Partial molar volume of solute

A particularly simple case is shown in Figure 18.1, in which the volume is a linear function of the mole number of glycolamide in a kilogram of water. In this case, the partial molar volume of solute is constant and is equal to the slope of the line. The partial molar volume represents the effective volume of the solute in solution, that is, the increase in volume per mole of solute added. From Equation (9.27), written for the volume function. 

Fig. 8.1 Volume per mole as a function of the molar fraction x2 of solute 2 in a binary perfect solution and in an ideal dilute solution v2 = the unitary partial molar volume of solute 2 extrapolated to x2 — 1.

Thus, if the partial molar volume of solute in aqueous solution is greater than the molar volume of solid solute, an increase in pressure will increase the chemical potential of solute in solution relative to that in the solid phase solute will then leave the solution phase until a lower, equilibrium solubility is attained. Conversely, if the partial molar volume in the solution is less than that in the solid, the solubility will increase with pressure. 

Source of Data. There are only a few local density data, and partial molar volumes of solutes at infinite dilution are scarce as well. Only two systems could be identified for which data for the calculation of the correlation volume are available CO2 + naphthalene and CO2 + pyrene. The augmented local density data in these systems were taken from ref 24 and the partial molar volume of the solute at infinite dilution in CO2 + naphthalene system from ref 8. Because the partial molar volume of the solute at infinite dilution for the CO2 + pyrene system was not available, it was taken equal to that for the CO2 + phenanthrene. The density and compressibility of the pure SCR CO2 were taken from refs 1 and 24, respectively, and the solubilities of naphthalene and p)rene in SCR CO2 from refs 28 and 29, respectively. 

The use of SCB as media for diemical reactions has increased during the past few years, as discussed in the next sectioiL The large partial molar volumes of solutes near the critical point result in unusualty large volumes of activation and large variations of certain reaction rate constants and selectivities with pressure. The following section on rate processes desolbes relatively novel crystallization processes that have commercial promise and transport properties in SCFs. The last two sections disr a variety of food, pharmaceutical, and environmental applications and provide an in-depth treatment of the design of commercial plants. 

A procedure similar to that above described, i.e. the choice of hydrocarbon compounds as reference molecules in order to evaluate contemporaneously the effects connected to the formation of a cavity and to the hydrophobic hydration, was first applied to the partial molar volumes by Terasawa et al. (61). In this case, of course, in equation 2 the intrinsic volumes V, calculated according to Bondi (101), of the molecules are to be considered instead of surface areas and AX (R) identifies itself with Comparison of hydrophilic solutes with imaginary hydrocarbons with exactly the same dimension allows to deduce that the interaction water-hydrophilic centres produces a shrinkage a(Y) in the volume, f.i. the partial molar volume of solutes containing one hydroxyl group is lower by 4.3 ml mol than that of the hypothetical hydrocarbon with the same intrinsic volume. Some other values of the shrinkage in volume due to some polar centres are (in ml mol ) ... 

K° being the isothermal compressibility of the pure solvent. This equation will be used later to explain the observed behavior of the standard partial molar volume of solutes near the solvent critical point. 

In this section we will briefly summarize the models proposed to assess the standard partial molar volume of solute at high temperature and pressure. 

If the mixture is a binary mixture of A and B, and xb is small, we may treat the mixture as a dilute solution of solvent A and solute B. As xb approaches 0 in this solution, Fb approaches a certain limiting value that is the volume increase per amount of B mixed with a large amount of pure A. In the resulting mixture, each solute molecule is surrounded only by solvent molecules. We denote this limiting value of Fb by F, the partial molar volume of solute B at infinite dilution. 

The appropriate partial molar volume Vi is the molar volume V or V of the pure substance, or the partial molar volume of solute B at infinite dilution. 

However, these indicative criteria it is difficult to apply directly because the partial molar volumes of solutes at infinite dilution Vj (T) = Fj (m 0 T) are usually not specially accurate. They are determined at each temperature T, by an extrapolation of experimental densities in very dilute solutions, / —>0, and evidently then-second derivatives with regard to temperature are expected to be even less accurate. In order to overcome this difficulty, it was proposed by the author to change these criteria and apply them for finite, low concentrations of solute in water. It follows from Eq. (2.49) that... 

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