Multicomponent Equilibrium Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 61

TABLE 3.9
Thermodynamic Transfer Functions for Methane from Different
Solvents (A) to Solvent B (Water, W) at 298 K
Solvent A G i H i S i Δ (kJ/mol) Δ (kJ/mol) Δ (kJ/mol)

Cyclohexane 7.61 − 9.95 − 17.56

1,4-Dioxane 6.05 − 11.89 − 17.94

Methanol 6.68 − 7.97 − 14.65

Ethanol 6.72 − 8.18 − 14.90

1-Propanol 6.69 − 8.89 − 15.56

1-Butanol 6.57 − 7.14 − 13.72

1-Pentanol 6.48 − 8.35 − 14.85

Source: From Franks, F. 1983. Water . London, England: The Royal Society of Chemistry;
Ben Naim, A. 1980. Hydrophobic Interactions . NewYork: Plenum Press.

88 J/mol/K) for a variety of
compounds.Thisiscalled Trouton'srule .Theconstancyoftheentropyofvaporization
is because the standard boiling points of liquids are roughly equal fractions of their
critical temperatures. Most liquids behave alike not only at their critical temperatures
but also at equal fractions of their critical temperatures. Hence different liquids should
have about the same entropy of vaporization at their normal boiling points. Therefore,
we have a convenient way of estimating the molar heat of vaporization of a liquid
from

The entropy of vaporization Δ S v is nearly constant ( ≈

Δ

S v = Δ H v /T b =

88 J/mol/K. Since the molar enthalpy of vaporization is an
approximate measure of the intermolecular forces in the liquid, Kistiakowsky (1923)
obtained the following equation:

Δ S v = 36.6 + 8.3 ln T b . (3.39)

Notice from Table 3.9 that Trouton's rule fails for highly polar liquids and for liquids
that have T b < 150 K.
For a considerable number of compounds of environmental significance, partic-
ularly high molecular weight compounds, reliable vapor pressure measurements are
lacking. As a consequence, we have to resort to correlations with molecular and
structural parameters.
Using the Clausius-Clapeyron equation as the starting point and the constancy of
heat capacity, C p , and Trouton's rule, the following equation can be derived for the
vapor pressure of liquids, P i (Schwarzenbach, Gschwend, and Imboden, 1993):

19 1 8.5 ln T b

T

,

T b
T

ln P i = − + (3.40)

where P i is in atmospheres.