Entropy of evaporation

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. 

As shown in the previous section a common feature of all systems in the liquid state is their molar entropy of evaporation at similar particle densities at pressures with an order of magnitude of one bar. Taking this into account a reference temperature, Tr, will be selected for systems at a standard pressure, p° = 105 Pa = 1 bar, having the same molar entropy as for the pressure unit, p = 1 Pa at T = 2.98058 K. As can easily be verified, the same value of molar entropy and consequently the same degree of disorder results at p if a one hundred-fold value of the above T-value is used in Eq. (6-14). This value denoted as Tw = 298.058 K = Tr is used as the temperature reference value for the following model for diffusion coefficients. The coincidence of Tw with the standard temperature T = 298.15 K is pure chance. 

When the pressure/ is expressed in atmospheres, then at the boiling point 7 the pressure/ = i and thus C R = AHjTb = AS. In this last expression we meet the latent heat of evaporation at constant pressure, divided by the boiling point temperature on the absolute scale according to Trouton s rule this quotient has an approximately constant value actually about 22 for normal liquids. This means, therefore, that the entropy of evaporation (at i atm.) also amounts approximately to 22 cal/mole degree (alkali halides 24 cal/mole degree). 

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. 

Lennard-Jones and Devonshire, with the potential energy function —ar "+br" ( 41.VIIC) calculated the molar entropy of evaporation ... 

Postponing model interpretations until the next sections, let us reconsider the relative constancy of S". It is Interesting to note that a similar trend is observed in the molar entropy of evaporation, For all the liquids mentioned in fig. 

Intuitively, surface and interfacial tensions may be expected to be related to a number of physical characteristics of the liquid or the liquid-vapour transition. Two of these are the enthalpy and entropy of evaporation, discussed in sec. 2.9. Other parameters that come to mind are the molar volume V, the isothermal compressibility and the expansion coefficient. The combination of certain powers of such parameters and y sometimes leads to products with interesting properties, like temperature independence or additivity. Severed of such scaling rules have been proposed over the past century, mostly with limited quantitative success. A few of these wUl now be discussed. 

We notice that A s is simply the entropy of evaporation for p = l atm. and is identical with the standard entropy change (2lfS ). 

This may be simplified if we assume the entropies of evaporation from the solution to obey Trouton s rule, and put... 

Tellurium-Halogen Compounds.—Enthalpies and entropies of evaporation of TeCU and of sublimation of TeBr4 have been measured. Using the above data, the equilibrium constant of the reaction ... 

The rale of constant entropy of melting was first observed by Richards [40], and should be compared to the rale of constant entropy of evaporation of 90 J K mol" by simple liquids as proposed by Trouton (see Sects. 1.1 and 2.5.7). Both rales are helpful in developing an understanding of the differences of transition temperatures for different materials. A general application of Richards s rale requires, however. 

Pepekin s study of the thermodynamic properties of difluoramino and nitro compounds [74,75] included many organic difluoramines besides the products of electrophilic difluoramination cited above. Properties reported include heats of combustion, formation, and atomization, Clausius-Clapeyron equation parameters, and the enthalpies and entropies of evaporation and sublimation. This collection of properties allowed estimation of group additivity parameters for general calculations of thermodynamic properties of organic difluoramines, which were compared to those of corresponding nitro groups. 

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