Solvents cohesive pressure

The cohesive pressure (c) of a solvent, otherwise known as cohesive energy density (CED), is a measure of the attractive forces acting in a liquid, including dispersive, dipolar and H-bonding contributions, and is related to the energy of vaporization and the molar volume (Equation 1.1) ... 

Table 1.5 Cohesive pressures (c), Hildebrand s solubility parameter (5), and internal pressures (n) for a range of representative solvents [1, 2]...

As already mentioned, the cavity term corresponds to the endoeigic process of separating the solvent molecules to provide a suitably sized and shaped enclosure for the solute, and measures the work required for such a purpose. This term is related to the tightness or structuredness of solvents as caused by intermolecular solvent/solvent interactions. The association of solvent molecules in the liquid state in order to accommodate the solute molecules can be quantified by means of the surface area and texture of the solute that are related with the m coefficient and by the cohesive pressure of the solvent given by fl. 

As a cavity has to he opened in a solvent in order to introduce a solute, the strength of the solvent-solvent bonding will be a factor in determining solubility. The cohesive pressure, c, is defined by eqn. 3.1. 

The square root of the cohesive pressure c as defined in eqn. 3.11 has been termed the solubility parameter 5 by Hildebrand and Scott (1962) because of its value in correlating and predicting the solvency of solvents for nonelectrolyte solutes. Solvency is defined as the ability of solvents to dissolve a compound. A selection of 5-values is given in table 3.10. 

The square route of the cohesive pressure is termed Hildebrand s solubility parameter (5). Hildebrand observed that two liquids are miscible if the difference in 5 is less than 3.4 units, and this is a useful rule of thumb. However, it is worth mentioning that the inverse of this statement is not always correct, and that some solvents with differences larger than 3.4 are miscible. For example, water and ethanol have values for 5 of 47.9 and 26.0 MPa°-, respectively, but are miscible in all proportions. The values in the table are measured at 25 °C. In general, liquids become more miscible with one another as temperature increases, because the intermolecular forces are disrupted by vibrational motion, reducing the strength of the solvent-solvent interactions. Some solvents that are immiscible at room temperature may become miscible at higher temperature, a phenomenon used advantageously in multiphasic reactions. 

In this connection, two other physical solvent properties are important the cohesive pressure c (also called cohesive energy density) and the internal pressure r of a solvent [98-100, 175]. 

Table 3-2. Cohesive pressures, c, internal pressures, k, and their ratio n = njc for thirty organic solvents, arranged in order of decreasing n, that is, in order of increasing structuredness , at 20 °C [99, 154, 175].

The final limitation of the pure electrostatic theory is its inability to predict solvent effects for reactions involving isopolar transition states. Since no creation, destruction, or distribution of charge occurs on passing from the reactants to the activated complex of these reactions, their rates are expected to be solvent-independent. However, the observed rate constants usually vary with solvent, although the variations rarely exceed one order of magnitude [cf. Section 5.3.3). These solvent effects may be explained in terms of cohesive forces of a solvent acting on a solute, usually measured by the cohesive pressure of the solvent [cf. Section 5.4.2). 

In any solution reaction, cavities in the solvent must be created to accommodate reactants, activated complex, and products. Thus, the ease with which solvent molecules can be separated from each other to form these cavities is an important factor in solute solubility cf. Section 2.1). Furthermore, because solubility and reactivity are often related phenomena, the intermolecular forces between solvent molecules must also influence rates of reaction. The overall attractive forces between solvent molecules gives the solvent as a whole a cohesion which must be overcome before a cavity is created. The degree of cohesion may be estimated using the surface tension, but a more reliable estimate is obtained by considering the energy necessary to separate the solvent molecules. This is known as the cohesive pressure c (also called cohesive energy density) [228-... 

