Enthalpy of vaporization relationships

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 ... 

Integrate the relationship given in CTQ 9d and show how to determine the enthalpy of vaporization of a liquid experimentally. 

Selected compound-specific functions, property-temperature-property relationships, or structure-temperature-property relationships are supplied and discussed in this book for density (Section 3.5), refractive index (Section 4.5), surface tension (Section 5.4), viscosity (Section 6.4), vapor pressure (Section 7.4), enthalpy of vaporization (Section 8.5), aqueous solubility (Section 11.8), and air-water partition coefficients (Section 12.5). 

It is, therefore, not surprising that there exists a definite relationship between Aand the enthalpy of vaporization, Av H, the former constituting a fraction between 0.2 and 0.3 of the latter, as is readily obtained from the data in Tables 3.1 and 3.9. The pressure dependence of the viscosity is also closely related to the free volume of the solvent. The fluidity (O = l/r ) is proportional to the ratio between the free and the occupied volume, the former, as mentioned above, being the difference between the actual molar volume and the intrinsic molar volume (Tables 3.1 and 3. 4) (Hildebrand 1978). In fact, the logarithm of the viscosity of liquids was found (Marcus 1998) to be described well for some 300 liquids by the empirical relationship ... 

Verification of this relationship in GC is provided by Figure 8.19, in which the log of the net retention volume is plotted versus 1 IT in accordance with Eq. (11). The slope of each line is proportional to that analyte s enthalpy of vaporization, and the fact that straight lines are obtained indicates that the enthalpy is constant as assumed. 

In the meantime, according to Trouton s rule, there is a simple relationship between the enthalpy of vaporization and the normal boiling temperature, 7], Avap7//10.5/f. If we substitute it into the above correlation, then ... 

The boiling point of COBrF, estimated from Fig. 16.6, is -20.3 C. The enthalpy of vaporization, derivable from these data, has not been reported and a plot of the data in a form suitable for the determination of this quantity is provided in Fig. 16.6. From the relationship given in Equation (16.11), and the slope of the line provided in Fig. 16.6, is calculated to be 22.9 t 0.6 kj mol from which the value of the Trouton constant is estimated to be 91 2 J mol" K [656a]. 

This relationship shows that it is possible to calculate the isosteric enthalpy of adsorption from calorimetric experiments. In summary, it has been shown how the enthalpies of adsorption are obtained either calorimetrically or from the dependence of the isotherms on temperature. Although the definitions given above for the different enthalpies of adsorption are rigorous, it is necessary to show that they exhibit the same properties as the enthalpy of vaporization, i.e., the heat necessary to vaporize one mole of liquid at constant pressure and using a reversible and isothermal process. Moreover, only the isosteric enthalpy is related in a simple way to the heat required in a process that is reversible and isothermic. Suppose that 8 moles of adsorbate are transferred to the gas phase at constant temperature and pressure. According to the first law of thermodynamics ... 

Puri, S., Chickos, J.S. and Welsh, W.J. (2002b) Three-dimensional quantitative structure-property relationship (3D-QSPR) models for prediction of thermodynamic properties of polychlorinated biphenyls (PCBs) enthalpy of vaporization. 

Since the enthalpy of vaporization depends linearly on the number of carbons to a high degree of accuracy [6], it is fair to suggest benzene, toluene, ethylbenzene (and the isomeric xylenes), form a homologous series, at least with respect to this property. The set of compounds benzene, phenol, and the various benzene-diols wherein an increasing number of hydroxy substituents putatively defines a homologous series might also define a linear relationship. 

The entropy of vaporization has a simple relationship to the enthalpy of vaporization. We begin with eq. (4.8). which we apply across the tie line from saturated liquid to saturated vapor. Along this path Tis constant and Q = Affvap. Therefore,... 

Retention time in gas chromatography is related to a combination of retention and volatility, similar to solubility in liquid chromatography. Predicting volatility is as difficult as predicting solubility. Volatility has been explained as the enthalpy of vaporization (Avap f), and a method for predicting volatility has been proposed." If the A apH values are available, it may be possible to predict retention time. Unknown A apH values have been calculated from the relationship between the van der Waals volume and reference AyapH values. The values are summarized with the corresponding reference values in Table 1 of the Appendix (p. 278). Values of A apH have also been related to capacity ratios. The correlation coefficients were 0.896 and 0.852 ( = 48) for DBl and CPSilS columns, respectively, which appear to be acceptable correlation coefficients, except that the relationship for allq l alcohols deviated from those of other compounds as seen Figure 4.4. 

Figure 4.4 The relationship between log k (240 °C) and the enthalpy of vaporization (Avapff) on CPSilS.

The ratio MiRTVA p H is called the ebulliometric constant. For the determination of solvent activities from ebulliometric data, tabulated ebulliometric constants should not be used, however. On the other side, it is sometimes recommended to use reference solutes to establish an experimental relationship for the equipment in use, i.e., unprecise data for the enthalpy of vaporization or perhaps some non-equilibrium effects cancel out of the calculation. Enthalpies of vaporization are provided by several data collections, e.g., by Maj er and Svoboda, or through the DIPPR database. 

According to the vapor pressure curve P = P T), there is a unique pressure for each temperature where a vapor-liquid equilibrium for a pure substance is possible, as long as both temperature and pressure are below their critical values. Similarly, there is a functional relationship between the enthalpy of vaporization and the boiling temperature... 

The Clausius-Clapeyron equation gives a well-founded relationship between the enthalpy of vaporization and the vapor pressure curve. 

The Clausius-Clapeyron equation is an accurate relationship between vapor pressure and enthalpy of vaporization and widely used for the estimation of enthalpies of vaporization from vapor pressure data (see Section 3.2.3). 

Figure 9.1, a plot of the log of net retention volume versus l/T for a few typical solutes illustrates this relationship. Straight lines are obtained over a limited temperature range in accordance with our prediction based on equation 1. The slope of each line is proportional to that solute s enthalpy of vaporization and can be assumed to be constant over the temperature range shown. 

An alternative graphical method for handling binary mixtures is that of Ponchon and Savarit, and while more cumbersome to use than McCabe-Thiele, it dlows for variations in the molar latent heat of vaporization and thus removes the principal assumption of the McCabe-Thiele method. As basic information it requires not only a y -x equilibrium relationship but also data on enthalpy of vaporization as a function of composition, and, except for a few mixtures, such data are not readily available. 

The diagram refers to the enthalpy relationships of a completely miscible binary system at a constant pressure of 1 atm. The mole fraction of component B is plotted horizontally from left to right and the enthalpy of the mixture, relative to the pure components in chosen reference states, is plotted vertically. Curve CD represents the enthalpy of the liquid phase, at its boiling-point, as a fimction of composition. Curve EF represents the enthalpy of the vapour above the boiling liquid as a function of its own composition. (Thus CE and DF are the enthalpies of vaporization of A and B respectively.) OH and IJ are typical tie-lines, i.e. a boiling liquid of composition ( is in equilibrium with vapour of composition H,... 

What is the relationship between metallic bond strength and enthalpy of vaporization ... 

A relationship has been found by Marcus [28] between the viscosities of solvents and their relative free molar volumes, (V-V )IV = (1-V IV), on the one hand, and their molar enthalpies of vaporization, ATT, on the other. The former describes the space available for the movement of the solvent molecules and the latter measures the tighmess of the mutual binding of the molecules. These values have to be modified by the number of hydroxyl groups, pertinent to the hydrogen bonding in solvents containing such groups ... 

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