Page 232 - Physical Chemistry

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At low T, the H term dominates and the liquid is more stable than the gas. At high Section 7.2
m
T, the T S term dominates and the gas is more stable. At low pressures, the in- One-Component Phase Equilibrium
m
crease of S with decreasing P (and increasing V ) makes the gas more stable than
m,gas m
the liquid.
vap H m /(kJ/mol)
Enthalpies and Entropies of Phase Changes
A phase change at constant T and P is generally accompanied by an enthalpy change,
H 2 O
often called the (latent) heat of the transition. (Certain special phase changes have
H 0; see Sec. 7.5.) One has enthalpies or heats of fusion (solid → liquid), sub-
limation (solid → gas), vaporization (liquid → gas), and transition (solid → solid—
see Sec. 7.4), symbolized by H, H, H, and H.
fus sub vap trs
Figure 7.1 shows that fusion, sublimation, and vaporization equilibria each exist
over a range of T (and P). H values for these processes change as the temperature of
the phase equilibrium changes. For example, H of vaporization of water for points
m
along the liquid–vapor equilibrium line AC in Fig. 7.1 is plotted in Fig. 7.4 as a func-
tion of the liquid–vapor equilibrium temperature. Note the rapid drop in H as the
vap m
critical temperature 374°C is approached.
We have H U P V, where usually P V V U. The U
vap vap vap vap vap vap
term is the difference between intermolecular interaction energies of the gas and liq-
uid: U U U . If P is low or moderate (well below the critical-
vap intermol,gas intermol,liq
point pressure), then U 0 and H U U . Figure 7.4
m,intermol,gas vap m vap m m,intermol,liq
Therefore H is a measure of the strength of intermolecular interactions in the liq-
vap m Molar enthalpy of vaporization of
uid. For substances that are liquids at room temperature, H values at the normal
vap m liquid water versus temperature.
boiling point run 20 to 50 kJ/mol. Each molecule in a liquid interacts with several other At the critical temperature 374°C,
molecules, so the molar energy for interaction between two molecules is substantially H becomes zero.
vap
less than H . For example, the main interaction between H O molecules is hydro-
vap m 2
gen bonding. If we assume that at 0°C each H atom in H O(l) participates in a hydro-
2
gen bond, then there are twice as many H bonds as H O molecules, and the 45-kJ/mol
2
H value indicates a 22-kJ/mol energy for each H bond. H values run substan-
vap m vap m
tially less than chemical-bond energies, which are 150 to 800 kJ/mol (Table 19.1).
An approximate rule for relating enthalpies and entropies of liquids to those of
gases is Trouton’s rule, which states that S for vaporization of a liquid at its
vap m,nbp
1
normal boiling point (nbp) is roughly 10 R:
2
1
S
¢ vap m,nbp ¢ vap H m,nbp >T nbp 10 R 21 cal>1mol K2 87 J>1mol K2
2
Trouton’s rule fails for highly polar liquids (especially hydrogen-bonded liquids) and
for liquids boiling below 150 K or above 1000 K (see Table 7.1). The accuracy of
Trouton’s rule can be improved substantially by taking
S
¢ vap m,nbp 4.5R R ln 1T nbp >K2 (7.12)
For T 400 K, Eq. (7.12) gives S 4.5R R ln 400 10.5R, which is
nbp vap m,nbp
Trouton’s rule. Equation (7.12) has been discovered several times by various workers
and is the Trouton–Hildebrand–Everett rule. See L. K. Nash, J. Chem. Educ., 61, 981
(1984) for its history. The physical content of Eq. (7.12) is that S is approxi-
vap m
mately the same for nonassociated liquids when they are evaporated to the same molar
volume in the gas phase. The R ln (T /K) term corrects for different molar volumes
nbp
of the gases at the different boiling points; see Prob. 7.20.
Table 7.1 gives S and H data for fusion (fus) at the normal melting point
m m
(nmp) and vaporization at the normal boiling point. The listed values of S pre-
vap m,nbp
dicted by the Trouton–Hildebrand–Everett (THE) rule indicate that this rule works
well for liquids boiling at low, moderate, and high temperatures but fails for hydrogen-
bonded liquids. As intermolecular attractions increase, both H and T increase.
vap m nbp