HCl is small as compared with the organic component, its apparent molar volume is approximated by the standard partial molar volume. The excess mixing term, 5, is ignored in the calculation of the apparent partial molar volume of the major component having a common anion. 

The experimental quantities reported in the study publication are indicated in the 10th column density (d) differential density (solution density minus water density) (dd) solution molar volume (V) solution specific volume (Vs) apparent molar volume (Vf) solute infinite dilution partial molar volume (Vo), excess volume (Ve), volume of mixing (Vm), compressibility factor (Z), virial coefficients (B, C, D, E), and soimd velocity (sv). 

This series of papers contains an extensive array of correlated data on aqueous electrolyte solutions, much of It having been calculated using the system of equations given In paper I In this series. The contents of these papers have been summarized by Pitzer In a chapter in the book edited by Pytkowicz (see Item [123]). The data Include activity and osmotic coefficients, relative apparent molar enthalpies and heat capacities, excess Gibbs energies, entropies, heat capacities, volumes, and some equilibrium constants and enthalpies. Systems of Interest Include both binary solutions and multi-component mixtures. While most of the data pertain to 25 °C, the papers on sodium chloride, calcium chloride, and sodium carbonate cover the data at the temperatures for which experiments have been performed. Also see Items [48], [104], and [124]. 

The properties of a dissolved substance are described in terms of partial, apparent, and excess total or molar properties, so we begin by discussing these terms, using volume as an example. 

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