HazMat Math; Calculating Vapor Concentrations

Previously, this column discussed utilizing a math concept to calculate vapor densities of gases and vapors. Calculating vapor density can enhance first responder safety because of a more precise idea of where the gases and vapors may be found at an incident. This column will also show how math can assist responders with calculating the approximate concentration of a gas or vapor within a container or even at an outside spill or release. The ability to approximate the vapor concentration at these sites will assist responders with critical risk assessment and rescue decisions.

It is a fact that liquids will evaporate at temperatures well below their boiling points. This happens because some of the molecules within the liquid gain enough energy to break away from the surface of the liquid and enter the vapor state. The rate or speed at which this happens depends upon surface wind velocity, and more importantly, temperature. It is important to realize that the evaporation process is very temperature dependent! That is, the higher the temperature the faster a liquid will evaporate. The converse is also true; the lower the temperature the slower a liquid will evaporate. This fact of nature can especially be observed with water and in your mind's eye you can probably visualize how fast a puddle of water evaporates on a summer day. One main difference with this concept is that different liquids will evaporate at different rates at the same temperature. This is a function of each liquid's individual vapor pressure.

Vapor pressure is a primary measure of a liquid's tendency to vaporize or evaporate. Vapor pressure is defined as the pressure characteristic at any given temperature of a vapor in equilibrium with its liquid or solid form. In other words, it is the tendency of a liquid to evaporate into the air, and if in a closed container the vapor will exert a pressure above the liquid and on the sides of the container. Vapor pressures are expressed in units of millimeters of mercury (mm/Hg) or pounds per square inch (psi) or atmospheres (atm). (For comparison purposes 760 mm/Hg = 14.7 psi = 1 atm) Many vapor pressures are measured at laboratory temperatures (approximately 68 F) and it is the temperature that is used in most of the data in the NIOSH Pocket Guide. (Table 1 depicts some materials and their vapor pressures at different temperatures.)

Vapor Pressures as a Function of Temperature of Selected Chemicals
Vapor Pressure (mm/Hg)
Chemical

1 mm/Hg

10 mm/Hg

40 mm/Hg

100 mm/Hg

760 mm/Hg
Benzene

-38.2 F

11.3 F

45.7 F

79.0 F

176.2 F
Butane

-150.7 F

-108.0 F

-74.4 F

-47.6 F

31.1 F
Ethyl Alcohol

-24.3 F

27.9 F

66.2 F

94.8 F

173.1 F
Propane

-200.0 F

-163.3 F

-134.3 F

-111.3 F

-43.8 F
Water

-18 F

52.3 F

93.3 F

122.3 F

212.0 F

The chemicals listed in the above table will all exert their vapor pressure whether or not they are in their containers. When in a container, they reach a state of equilibrium where some of the molecules change from a liquid to a vapor state and other molecules go from a vapor state to a liquid state. When the release is outside of the container the molecules that go from a liquid to a vapor state simply mix with the atmosphere and in time will move away from the liquids surface. As the molecules change to vapors the liquid evaporates and in time will be depleted. The rate of evaporation will be accelerated with higher winds and higher temperature. Also, recognize that the higher the vapor pressure the greater the tendency a material has to become a gas or vapor. All materials will have a vapor pressure of 760 mm/Hg or greater at their boiling points. This also means that any material with a vapor pressure greater than 760 mm/Hg (at any temperature) will be a gas.

Selected Chemicals and Vapor Pressures at 68 F
Chemical

Vapor Pressure (mm/Hg)
Benzene

75
Chlorine

4788 or 6.3 atm
Ethylene Oxide

1064 or 1.4 atm
Fuel Oil #4

2
Methylene Chloride

350
Water

25

Calculating Vapor Concentration

Also, realize that there is a direct relationship between the vapor pressure of a liquid and the maximum concentration that its vapor or gas may achieve when mixed with air in the open environment or even in a container. This fact is because higher vapor pressures above the surface of a substance require that more molecules of the substance be physically present. With this in mind and if the vapor pressure of a material is known the approximate concentration that the material may produce can be calculated. The equations that can be used are;

To find the percent (%) concentration for a material multiply the vapor pressure of the material in mm/Hg by 100 and divide by 760.

% concentration

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