## The Empirical Gas Laws: Vapor Pressure

James Richard Fromm

All solids and liquids, that is, all substances in condensed phases, exhibit a vapor pressure. This is a pressure of the substance in the gas phase which is established at a particular temperature. The vapor pressure of a substance depends upon the temperature. A table of vapor pressures at 25oC for a few selected substances is given below.

##### Table: Vapor Pressures and Densities of Pure Substances at 25oC
 Substance Vapor Pressure (kPa) Density (kg/m3 H2O(l) 3.1691 0.99702 CH3OH(l) 16.8511 0.791 C2H5OH(l) 7.8279 0.785 C6H6(l) 12.6893 0.899 Hg(l) 0.2460 13.5340 I2(s) 0.1889 4.93

If a dish of water is placed in a chamber which is evacuated by means of a vacuum pump, the pressure will drop only until the vapor pressure of water at that temperature is reached. The liquid water will then boil, replacing the water vapor as the pump removes it, until either the liquid water has all boiled away or the pump is shut off. The pressure in the chamber while this is going on will remain constant at the vapor pressure of water.

The vapor pressure of any pure substance is characteristic of that substance and of its temperature. At room temperature the vapor pressure of ethanol is much higher, and the vapor pressure of mercury or potassium chloride is much lower, than is the vapor pressure of water. Since water is the most important as well as one of the most common substances on earth, its vapor pressure at different temperatures is given in the Table below.

##### Table: Vapor Pressure and Density of Water at Different Temperatures
 Temperature (oC) Vapor Pressure (kPa) Density (kg/m3) 0.01 0.61173 0.99978 1 0.65716 0.99985 4 0.81359 0.99995 5 0.87260 0.99994 10 1.2281 0.99969 15 1.7056 0.99909 20 2.3388 0.99819 25 3.1691 0.99702 30 4.2455 0.99561 35 5.6267 0.99399 40 7.3814 0.99217 45 9.5898 0.99017 50 12.344 0.98799 55 15.752 0.98565 60 19.932 0.98316 65 25.022 0.98053 70 31.176 0.97775 75 38.563 0.97484 80 47.373 0.97179 85 57.815 0.96991 90 70.117 0.96533 95 84.529 0.96192 100 101.32 0.95839 105 120.79 0.95475

The vapor pressure of all substances increases, and in many cases increases very significantly, with temperature as shown in the Figure below. The bond structure of solids is in general stronger than that in liquids, and as a general rule the vapor pressures of solids are much lower than those of similar liquids at the same temperature.

#### Vapor Pressure As a Partial Pressure

Collection of gases over any liquid which has a vapor pressure, such as water, is carried out as shown in the Figure below. The total pressure measured, p, is the sum of the partial pressure of the collected gas and the partial pressure of the gas phase of the liquid, which is its vapor pressure. If the liquid is water, as is most often the case, the pressure of the gas collected must be:

p(gas) = p - p(H2O)

The measured or total pressure is obtained using a barometer and manometer. The vapor pressure of water at the appropriate temperature is obtained from a table such as that given above.

Example. A volume of 546.3 mL of hydrogen is collected over water at 30oC when the atmospheric pressure is 100.45 kPa. The actual pressure of the hydrogen and the amount of hydrogen present are calculated as follows. The vapor pressure of water at 30oC is 4.246 kPa so the actual pressure of the hydrogen is 100.45 - 4.25 = 96.20 kPa. The amount of hydrogen present is (96.20 kPa)(0.5463 dm3)/(8.314 kPa dm3/mol K)(303.15 K) = 0.0209 mol H2.