The Haber Rule: The Effect of Poisonous Gas Concentration

[Woodnyet]

The Haber Rule: The Effect of Poisonous Gas Concentration

Fritz Haber was a German scientist during the time of the First World War. He was in charge of the notorious
German chemical weapons program during the war. He invented many of the poison gases which were used,
and was later criticised for his work. For all of the bad he had attained, he actually out did himself by his good
discoveries, such as a commercially-feasible method of manufacturing ammonia, for fertilizers (thus saving
the world from famine.) His motivation, however, may have been for the production of cheap ammonia, in order
to manufacture explosives for wartime use.

He is credited with many other discoveries, one of which came to be known as 'Haber's Rule' (explained below.)
I have done some research on the application of this principle to airborne particulate matter. See the links below
to various studies which have suggested, or established, links to this well-known scientific principle.

Haber's Rule may especially apply to wood smoke particles, since they tend to accumulate in the lungs, and are
principally non-polar. The smallest of these particles, the less-than-2.5 micron particle size, may be the most
destructive of all, since such small particles can traverse into the deepest recesses of the lungs.

Any airborne chemical compound which is non-polar (that is, non-water soluble; water is, by contrast, highly polar)
can tend to collect in the lungs, or be absorbed into the bloodstream, where it ultimately ends up in a fat cell (fats
are also non-polar, thus tend to attract the non-polar chemical to itself.) This is how airborne dioxins and polycyclic
aromatic hydrocarbons terminally reach the body's fat cells, where they tend to continue to accumulate over time.

"In his studies of the effects of poison gas, Haber noted that exposure to a low concentration of a poisonous gas for a long time often had the same effect (death) as exposure to a high concentration for a short time. He formulated a simple mathematical relationship between the gas concentration and the necessary exposure time. This relationship became known as Haber's rule."

Fritz Haber

"Haber's rule is a mathematical statement of the relationship between the concentration of a poisonous gas and how long the gas must be breathed to produce death, or other toxic effect. The rule was formulated by German chemist Fritz Haber in the early 1900s.

Haber's rule states that, for a given poisonous gas, , where C is the concentration of the gas (mass per unit volume), t is the amount of time necessary to breathe the gas, in order to produce a given toxic effect, and k is a constant, depending on both the gas and the effect. Thus, the rule states that doubling the concentration will halve the time, for example.

Haber's rule is an approximation, useful with certain inhaled poisons under certain conditions, and Haber himself acknowledged that it was not always applicable. It is very convenient, however, because its relationship between C and t appears as a straight line in a log-log plot. In 1940, statistician C. I. Bliss published a study (Bliss, 1940) of toxicity in insecticides in which he proposed more complex models, for example, expressing the relationship between C and t as two straight line segments in a log-log plot. However, because of its simplicity, Haber's rule continued to be widely used. Recently, some researchers have argued (Miller et al., 2000) that it is time to move beyond the simple relationship expressed by Haber's rule and to make regular use of more sophisticated models."

Haber's Rule

Haber's Rule is cited in these articles:

Habers rule... cumulative ... together with ozone, especially PM10 particulates ...
http://ec.europa.eu/health/ph_risk/comm ... t38_en.htm

On the Importance of Exposure Variability to the Doses of Volatile Organic Compounds
S. M. Rappaport*,1, L. L. Kupper and Y. S. Lin*
http://toxsci.oxfordjournals.org/cgi/co ... l/83/2/224

Toxicity of Military Smokes and Obscurants/Committee on Toxicology,
Commission on Life Sciences, National Research Council
http://books.nap.edu/catalog.php?record_id=5582

Chemical mutagens: Dosimetry, Haber's rule and linear systems
W. H. Olson and R. B. Cumming/Journal of Theoretical Biology Volume 91, Issue 3, 7 August 1981, Pages 383-395
http://www.sciencedirect.com/science?_o ... 6c6cdc4568

PDF files

Characteristics of atmospheric particulate matter
http://nepap.ivl.se/Reports/NEPAP_MLA_WP5.pdf

Research Priorities for Airborne Particulate Matter
http://www.epa.gov/oppt/aegl/pubs/tsd65.pdf

Other Publications: American Chemistry Council Long-range Research (PDF file)
http://www.americanchemistry.com/s_acc/ ... 1&DID=5114

PayPerView
Prediction of the Toxic Effects of Fire Effluents/Gordon E. Hartzell
http://jfs.sagepub.com/cgi/content/abst ... 179?ck=nck

About Haber's Rule:

Toxicology (next 4 articles:)
http://www.sciencedirect.com/science/journal/0300483X

The use of Haber’s Law in standard setting and risk assessment
David W. Gaylor/Toxicology/Vol149/no1

Haber’s rule: a special case in a family of curves relating concentration and duration
of exposure to a fixed level of response for a given endpoint/Toxicology/Vol149/no1
Frederick J. Miller, , Paul M. Schlosser and Derek B. Janszen

The role of time in toxicology or Haber’s c×t product
Karl K. Rozman/Toxicology/Vol149/no1

The Haber-Weiss reaction and mechanisms of toxicity*1
James P. Kehrer/Toxicology/Vol149/no1

[Woodnyet]

These are some additional research papers pertaining to Haber's Rule. Many studies over the years have
empirically demonstrated Haber to have been correct in his original theory. The only modern developmental
addition to his discovery is the proper mathematical modeling technique may be a bit more complicated than
he had originally surmised.

