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Hildebrand rule

HILDEBRAND RULE. The entropy of vaporization, i.e.. the ratio of the heal of vaporization to the temperature at which it occurs, is a constant for many substances if it is determined at the same molal concentration of vapor for each substance. [Pg.777]

Finally we mention that the free-volume concept leads to an interpretation of the Trouton and Hildebrand rules. ] ... [Pg.200]

The mixture cohesive energy density, coh-m> was not to be obtained from some mixture equation of state but rather from the pure-component cohesive energy densities via appropriate mixing rules. Scatchard and Hildebrand chose a quadratic expression in volume fractions (rather than the usual mole fractions) for coh-m arid used the traditional geometric mean mixing rule for the cross constant ... [Pg.50]

Deviations from idealized behaviours (e.g. ideal gas laws, ideal solution laws, Trouton s or Hildebrand s rule, etc,). [Pg.556]

References Van t Hoff, Bildung und Spaltung von Doppelsalzen (1897) van t Hoff, Zur Bildung der Ozeanischen Salzablagerung, I (1905), II, (1909) Findlay, The Phase Rule (1927) Hildebrand, J. Ind. Eng. Chem., 10, 96 (1918) Stewart, Some Physico-chemical Themes, Chap. IV (1922). [Pg.109]

As already mentioned, interactions between unlike species are generally unfavorable. This observation is, in fact, the basis for the rule of thumb that like dissolves like. This rule is obviously very qualitative, but it has now been sucessfully extended to provide a quantitative basis for finding potential solvents for a polymer. In the theory of Hildebrand, it is acknowledged that AHiis is almost certainly going to be positive. The goal is then to find a means to make AHiis as small as possible. Specifically, it is given by the equation... [Pg.30]

The properties of the stationary phase manifest themselves in the activity coefficient in eqn.(3.6). A very simple expression for the activity coefficient can be obtained from the concept of solubility parameters (see section 2.3.1). This expression can be seen as a special form of Hildebrand s regular mixing rule, and it reads [303]. [Pg.40]

As a conclusion from the Hildebrand/Trouton Rule, the definition of a standard vapor phase in a standard state with a well known amount of disorder can be made. This definition can be used as a starting point for modeling diffusion coefficients of gases and liquids. [Pg.166]

JK mol-1 the value V°L = 0.91 cm3mol is obtained. An interpretation of the Hildebrand/Trouton Rule is that this free volume, V°L, allows for the freedom of movement of molecules (particles) necessary for the liquid state at the temperature Th. The explanation of the constant entropy of evaporation is that it takes into account only the translational entropy of the vapor and the liquid. It has to be pointed out that V°L does not represent the real molar volume of a liquid, but designates only a fraction of the corresponding molar volume of an ideal gas Vy derived from the entropy of evaporation. The real molar volume VL of the liquid contains in addition the molar volume occupied by the molecules V0. As a result the following relations are valid VL -V°L + V0 and Vc=Vq + V0. However, while V] < V0 and VL is practically independent of the pressure, V0 VaG in the gaseous phase. Only in the critical phase does VCIVL = 1 and the entropy difference between the two phases vanishes. [Pg.166]

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. [Pg.12]

There are many parameters that have been used to describe the attractive forces (dispersive, dipolar and hydrogen bonding) present within a solvent or liquid. However, Hildebrand s solubility parameter (8) is probably the most commonly used. In general, two liquids are miscible if the difference in 8 is less than 3.4 units. Also, if a solid e.g. a polymer) has a 8 similar to the solvent, it will dissolve. However, there are exceptions to this rule especially with polar solvents and solutes. Therefore, it is often worth testing solubility or solvent miscibility on a small scale even if data are available. [Pg.16]

Rodebush, from statistical considerations and Hildebrand s modification of Trouton s rule ( 14.VIIIL), deduced the rather curious formula ... [Pg.270]

Besides Trouton s rule we must also mention the modification introduced by Hildebrand, who suggested that the entropies of vaporization should be taken not at the boiling point, but at a temperature such that the concentration c=pjRT) in the vapour phase is a constant. In general, Hildebrand s rule holds more accurately than Trouton s rule. It should be noted, however, that neither of these rules follows from the law of corresponding states, according to which the entropies should be the same at corresponding temperatures, that is to say for a definite value of the ratio T/Tc- ... [Pg.198]

The second rule is illustrated by the following figures given by Hildebrand. [Pg.358]

Following the introduction of the Hildebrand model, the topic of solubility parameters has been extensively discussed (Hildebrand and Scott, 1962 Hildebrand et al., 1970 Kumar and Prausnitz, 1975 Barton, 1983), and values of S can be found in these reference works. As a general rule, compounds having stronger London forces will be characterized by larger solubility parameters values. [Pg.13]

Hildebrand and Scott used the geometric mean rule to describe the interaction between molecules of two unlike species to arrive at the total solubility parameter. Strictly speaking, this was valid for nonpolar type molecules only. The fact that Equation 10.4 has produced hundreds of satisfactory correlations of solubility, swelling, permeation, surface phenomena, etc., confirms that the geometric mean rule is likewise applicable to molecules engaging in permanent dipole-permanent dipole and hydrogen bonding interactions as well. [Pg.543]

Toluton-Hildebrand s empirical rule indicates that the boiling points (K) linearly relate to the latent heat of vaporization [1, 11]. Thus the intermolecular attraction energy needs to be reconsidered for a better understanding of the boiling point, especially of fluorinated organic molecules. [Pg.3]

Trouton s rule fails for associated liquids such as water, alcohols, and amines. It also fails for substances with boiling points of 150 K or below. Hildebrand s rule, which we describe later, includes these low-boiling substances, but not associated liquids. [Pg.174]


See other pages where Hildebrand rule is mentioned: [Pg.9]    [Pg.474]    [Pg.9]    [Pg.474]    [Pg.52]    [Pg.175]    [Pg.92]    [Pg.13]    [Pg.13]    [Pg.24]    [Pg.166]    [Pg.72]    [Pg.19]    [Pg.351]    [Pg.365]    [Pg.80]    [Pg.516]    [Pg.232]    [Pg.199]    [Pg.162]    [Pg.254]    [Pg.365]    [Pg.106]    [Pg.109]    [Pg.211]    [Pg.644]    [Pg.446]    [Pg.276]   
See also in sourсe #XX -- [ Pg.777 ]




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