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. 29a-c. Effects of three parameters of the equation of states in the text, (a) With increasing a, the transition temperature decreases when p and the molar volume of solute are equal to zero, (b) with decreasing P, discontinuity increases when a and the molar volume of solute are equal to zero, and (c) with increasing v the swelling ratio decreases and the transition temperature slightly increases when a and p are equal to zero. 

In the event that the molar volumes of solute and solvent are not comparable, and the thermal agitation is not adequate to achieve maximum entropy of mixing, a nonideal entropy of mixing exists (Bustamante et al., 1989). Two equations that account for the nonideal entropy of mixing have been derived by considering the partial molal volurfiA,and the volume fraction, occupied by each solution component. The L rst was developed by Flory and Huggins (Hildebrand, 1949 Kertes, 1965) ... 

Strictly speaking, this holds only for both the solution and pure component under the vapor pressure of component i. However, because the molar volumes of solutions are small, the result is little changed at other pressures. 

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.

FIGURE 6.4 Plot of the predicted diffusion coefficients vs. the molar volumes of solutes along with the experimental data. [Graph reconstructed from data by Kuu et al. in Treatise on Controlled Drug Delivery, A. Kydonies (Ed.), Marcel Dekker, New York, 1992, p. 51.]... 

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. 

From Wilke-Chang correlation, D°AB=7.4xlO 8(tMB) TAlBVA - , where D°AB/cm l is mutual diffusion coefficient of solute A in solvent B, Mb /g-mok is molecular weight of solvent B, tib /cp is viscosity of solvent B, Va /cm3-mol is molar volume of solute A at its nomial boiling temperature, and is association factor of solvent B. 

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. 

Molar volume, m /mol Molar volume of solute, m /mol Molar volume of solvent, m /mol Partial molar volume of the /th component, m /mol Pressure, Pa... 

Tc, numbers of adsorbent sites occupied by the solute and solvent, respectively, and V and van der Waals molar volumes of solute and solvent, respectively Kf is the ratio of the equilibrium concentrations of the solute in the stationary and mobile phases at infinite dilution of the solute ... 

However, its value is negative because the molar volume of solution vl decreases with CO2 dissolution. So there is no expansion as such, inasmuch as the molar volume of the solution is mostly less than that of the pure solvent... 

It may be noted that the occurrence of a minimum value of the molar volume of the binary (solvent-C02) solution is due to the reduction of the partial molar volume of the solvent vi, which is the actual indicator for lowering its solvent power for the solid solute, rather than RTVE or RMVE per se (47). With increasing CO2 dissolution, the liquid molar volume of solution Vl or simply v decreases, since vl < vi- It passes through a minimum, when V = vi = V2, and then increases if vi > V2, as follows ... 

It may be noted that even in the case of a system comprising a solvent and a less dense antisolvent (e.g., ethanol-C02), that is, for vi > V2, the liquid molar volume of solution v first marginally decreases with Xi and then exceeds V2 at a high value of Xi. That is, a minimum in the molar volume occurs where V = vi = V2. However this may not be sharp at all. Even for a system in which the organic liquid solvent is lighter than CO2 (e.g., hexane, where vi < V2), the minimum value in the molar volume is also not prominent rather, it flattens out as Xi approaches unity. As a consequence, RMVE is insensitive to CO2 mole fraction Xi for several systems RMVE was earlier suggested by... 

V = molar volume of solution at normal boiling point, cmVg-mole... 

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