This is nothing unusual — many behaviors of common natural events do not necessarily obey an expected
predictive formula — nature is much more complicated than that, with many variables (including the myriad
of unknowns) taking effect.

For example, my own research into the behavior of water evaporation (while studying refrigeration) revealed
a rather strange property of the atmospheric humidity saturation curve: it does not obey a predicted strictly
exponential model, rather, it exhibits a hybrid linear/exponential model. I am not going to publish those results
here, as they would be a bit off-topic. (If anyone is interested in my calculations, please send me a PM and I
will gladly explain them.)

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The use of Haber’s Law in standard setting and risk assessment
David W. Gaylor

Abstract
Haber’s Law simply states that the incidence and/or severity of a toxic effect depends on the total exposure,
i.e. exposure concentration (c) rate times the duration time (t) of exposure (c×t). This rule, within constraints,
is often used in setting exposure guidelines for toxic substances. Establishing reference doses (acceptable daily
intakes) for long-term exposures when only the results of short-term studies are available requires the use of
an uncertainty (safety) factor. The value of this uncertainty factor often approximates a value comparable to
Haber’s Law for extrapolation from short-term to long-term exposure durations. As a default procedure, cancer
risk estimates are generally based on the average lifetime daily dose which is derived from the total cumulative
exposure, i.e. Haber’s (c×t). This has been shown both theoretically and empirically to be valid within a factor
of 20 for carcinogenesis. This provides some credence for the use of an additional safety factor of 10, in some
instances, for exposures of children to carcinogens. Finally, a generalization of Haber’s Law, exposure
concentration raised to a power times exposure duration, is discussed.

_________________________________________________________________________________________
Using Haber’s Law to define the margin of exposure
John Doull, and K. K. Rozman
________________________________________________________________________________________
Haber's rule: a special case in a family of curves relating concentration and duration
of exposure to a fixed level of response for a given endpoint.
Miller FJ, Schlosser PM, Janszen DB.
http://www.ncbi.nlm.nih.gov/pubmed/1096 ... rom=pubmed

The concept that the product of the concentration (C) of a substance and the length of time (t) it is
administered produces a fixed level of effect for a given endpoint has been ascribed to Fritz Haber, who was
a German scientist in the early 1900s. He contended that the acute lethality of war gases could be assessed
by the amount of the gas in a cubic meter of air (i.e. the concentration) multiplied by the time in min that the
animal had to breathe the air before death ensued (i.e. C x t=k). While Haber recognized that C x t=k was
applicable only under certain conditions, many toxicologists have used his rule to analyze experimental data
whether or not their chemicals, biological endpoints, and exposure scenarios were suitable candidates for the
rule. The fact that the relationship between C and t is linear on a log-log scale and could easily be solved by
hand, led to early acceptance among toxicologists, particularly in the field of entomology. In 1940, a statistician
named Bliss provided an elegant treatment on the relationships among exposure time, concentration, and the
toxicity of insecticides. He proposed solutions for when the log-log plot of C and t was composed of two or
more rectilinear segments, for when the log-log plot was curvilinear, and for when the slope of the dosage-
mortality curve was a function of C. Despite the fact that Haber's rule can underestimate or overestimate
effects (and consequently risks), it has been used in various settings by regulatory bodies. Examples are
presented from the literature of data sets that follow Haber's rule as well as those that do not. Haber's rule
is put into perspective by showing that it is simply a special case in a family of power law curves relating
concentration and duration of exposure to a fixed level of response for a given endpoint. Also shown is how
this power law family can be used to examine the three-dimensional surface relating C, t, and varying levels
of response. The time has come to move beyond the limited view of C and t relationships inferred by Haber's
rule to the use of the broader family of curves of which this rule is a special case

__________________________________________________________________________________________________
Does Haber's Law Apply to Human Sensory Irritation?
Dennis Shusterman; Elizabeth Matovinovic; Andrew Salmon

