Hildebrand’s rule

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

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- ... 

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. 

Boiling point. Hildebrand s rule. Another convenient method is based on the empirical relationship which relates AHp at 25°C with the boihng point, T, of non-polar liquids ... 

Solubility parameters have also been evaluated by Hildebrand s rule [10] that entropies of vaporization for normal liquids are the same when evaluated at temperatures where the vapors have equal molal volumes. It was argued that AfT P depends only on the boiling temperature. 

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]. 

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. 

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. 

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

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. 

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. 

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