Trouton relation

Combining Eqs. 3.1-31 and3.1-26, we obtain the so-called Trouton relation, which defines the Trouton viscosity (13). 

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... 

If we wish to know the enthalpy of formation of liquid Se2Cl2, we can estimate the enthalpy of condensation (perhaps from Trouton s rule [13] or by comparison with related sulfur compounds) and can add it to the value of A// , obtained in Equation (4.49). 

Vapour pressure. Vapour pressure (vp) of non associated liquids can be related to temperature (T) using the impirical equation of McGowan (35) which is based on a combination of Trouton s rule and the Clapeyron-Clausius equation as follows -... 

Repulsive forces determine, for example, the melting point of a solid. Whenever the packing is efficient, the melting point tends to be high. The attractive forces, on the other hand, govern the heat of vaporization and therefore the boiling point. Trouton s rule, which relates the normal boiling point of a liquid to its heat of vaporization, is a manifestation of this relation. 

For incompressible materials, Trouton s coefficient can be related to X = 3tj, so that... 

Occasionally one has available a single vapor pressure point—for example, the normal boiling point—but wishes approximate vapor pressures at other temperatures. Some of the simplest schemes are based on Eq. (2). If the compound is not likely to self-associate through hydrogen bonds or other specific interactions, the Trouton constant (Mfvap/Tboinng) is approximately 21 cal/mol°. Substitution of this value into Eq. (2) shows that the vapor pressure is related to normal boiling point Tb by Eq. (13). 

Trouton and Eysenck (1961) have pointed out that psychedelic experience is influenced not only by factors related to drug administration, but by personality, physiology, set, and setting. In their account, they also mention "suggestion" and "reinforcement of responses by the experimenter," which suggests the importance of language in determining how a subject reacts. 

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. 

It should, however, be borne in mind that the theoretical argument can in fact tell us something about the heat of evaporation but not about the boiling point itself, except when the entropy of evaporation (AH/T = Trouton constant, p. 88) shows no differences for related compounds. This is almost correct in the above-mentioned case of cis- and trans-dichloroethylene, namely 21.64 and 21.52 cal/mol. deg., respectively. 

A relation between the parachor and zero-point molar volume Fq was proposed 3 Eucken suggested [P]=2-9Fq. De Carvalho, by assuming that the internal heat of evaporation is proportional to the free molar surface energy ( 6.VIIIG), La=kE and Trouton s rule ( 14.VIII L), LjTb= % found orF2/3/rj=const, If a is in dynes/cm. and F in cm. ... 

Herz,3 from the equation Ma jTb=l l6xlO and Trouton s equation ( 14.VIII L), MlJTb=2l, found a /l =0-0552, and from the relations PcTblQcTc—0 66pclQc=h> he found a =0-0552pcTblQcTc=0-0364pelQc. 

This relation was found by some obscure reasoning by Pictet, and was stated as an empirical result by Trouton it is generally called Troutori s rule. The average value of the constant ( Trouton coefficient ) for normal liquids... 

Kireev said Trouton s rule applies to each component of mixtures of normal liquids if p//mj=const., where p/=partial pr sure, w/=fractional amount. The Trouton coefficient MlJTb—Ks is related to the critical point coefficient S =0-447 log r6+2-562 by the equation 5=0-195 Ki/i -t-l-71. 

The value of the Trouton s constant for OsOFg, 23-4 e.u. is similar to values reported for related compounds, The following values for hexafluorides WF, 21-8, ReFg 22-3. OsFg 210, IrF, 22-6, and PtF, 20-6 e.u., show that OsOFg is not sigi cantly more associated in the liquid phase, than is, for example, IrF,. It is possible that all of these values are equivalent within the experimental error. 

By applying the Clapeyron equation and Trouton s rule to an ideal binary mixture, Rose derived the relation... 

Thomas presented an interesting paper (2021) relating H bonding and viscosity, and he was quick to point out the approximate nature of his treatment. He combined a modification of Andrade s viscosity equation with a relation between vapor pressure and latent heat of vaporization and still another function relating the heat of H bonding with the degree of association. From these he calculated an approximate heat of vaporization and compared it to a nonassociated value from a modified Trouton rule equation. The difference is called... 

Dimethylformamide and related solvents, such as dimethyl sulphoxide, have high Trouton constants and high dipole moments (Table 1, and... 

Wilson, G.M., Interpretation of Trouton s law in relation to equation of state properties. Equations of State, Theories and Applications, American Chemical Society Symposium Series 300, Washington, D.C, 1986. 

As a general rule the value of the chemical constant is about 3 Another mteresting relation is that known as Troutons Law According to this law the molecular latent heat of vaporisation divided by the boiling point2 is a constant The limits of applicability will be seen from the following table (Lougumine s data, Wmkelmann s Handbuch, vol 111) —... 

The relations between chemical equilibrium and Trouton s coefficient are therefore unmistakable, and may be employed with advantage. We must not, however, lose sight of the fact that the equations with which we are dealing are only approximately true. The exact treatment of the problem, which depends on the use of the specific heats of gases down to very low temperatures, will be learned in Chapters XIII and XIV, where it will also be seen that these specific heats are mostly inaccessible to experiment at the present time. This is the reason why I have thought it necessary to devote so much space to the treatment of the approximation formula. 

The problem is to be attacked in quite another manner when our concern is simply to calculate chemical equilibria in this case it will of course be best to derive the chemical constants from actual chemical equilibria. I have naturally worked in both directions in my numerous calculations, of which I have published, of course, only a small fraction. In my publications I have laid less stress on the accurate calculation of equilibria than on the remarkable fact, that quantities like Trouton s coefficient, and in particular certain coefficients in my vapour-pressure formula, bore a dose relation to chemical equilibria. Those who are not very practised in thermodynamical calculations will hardly have recognized this distinction, and for this reason a repetition of the calculation of the ammonia equilibrium will be desirable. 

If the molar entropy of vaporization can be treated as a constant, as Trouton s rule suggests, then the relative elevation of the boiling point, AT/T, is universally related to the mole fraction X2 according to Eq. (6.85). 

Prom the comparison of Eqs. (5.65) and (5.73), we see that the tensile viscosity is three times the shear viscosity. This is Trouton s well-known rule, which is analogous to the relation of Young s modulus being three times the shear modulus for an isotropic incompressible material. 

The definition of the Trouton ratio given by equation (1.26) is somewhat ambiguous, since it depends on both e and y, and some convention must therefore be adopted to relate the strain rates in extension and shear. To remove this ambiguity and at the sametime to provide a convenient estimate of behaviom in extension, Jones etal. [1987] proposed the following definition of the Trouton ratio ... 

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