Abstract
Irritation of the eyes, nose, and throat by airborne chemicals—also referred to as “sensory irritation”—is an
important endpoint in both occupational and environmental toxicology. Modeling of human sensory irritation
relies on knowledge of the physical chemistry of the compound(s) involved, as well as the exposure parameters
(concentration and duration). A reciprocal relationship between these two exposure variables is postulated
under Haber's law, implying that protracted, low-level exposures may be toxicologically equivalent to brief,
high-level exposures. Although time is recognized as having an influence on sensory irritation, the quantitative
predictions of Haber's Law have been addressed for only a handful of compounds in human experimental
studies. We have conducted a systematic literature review that includes a semiquantitative comparison of
psychophysical data extracted from controlled human exposure studies versus. the predictions of Haber's law.
Studies containing relevant data involved exposures to ammonia (2), chlorine (2), formaldehyde (1), inorganic
dusts such as calcium oxide (1), and the volatile organic compound 1-octene (1). With the exception of dust
exposure, varying exposure concentration has a proportionally greater effect on sensory irritation than does
changing exposure duration. For selected time windows, a more generalized power law model (cn t = k)
rather than Haber's law per se (c t = k) yields reasonably robust predictions. Complicating this picture,
however, is the frequent observation of intensity-time “plateauing,” with time effects disappearing, or even
reversing, after a relatively short period, depending on the test compound. The implications of these complex
temporal dynamics for risk assessment and standard setting have been incompletely explored to date.
___________________________________________________________________________________________________
Does Haber's law apply to human sensory irritation?
Dennis Shusterman; Elizabeth Matovinovic; Andrew Salmon
___________________________________________________________________________________________________

[Ernest Grolimund]

NESCAUM wrote a report on OWB's and graphed pm2.5 for an ave of about 2,000 mcg/m3 for 3 minutes. The extreme peak was 8,000 mcg/m3. Dr. Brown wrote a report on OWB's where scientists said 30 mcg/m3 for 3 hrs can cause heart and asthma attacks. Equating 2,000 mcg/m3 x T = 30 mcg/m3 x 3 hrs and solving for t gives 3 minutes. Therefor, if you get stuck in the worst plume of an owb, when it is getting damped down and choked for idling, you could have a heart or asthma attack in 3 minutes if you have asthma or heart disease. THREE MINUTES!!!! Yes? No?

Also, the owb in the Nescaum report put out more pm2.5 in the first hour, 180 mcg/m3. This means that 1/2 hour of expsure to the start up smoke can be deadly. ONE HALF HOUR. Yes? No? And this is just considering pm2.5. About 180 air toxics are attached. The Maine DEP says toxics don't matter to them. They do not have to enforce that. But Maine nuisance case law says when life and health are at risk, then the greatest care must be excercised. This means to me anyhow, that guidelines for air toxics must be enforced. If so, benzene, and acrolein and other toxics are doubling or tripling the risk or multiplying the risk 180 times ! The thought has come to me that this is gross negligence on the part of the governments, federal, state and local. See Atty Pletten's briefs and 64 ME 120. ' The highest degree of care must be excercised when life and health are at risk. Benzene and airtoxics as well as pm2.5 are associated with deaths and cancer individually. The right to life must be protected. We should not kill. Yes? No?

The EPA rule requiring enforcement of toxics guidelines for only large regulated facilities seems unconstitutional. Nancey Sutley worked in L.A. and L.A. ruled that all woodburning together added up to 4 power plants. Where are the pro bono lawyers?

[Woodnyet]

The following charts illustrate how Haber's Rule works. It applies to ambient poison gas
in this case, but can apply to just about anything, a good example being alcohol consumption.

The "poison gas" type is arbitrary. Different poisons have differing toxicities, which may be
more or less than what is given here. Nonetheless, the curve applies. This "curve" is that of
a rational function: xy = c [where in this case, c = 500)

On the vertical axis, we have poison gas concentration, in parts per million.
On the horizontal axis, we have exposure time, in hours.

Here is how the charts work. Remember basic algebra? An area of a rectangle equals the base
times the height. Notice the blue squares. There are three different shapes, a tall one, a nearly-
square one, and a flat one. In each of these rectangles, the same formula applies: A = b X h.

For the first, 0.5 X 1000 = 500
For the second, 2.0 X 250 = 500
For the third, 10 X 50 = 500

Notice that all of the rectangles have the same area (500 units) This can be considered to be
the "exposure factor." That is, no matter whether we inhale a concentration of 1000 ppm for
half hour, or 250 ppm for 2 hours, or 50 ppm for 10 hours, we always inhale the same total
AMOUNT of particulates, in this case, 500 units of pollutants. This might be measured in
micrograms, milligrams, or other unit of mass. That is, we inhale, for example, 500 micro-
grams in 1/2 hr, 2 hrs, or 10 hrs, depending on the ambient concentration of poison gas.

[Woodnyet]

from Miller et al
http://www.sciencedirect.com/science/ar ... 3X00002298