View source for Haber's rule

{{short description|Toxicology relationship between the concentration of a poisonous gas and duration breathed}}
In [[toxicology]], '''Haber's rule''' or '''Haber's law''' 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 [[Germany|German]] [[chemist]] [[Fritz Haber]] in the early 1900s.

==Rule==
Haber's rule states that, for a given poisonous gas, <math>tC = k</math>, where <math>C</math> is the concentration of the gas (mass per unit volume), <math>t</math> is the amount of time necessary to breathe the gas to produce a given toxic effect, and <math>k</math> 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.

It makes [[Equivalent (chemistry)|equivalent]] any two groupings of [[dose concentration]] and [[exposure time]] that have equivalent [[mathematical product]]s.  For instance, if we assign [[dose (biochemistry)|dose]] [[concentration]] the [[symbol]] C, and [[time]] the classic t, then for any two dose [[conceptual model|schema]], if C<sub>1</sub>t<sub>1</sub>=C<sub>2</sub>t<sub>2</sub>, then under Haber's rule the two dose schema are equivalent.

Haber's rule is an approximation, useful with certain inhaled poisons under certain conditions, and Haber himself acknowledged that it was not always applicable. If a substance is efficiently eliminated in the host, for example, then Haber's Law breaks down in the limit of t approaching the [[Order of reaction|order]] of the [[half-life]] of the [[drug]], rewriting the equation as the integral ∫Cdt = constant for arbitrary varying C and elapsed time T.  It is very convenient, however, because its relationship between <math>C</math> and <math>t</math> appears as a straight line in a [[log-log plot]].

In 1940, [[statistician]] C. I. Bliss published a study of [[toxicity]] in [[insecticide]]s in which he proposed more complex [[mathematical model|models]], for example, expressing the relationship between <math>C</math> and <math>t</math> as two straight line segments in a [[log-log plot]].<ref>{{cite journal | author=C. I. Bliss | title= The relation between exposure time, concentration and toxicity in experiments on insecticides | journal=Annals of the Entomological Society of America | year=1940 | volume=33 | issue= 4 | pages=721–766| doi= 10.1093/aesa/33.4.721 }}</ref> However, because of its simplicity, Haber's rule continued to be widely used. Recently, some researchers have argued that it is time to move beyond the simple relationship expressed by Haber's rule and to make regular use of more sophisticated models.<ref>{{cite journal |author1=F. J. Miller |author2=P. M. Schlosser |author3=D. B. Janszen | title=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 | journal=Toxicology | date=August 14, 2000 | volume=149| issue =  1 | pages=21–34 | pmid=10963858 | doi=10.1016/S0300-483X(00)00229-8|bibcode=2000Toxgy.149...21M }}</ref>

==See also==
*{{LD50}}
*[[Toxicology]]
*[[Chemical warfare]]
*[[Area under the curve]]

==References==
{{reflist}}

[[Category:Eponymous chemical rules]]
[[Category:Pharmacokinetics]]
[[Category:Toxicology]]
[[Category:Fritz Haber]]