Page 267 - Physical Chemistry

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Chapter 8
Real Gases

Figure 8.4
Condensation of a gas. The system
is surrounded by a constant-T bath
(not shown).

R S T U W Y

gas liquefies until at point W we have all liquid. See Fig. 8.4. For all points between
S and W on the isotherm, two phases are present. Moreover, the gas pressure above
the liquid (its vapor pressure) remains constant for all points between S and W. (The
terms saturated vapor and saturated liquid refer to a gas and liquid in equilibrium
with each other; from S to W, the vapor and liquid phases are saturated.) Going from
W to Y by pushing in the piston still further, we observe a steep increase in pressure
with a small decrease in volume; liquids are relatively incompressible. The isotherm
RSTUWY in Fig. 8.3 corresponds to the vertical line RSY in Fig. 7.1.
Above the critical temperature (374°C for water) no amount of compression will
cause the separation out of a liquid phase in equilibrium with the gas. As we approach
the critical isotherm from below, the length of the horizontal portion of an isotherm
where liquid and gas coexist decreases until it reaches zero at the critical point. The
molar volumes of saturated liquid and gas at 300°C are given by the points W and S.
As T is increased, the difference between molar volumes of saturated liquid and gas
decreases, becoming zero at the critical point (Fig. 7.2).
The pressure, temperature, and molar volume at the critical point are the critical
pressureP ,thecriticaltemperatureT ,andthecritical(molar)volumeV .Table8.1
c c m,c
lists some data.
For most substances, T is roughly 1.6 times the absolute temperature T of the
c nbp
normal boiling point: T 1.6T . Also, V is usually about 2.7 times the normal-
c nbp m,c
boiling-point molar volume V . P is typically 10 to 100 atm. Above T , the molec-
m,nbp c c
3
ular kinetic energy (whose average value is kT per molecule) is large enough to over-
2
come the forces of intermolecular attraction, and no amount of pressure will liquefy
the gas. At T , the fraction of molecules having sufficient kinetic energy to escape
nbp
from intermolecular attractions is large enough to make the vapor pressure equal to
1 atm. Both T and T are determined by intermolecular forces, so T and T are
c nbp c nbp
correlated.
Usually one thinks of converting a gas to a liquid by a process that involves a sud-
den change in density between gas and liquid, so that we go through a two-phase
region in the liquefaction process. For example, for the isotherm RSTUWY in Fig. 8.3,
two phases are present for points between S and W: a gas phase of molar volume V
mS
and a liquid phase of molar volume V . (Because T and P are constant along SW, the
mW
gas and liquid molar volumes each remain constant along SW. The actual amounts of
gas and liquid change in going from S to W, so the actual volumes of gas and liquid
vary along SW.) Since V V , the gas density is less than the liquid density.
mS mW
However, as noted in Sec. 7.2, one can change a gas into a liquid by a process in which
there is always present only a single phase whose density shows no discontinuous
changes. For example, in Fig. 8.3, we could go vertically from R to G, then isother-
mally to H, and finally vertically to Y. We end up with a liquid at Y but, during the
process RGHY, the system’s properties vary continuously and there is no point at
which we could say that the system changes from gas to liquid.