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12.6 Phase Changes
dynamic equilibrium of condensation and evaporation is called the equilibrium vapor pressure. We often use the simpler term “vapor pressure” when we talk about the equilibrium vapor pressure of a liquid. This practice is acceptable as long as we know the meaning of the abbreviated term. It is important to note that the equilibrium vapor pressure is the maximum vapor pressure a liquid exerts at a given temperature and that it is constant at constant temperature. Vapor pressure does change with temperature, however. Plots of vapor pressure versus temperature for three different liquids are shown in Figure 12.28. We know that the number of molecules with higher kinetic energies is greater at the higher temperature and therefore so is the evaporation rate. For this reason, the vapor pressure of a liquid always increases with temperature. For example, the vapor pressure of water is 17.5 mmHg at 20°C, but it rises to 760 mmHg at 100°C.
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Animation: Equilibrium Vapor Pressure
Equilibrium vapor pressure is independent of the amount of liquid as long as there is some liquid present.
Heat of Vaporization and Boiling Point A measure of how strongly molecules are held in a liquid is its molar heat of vaporization (DHvap), defined as the energy (usually in kilojoules) required to vaporize one mole of a liquid. The molar heat of vaporization is directly related to the strength of intermolecular forces that exist in the liquid. If the intermolecular attraction is strong, it takes a lot of energy to free the molecules from the liquid phase. Consequently, the liquid has a relatively low vapor pressure and a high molar heat of vaporization. The previous discussion predicts that the equilibrium vapor pressure (P) of a liquid should increase with increasing temperature as shown in Figure 12.28. Analysis of this behavior reveals that the quantitative relationship between the vapor pressure P of a liquid and the absolute temperature T is given by the Clausius-Clapeyron equation: ln P 5 2
DHvap RT
1C
(12.1)
in which ln is the natural logarithm, R is the gas constant (8.314 J/K ? mol), and C is a constant. The Clausius-Clapeyron equation has the form of the linear equation y 5 mx 1 b: DHvap 1 ln P 5 a2 ba b 1 C R T D y 5
D m
D D x 1b
Figure 12.28
Vapor pressure (atm)
2
Diethyl ether
Water
Mercury
1
–100
0 34.6
100 200 Temperature (°C)
357 400
The increase in vapor pressure with temperature for three liquids. The normal boiling points of the liquids (at 1 atm) are shown on the horizontal axis. The strong metallic bonding in mercury results in a much lower vapor pressure of the liquid at room temperature.