Trouton

Trouton s rule The latent heat of vaportza lion (A/fvap) of liquid of molecular weight (A/) and boiling point (7 K) are related by the expression... 

Por most normal liquids the constant has a value of approx. 88JmolK" . Associated liquids show marked variations from this value. The Trouton constant is the molar entropy of vaporization. 

The quantity zoi will depend very much on whether adsorption sites are close enough for neighboring adsorbate molecules to develop their normal van der Waals attraction if, for example, zu is taken to be about one-fourth of the energy of vaporization [16], would be 2.5 for a liquid obeying Trouton s rule and at its normal boiling point. The critical pressure P, that is, the pressure corresponding to 0 = 0.5 with 0 = 4, will depend on both Q and T. A way of expressing this follows, with the use of the definitions of Eqs. XVII-42 and XVII-43 [17] ... 

Enthalpy of Vaporization (or Sublimation) When the pressure of the vapor in equilibrium with a liquid reaches 1 atm, the liquid boils and is completely converted to vapor on absorption of the enthalpy of vaporization ISHv at the normal boiling point T. A rough empirical relationship between the normal boiling point and the enthalpy of vaporization (Trouton s rule) is ... 

A great many liquids have entropies of vaporization at the normal boiling point in the vicinity of this value (see benzene above), a generalization known as Trouton s rule. Our interest is clearly not in evaporation, but in the elongation of elastomers. In the next section we shall apply Eq. (3.21) to the stretching process for a statistical—and therefore molecular—picture of elasticity. 

Troubleshooting Trouton constant Troxerutin [7085-55-4] Troysan 174 Troysan 192 True color holograms TrueType Truex process Truncatella sp. Truscottite [12425-42-2] Truxal Trycol... 

Enthalpies of vaporization, at the normal boiling point, T, can be estimated roughly with the simple rule of Pictet and Trouton (19) which... 

It is equivalent to say that entropy of vaporization is a constant value for non-associating Hquids. Associating Hquids, eg, ammonia, water, methanol, and ethanol, do not obey the rule of Pictet and Trouton. Despite its simplicity, the Pictet-Trouton view of Hquid vaporization (19) is an exceUent example of the many rules of thumb that have been useful aids in engineering calculations for decades (5,7,8,9,21). However, proper appHcation requires an understanding of the physical reasoning behind each rule. 

This rule was published by Trouton it appears to have been... 

By analogy with Trouton s rule we may expect that ... 

Transition, 19, 309, 461, 487 Trevelyan rocker, 25 Triple point, 214, 252 Trouton s rule, 234 True equilibrium, 90... 

Table 7.1 lists the standard entropies of vaporization of a number of liquids. These and other data show a striking pattern many values are close to 85 J-K 1-mol h This observation is called Trouton s rule. The explanation of Trouton s rule is that approximately the same increase in positional disorder occurs when any liquid is converted into vapor, and so we can expect the... 

Self-Test 7.7A Use Trouton s rule to estimate the standard enthalpy of vaporization of liquid bromine, which boils at 59°C. 

The normal boiling point of methanol is lower than predicted by Trouton s rule. Provide a molecular interpretation for this observation. 

Trouton s rule The empirical observation that the entropy of vaporization at the boiling point (the enthalpy of vaporization divided by the boiling temperature) is approximately 85 J-K—1 -mol 1 for many liquids. 

According to Trouton s rule, the entropy of vaporization of an organic liquid is a constant of approximately 85 J-mol 1 -K 1. The relationship between entropy of fusion, enthalpy of fusion, and melting point is given by... 

ASfus° = 9.79 J-K for Na ASfus° = 7.12 J-K. These numbers are reasonably close but clearly much smaller than the value associated with Trouton s rule. 

After evaporating the solvents and hydrogen halides the free acids can be purified by fractional distillation in vacuo. It was not possible to isolate the acid with X = J (7). The high value of the Trouton constant (25.1 cal/Mol °K) (7) seems to indicate, that H[P02FC1] and H[P02pBr] as well are associated over hydrogen bridges. 

The ratio of extensional viscosity r e to shear viscosity r s is known as the Trouton ratio, which is three for Newtonian fluids in uniaxial extension and larger than three for non-Newtonian fluids. For a viscoelastic fluid such as a polymer in solution, the uniaxial extensional viscosity characterizes the resistance of the fluid... 

A very rough estimate can be obtained from Trouton s rule (Trouton, 1884), one of the oldest prediction methods. 

Oscillatory shear experiments are the preferred method to study the rheological behavior due to particle interactions because they directly probe these interactions without the influence of the external flow field as encountered in steady shear experiments. However, phenomena that arise due to the external flow, such as shear thickening, can only be investigated in steady shear experiments. Additionally, the analysis is complicated by the different response of the material to shear and extensional flow. For example, very strong deviations from Trouton s ratio (extensional viscosity is three times the shear viscosity) were found for suspensions [113]. 

As in PP-based nanocomposite systems, the extended Trouton rule, 3r 0 (y t) = r E (so t), also does not hold for PLANC melts, in contrast to the melt of pure polymers. These results indicate that in the case of P LANC, the flow induced internal structural changes also occur in elongation flow [48], but the changes are quite different in shear flow. The strong rheopexy observed in the shear measurements for the PLA-based nanocomposite at very slow shear rate reflects the fact that the shear-induced structural change involved a process with an extremely long relaxation time. 

As was described in Chapter 6, the entropy of vaporization is a worthwhile piece of evidence in studying the association that occurs in liquids and vapors. In the case of [A1(C2H5)3]2, the entropy of vaporization (176.6 J mol-1 KT1) is almost exactly twice the value of 88Jmol-1K-1 predicted by Trouton s rule,... 

This indicates that in the process of vaporization 1 mole of liquid is converted into 2 moles of vapor. Therefore, we conclude that [Al(C2ff5)3]2 dimers are present in the liquid, but the vapor consists of monomeric Al(C2ff5)3 units. Examination of the data for [Al(Cff3)3]2 shows an entropy of vaporization of 112.61 mol 11<, which is greater than the value of 881 mol-1 K 1 predicted by Trouton s rule, but it is lower than twice the value. This value could be interpreted as corresponding to a liquid that is only partially dimerized being converted completely into monomer during vaporization. 

---