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. thermostated at 25 C H2O vapor at 10 torr 24 torr 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: P (torr) V (L/mole) ~ 1.9 x 103 ~ 800 25 oC isotherm 24 10 How are molar volume and density related? 5.1

Continued decreasing of the volume results in the condensation of more liquid water: thermostated at 25 oC 24 torr 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: P (torr) V (L/mole) Vvap ~ 800 Vliq ~ 0.018 25 oC isotherm 24 Notice how much smaller the molar volume of the liquid phase is compared to the molar volume of the vapor. 5.2

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: thermostated at 25 oC Why do further attempts to decrease the volume require very high pressures (see the PV diagram below)? P (torr) V (L/mole) Vvap ~ 800 Vliq ~ 0.018 25 oC isotherm 24 5.3

Why don’t both phases expand? 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: 25 oC T > 25 oC Increase T On heating the less compressible liquid phase expands at the expense of the more compressible gas phase. Why don’t 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: P (torr) V (L/mole) Vvap Vliq 25 oC isotherm 24 T > 25 oC isotherm 5.4

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: P (torr) V (L/mole) isotherm at the critical temperature, Tc critical molar volume, Vc critical pressure, Pc critical point vapor liquid liquid & vapor in equil. 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. 5.5

Could you sketch isobars on a plot of volume versus temperature or isometrics on a plot of pressure versus temperature? 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. Critcal opalescence in SF6 is shown at: http://www.physics.brown.edu/Studies/Demo/thermo/demo/4c5010.htm An extensive list of critical temperatures and pressures can be found at http://www.flexwareinc.com/gasprop.htm . 5.6