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David F. Peterson

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   =   Vapor pressure (mm/Hg) X 100
         760

To find the concentration in parts per million (ppm) multiply the vapor pressure of the material in mm/Hg by 1,000,000 and divide by 760.

ppm concentration   =   Vapor pressure (mm/Hg) X 1,000,000
         760

The only restriction in using these equations is that the concentration of a gas or vapor cannot exceed 100% by volume or its equivalent of 1,000,000 ppm regardless of the answer obtained.

The following are some examples using the above equations.

From Table 1 it is noted that ethyl alcohol has a vapor pressure of 40 mm/Hg at 66.2 F. To find the approximate concentration of ethyl alcohol at this temperature we can use the first formula.

% concentration   =   40 mm/Hg X 100   =   5.26 %
         760

We find that there would be a maximum concentration of 5.26 % vapors above this spill at 66.2 F.

To find the ppm concentration of the same material we would use the second formula.

ppm concentration   =   40 mm/Hg X 1,000,000   =   52,631.6 ppm
         760

(Conversion of percent to ppm involves multiplying the figure by 10,000. In other words, 1% equals 10,000 ppm and 100% equals 1,000,000 ppm).

One other example has benzene in a partially filled tank on an 80 F day. To calculate the approximate concentration in ppm within the tank we would use the data from Table 1. Benzene has a vapor pressure of 100 mm/Hg at approximately 79 F or 80 F. The formula to use would be ppm concentration equals 100 mm/Hg multiplied by 1,000,000 and divided by 760, which would equal 131,579 ppm, or 13.1579%. This level exceeds the flammable range of 1.2% to 7.8% and the IDLH of 500 ppm. For benzene.

The 1300 Rule

With all of the scientific theory from above aside there is a shortcut. The "1300 Rule" was developed to assist responders with finding the approximate concentration of a material based on the formulas above. The formula for finding the percent concentration is;

% concentration = vapor pressure X 100 divided by 760

If we do the math in the above equation we find that 100 divided by 760 is 0.13158. So then all we would have to do at the spill scene is multiply 0.13158 by the vapor pressure of the material that has been released to find the percent concentration. Again, for ethyl alcohol this would be 40 X 0.13158 which equals 5.26%. If we want to find the ppm we would multiply 40 by 1315.8 (1,000,000 divided by 760 from the second formula) and the product is 52,632 ppm.

Where the shortcut comes in is we simply round the 1315.8 figure to 1300 to find the concentration in ppm. At the spill emergency we would multiply 1300 by the product's vapor pressure to get an answer that will be provide within approximately 1 to 2 % accuracy of the actual concentration in ppm. As an example, the vapor pressure of ethyl alcohol is 40 mm/Hg (at 66.2 F) multiplied by 1300 equals 52,000 ppm, which equates to 5.2%.

Application

All of this is well and good but what application does it have for responders in the field? If the approximate concentration of a material's vapors above or near the spill (or even in a container) can be found responders can compare it to other values such as the flammable range and biological indices for the material. These comparisons can assist with risk assessment and even with decisions on whether to conduct emergency rescue measures. For instance, if there were a spill of ethyl alcohol on a day with a temperature very close to 66.2 F we would find the maximum concentration above and near the spill to be approximately 5.2% (52,000 ppm). Through research we can find that ethyl alcohol has a flammable range of 3.3% to 19% and a flash point of 55 F, which means that the scene represents a distinct flammability problem. Furthermore, the Immediately Dangerous to Life and Health (IDLH*) level for ethyl alcohol is listed as 3,300 ppm but this scenario would present over 52,000 ppm. This atmosphere would represent a toxic exposure concern for victims within the spill area especially for prolonged exposures. If it can be observed that victims are in the spill area responders can be greatly aided with this information as they can better make a decision on whether to rescue viable victims. However, this type of information may also be used to determine if body recovery is in order (an entirely different response from rescue). All of these considerations are part of the risk benefit analysis process.

One other application involves the fact that vapor pressure is temperature dependent. If a container is experiencing an increase in vapor pressure from some heat source either remove the heat or cool the container. The cooler the product the lower the vapor pressure will be.

Remember that these vapor concentrations, whether calculated for an outdoor spill or for the concentration within a container, are only approximations. To be sure the only totally accurate method for determining airborne concentrations are through air monitoring efforts with appropriate instrumentation. These calculations should only be used as one tool in the risk assessment process. Use these concepts in good health and lets be careful out there!

* IDLH is defined in the NIOSH Pocket Guide to Chemical Hazards as a maximum concentration above which only a highly reliable breathing apparatus providing maximum worker protection was permitted. These values are based on the effects that might occur as a consequence of a 30-minute exposure. The 30-minute period was not meant to imply that workers should stay in the work environment any longer than necessary. Every effort should be made to exit immediately.

Resources:

• NIOSH Pocket Guide to Chemical Hazards, June 1997
• Handbook of Chemical Hazard Analysis Procedures by the Federal Emergency Management Agency (FEMA), U.S. Department of Transportation (DOT), U.S. Environmental Protection Agency (EPA)