Trouton entropy

A topic of abiding interest is the issue of characterizing the order in liquids which may be defined as the entropy deficit due to preferential orientations of molecular multipoles relative to random orientations (orientational order) and nonuniformly directed intermolecular forces (positional order). Phenomenologically, two criteria are often claimed to be relevant for deciding whether or not a liquid is to be viewed as ordered the Trouton entropy of vaporization or Trouton quotient and the Kirkwood correlation factor gK. Strictly speaking, however, both are of limited relevance to the issue. 

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. 

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. 

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. 

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... 

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... 

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. 

Trouton s rule states that for most normal liquids the entropy of vaporization per mole 21 e.u. By a normal liquid, we mean which is not associated. In general association in the liquid state may be expected when intermolecular forces of a dominant type operate. Dipole moments, hydrogen bonding etc., lead to this situation. Abnormally high boiling points are a consequence of molecular association in the liquid state. 

The degree of association of molecules in a liquid can be estimated by means of its Trouton constant (Nash, 1984). At the normal boiling temperature, Tpp, vaporization proceeds with standard molar changes of enthalpy, AH%, and entropy, AS°bp, from which Trouton s rule is derived as given in eqn. 3.10. 

The entropy, Spontaneous vs non-spontaneous, Reversible and irreversible processes, Calculation of entropy changes (Isothermal, isobaric, isochoric, adiabatic), Phase changes at equilibrium, Trouton s rule, Calculation for irreversible processes... 

Trouton s Rule of Constant Entropy of Vaporization at the Boiling Point... 

This A p-S Tt,) value is typical for many other organic compounds that boil at very different temperatures (Table 4.2). In fact, long ago, Trouton (1884) recognized that the entropy of vaporization at the boiling point for many apolar and monopolar substances is more or less constant between 85 and 90 J moT1 K 1. Note that the constancy of A S Ti,) implies that there must be a close relationship between AmpH,(Tb) and Tb. 

This expression reflects a weak relationship between the apolar or monopolar compound boiling temperature and entropy of vaporization, but substantially verifies Trouton s empirical observation. 

It is of some interest to apply Trouton s rule (entropy of vaporization at the boiling point is a constant) to the above data. Unfortunately, boiling points are known only for nitric acid and some of the aliphatic nitrates. Their Trouton constants (AH p/Tbp) are 20.2 and ca 22.8 entropy units, respectively. Thus they straddle the normal Trouton constant of 21 eu. This observation, coupled with the observed constancy of the specific heat of vaporization, suggests that intermolecular bonding in nitrate esters may be relatively weak, or at least consistent... 

Associated Liquids. The description given above is adequate only for liquids composed of spherically symmetric molecules or molecules that are nearly so. These constitute ihe so-called normal liquids, which obey reasonably well the law of corresponding stales, for which the entropy ul vaporization at the boiling point Iras ihe Trouton s rule value of approximately 21 cal/deg. For molecules containing large dipole moments, or those forming mutual hydrogen bonds, the concept of the probability... 

Table 4.1 The structuredness of solvents, measured by their Trouton s constant, the entropy deficit, the dipole orientation correlation coefficient, and the heat capacity density...

Of particular interest are changes in enthalpy, such as the heat of fusion, Af us//, and the heat of vaporization, Avap//, as well as the corresponding changes of entropy. A useful observation, discussed in Chapter 3, is Trouton s rule, that entropies of vaporization are often 85 J K mol. 

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. 

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