Critical Point

1
Critical Point Consider what happens when the
volume of 1.0 mole of water vapor initially at 10
torr is decreased at a constant temperature of 25
oC.
The pressure of the vapor will continue to rise
until the equilibrium vapor pressure of water of
24 torr at 25 oC is reached and liquid water
begins to condense from the vapor. This behavior
can be followed on a plot of pressure versus
molar volume or PV diagram
How are molar volume and density related?
2
Continued decreasing of the volume results in the
condensation of more liquid water
What happens to the pressure of the water vapor,
as the volume is decreased while both liquid and
vapor phases are present? Both the volumes of
the vapor and the liquid phases can be
represented on the PV diagram
Notice how much smaller the molar volume of the
liquid phase is compared to the molar volume of
the vapor.
3
As the volume is further decreased vapor
continues to condense, until eventually a point
is reached where all the vapor has condensed to
liquid and the piston is resting on the liquid
surface
Why do further attempts to decrease the volume
require very high pressures (see the PV diagram
below)?
4
Suppose we increase the temperature while holding
the volume constant (by fixing the position of
the piston with stops) at a point where both the
liquid and vapor phases are present
On heating the less compressible liquid phase
expands at the expense of the more compressible
gas phase. Why dont both phases expand? In
addition heating results in a transfer of
molecules (mass) from the liquid phase to the
vapor phase. Both of these processes result in
an increase in the molar volume of the liquid and
a decrease in the molar volume of the vapor
5
If the heating at constant volume is continued, a
point is eventually reached where the molar
volumes of the liquid and vapor phases are equal.
At this point called the critical point the
physical properties of the liquid and vapor
phases are identical and it is no longer possible
to distinguish between the liquid and vapor
phases
Note that the dome-shaped loci of the molar
volumes of the liquid and vapor at equilibrium at
different temperatures define a boundary
separating the liquid and vapor phases and
therefore the above diagram is an example of a
phase diagram. At temperatures greater than the
critical temperature is it possible to condense a
vapor in the usual sense? Could you sketch how
the van der Waals equation would appear on the
above PV diagram at temperatures less and greater
than the critical temperature over a range of
molar volumes covering both the liquid and vapor
phases? This link will take you to a spreadsheet
which will allow you to plot PV isotherms for a
van der Waals gas.
6
Could you sketch isobars on a plot of volume
versus temperature or isometrics on a plot of
pressure versus temperature? What is the value of
the isothermal compressibility at the critical
point? At the critical point, where the liquid
and vapor phases are just balanced between
distinguishable and indistinguishable, relatively
large scale molecular aggregations exist in the
fluid whose dimensions are on the same order as
the wavelengths of visible light and hence
scatter visible light strongly in a phenomenon
known as critical opalescence. Critical
opalescence in SF6 is shown at T
lt Tc T Tc T gt Tc These images were taken
web site originally maintained by the Physics
Department at Brown (http//www.physics.brown.edu)
An extensive list of critical temperatures and
pressures can be found at http//www.flexwareinc.c
om/gasprop.htm .