Values of c are calculated from experimentally determined enthalpies (heats) of vapourization of the solvent to a gas of zero pressure, AH, at a temperature T, as well as from the molecular mass M, the density of the solvent g, and the gas constant, R. The cohesive pressure characterizes the amount of energy needed to separate molecules of a Hquid and is therefore a measure of the attractive forces between solvent molecules. The cohesive pressure c is related to the internal pressure n, because cohesion is related to the pressure within a liquid cf. Eq. (3-6) in Section 3.2 for the precise definition of n. ... 

Since the internal pressure is actually defined in a slightly different way, values of internal pressure approach those of the cohesive pressure only for nonpolar and non-associated solvents (cf Table 3-2 in Section 3.2) [228-232, 237], Internal pressure is a measure of the instantaneous volume derivative of the cohesive pressure during isothermal expansion of a hquid (cf Eq. (3-6) in Section 3.2). Because of the experimental difficulty in obtaining real internal pressures, it is usual to refer to A Fv/ Fm as the internal pressure of a hquid. 

A reasonable assumption in some cases is that Fa = lA + Fb, thus the first term in Eq. (5-82) becomes zero. The second term is constant for all solvents if molar volumes and cohesion pressures of reactants and activated complex are the same in these solvents. Thus, under certain conditions, the third term is the most important. In gas-phase reactions, only the second term is left (8s = 0 for the gas phase). 

Fig. 5-8. Correlation oilgik/kf) [35] and the cohesive pressure <5 [238] in the Diels-Alder dimerization of cyclopentadiene at 40 °C (rate constants relative to acetone as slowest solvent) ...

Fig. 5-9. Correlation oi g kjkf) [167] and the cohesive pressure 5 [238] in the dissociation of 1-diphenylmethylene-4-triphenylmethyl-2,5-cyclohexadiene ( hexaphenylethane ) at 0 °C cf. Eq. (5-56) in Section 5.3.4 (rate constants relative to acetonitrile as slowest standard solvent) ...

The concept of cohesive pressure (or internal pressure) is useful only for reactions between neutral, nonpolar molecules in nonpolar solvents, because in these cases other properties of the solvents, such as the solvation capability or solvent polarity, are neglected. For reactions between dipolar molecules or ions, the solvents interact with reactants and activated complex by unspecific and specific solvation so strongly that the contribution of the cohesive pressure terms of Eq. (5-81) to In /r is a minor one. It should be mentioned that cohesive pressure or internal pressure are not measures of solvent polarity. Solvent polarity refiects the ability of a solvent to interact with a solute, whereas cohesive pressure, as a structural parameter, represents the energy required to create a hole in a particular solvent to accommodate a solute molecule. Polarity and cohesive pressure are therefore complementary terms, and rates of reaction will depend... 

An important measure of the total molecular cohesion per unit volume of liquid is the cohesive pressure c (also called cohesive energy density), which characterizes the energy associated with all the intermolecular solvent/solvent interactions in a mole of the solvent. The cohesive pressure is defined as the molar energy of vapourization to a gas at zero pressure, Af/y, per molar volume of the solvent, V, according to Eqs. (3-5) and (5-76) in Sections 3.2 and 5.4.2, respectively [93, 94]. The cohesive pressure c is related to the internal pressure n cf. Eq. (3-6) and Table 3-2 in Section 3.2. 

A. F. M. Barton Handbook of Solubility Parameters and other Cohesion Parameters, CRC Press, Boca Raton/Florida, 1983. [232] M. R. J. Dack The Importance of Solvent Internal Pressure... 

There are a plethora of physical constants that can be used to classify solvents key constants include melting and boiling points, viscosity, density, dipole moment, dielectric constant, specific conductivity, and cohesive pressure. The physical constant or constants that are considered most important really depend upon the application. For example, in a synthesis that involves conducting a reaction at elevated temperature, then boiling point may be the most important constant, however, if microwave heating is to be used then knowing the dielectric constant of the solvent is also essential.8,9... 

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