0.17 Phase equilibrium and intermolecular interactions  (Page 4/7)

Note that, in varying either the amount of liquid initially or the fixed volume of the container, the amount of liquid water that evaporates must be different in each case. This can be seen fromthe fact that the volume available for vapor must be different in varying either the volume of the container or the initial volume ofthe liquid. Since we observe that the pressure of the vapor is the same at a fixed temperature, the differing volumes reveal differingnumbers of moles of water vapor. Clearly it is the pressure of the vapor, not the amount, which is the most important property in establishing theequilibrium between the liquid and the vapor. We can conclude that, at a given fixed temperature, there is a single specific pressureat which a given liquid and its vapor will be in phase equilibrium. We call this the vapor pressure of the liquid.

We can immediately observe some important features of the vapor pressure. First, for a given substance, thevapor pressure varies with the temperature. This can be found by simply increasing the temperature on the closed container in thepreceding experiment. In every case, we observe that the equilibrium vapor pressure increases with increases in the temperature.

The vapor pressures of several liquids at several temperatures are shown here . The vapor pressure for each liquid increases smoothly with the temperature, althoughthe relationship between vapor pressure and temperature is definitely not proportional.

Vapor pressures of various liquids

Second, [link] clearly illustrates that the vapor pressure depends strongly on what the liquid substance is. Thesevariations reflect the differing volatilities of the liquids: those with higher vapor pressures are more volatile. In addition, there is avery interesting correlation between the volatility of a liquid and the boiling point of the liquid. Without exception, the substanceswith high boiling points have low vapor pressures and vice versa.

Looking more closely at the connection between boiling point and vapor pressure, we can find an importantrelationship. Looking at [link] , we discover that the vapor pressure of each liquid is equal to 760torr (which is equal to 1 atm) at the boiling point for that liquid. How should we interpret this? At an applied pressure of 1atm, the temperature of the phase transition from liquid to gas is the temperature at which the vapor pressure of the liquid is equalto 1 atm. This statement is actually true regardless of which pressure we consider: if we apply a pressure of 0.9 atm, theboiling point temperature is the temperature at which the liquid as a vapor pressure of 0.9 atm. Stated generally, the liquid undergoesphase transition at the temperature where the vapor pressure equals the applied pressure.

Observation 3: phase diagrams

Since the boiling point is the temperature at which the applied pressure equals the vapor pressure, then we canview [link] in a different way. Consider the specific case of water, with vapor pressure given here . To find the boiling point temperature at 1 atm pressure, we need to findthe temperature at which the vapor pressure is 1 atm. To do so, we find the point on the graph where the vapor pressure is 1 atm andread off the corresponding temperature, which must be the boiling point. This will work at any given pressure. Viewed this way, forwater [link] gives us both the vapor pressure as a function of the temperature and the boiling point temperature as a function of the pressure. They are the same graph.