toxicology Toxicology is a scientific discipline, overlapping with biology, chemistry, pharmacology, and medicine, that involves the study of the adverse effects of chemical substances on living organisms and the practice of diagnosing and treating ex ...

, Haber's rule or Haber's law is a

mathematical Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

statement of the relationship between the

concentration In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', '' molar concentration'', '' number concentration'', ...

of a poisonous

gas Gas is a state of matter that has neither a fixed volume nor a fixed shape and is a compressible fluid. A ''pure gas'' is made up of individual atoms (e.g. a noble gas like neon) or molecules of either a single type of atom ( elements such as ...

and how long the gas must be breathed to produce death, or other

toxic Toxicity is the degree to which a chemical substance or a particular mixture of substances can damage an organism. Toxicity can refer to the effect on a whole organism, such as an animal, bacterium, or plant, as well as the effect on a subst ...

effect. The rule was formulated by

German German(s) may refer to: * Germany, the country of the Germans and German things **Germania (Roman era) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizenship in Germany, see also Ge ...

chemist A chemist (from Greek ''chēm(ía)'' alchemy; replacing ''chymist'' from Medieval Latin ''alchemist'') is a graduated scientist trained in the study of chemistry, or an officially enrolled student in the field. Chemists study the composition of ...

Fritz Haber Fritz Jakob Haber (; 9 December 1868 – 29 January 1934) was a German chemist who received the Nobel Prize in Chemistry in 1918 for his invention of the Haber process, a method used in industry to synthesize ammonia from nitrogen gas and hydrog ...

in the early 1900s.

Rule

Haber's rule states that, for a given poisonous gas,

tC = k

, where

C

is the concentration of the gas (mass per unit volume),

t

is the amount of time necessary to breathe the gas 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. It makes

equivalent Equivalence or Equivalent may refer to: Arts and entertainment *Album-equivalent unit, a measurement unit in the music industry *Equivalence class (music) *'' Equivalent VIII'', or ''The Bricks'', a minimalist sculpture by Carl Andre *'' Equiva ...

any two groupings of dose concentration and

exposure time In photography, shutter speed or exposure time is the length of time that the film or digital sensor inside the camera is exposed to light (that is, when the camera's shutter is open) when taking a photograph. The amount of light that rea ...

that have equivalent

mathematical product In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called ''factors''. For example, 21 is the product of 3 and 7 (the result of multiplication), and x\cd ...

s. For instance, if we assign dose

the

symbol A symbol is a mark, Sign (semiotics), sign, or word that indicates, signifies, or is understood as representing an idea, physical object, object, or wikt:relationship, relationship. Symbols allow people to go beyond what is known or seen by cr ...

C, and

time Time is the continuous progression of existence that occurs in an apparently irreversible process, irreversible succession from the past, through the present, and into the future. It is a component quantity of various measurements used to sequ ...

the classic t, then for any two dose

schema Schema may refer to: Science and technology * SCHEMA (bioinformatics), an algorithm used in protein engineering * Schema (genetic algorithms), a set of programs or bit strings that have some genotypic similarity * Schema.org, a web markup vocab ...

, if C₁t₁=C₂t₂, 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 Order, ORDER or Orders may refer to: * A socio-political or established or existing order, e.g. World order, Ancien Regime, Pax Britannica * Categorization, the process in which ideas and objects are recognized, differentiated, and understood ...

of the

half-life Half-life is a mathematical and scientific description of exponential or gradual decay. Half-life, half life or halflife may also refer to: Film * Half-Life (film), ''Half-Life'' (film), a 2008 independent film by Jennifer Phang * ''Half Life: ...

of the

drug A drug is any chemical substance other than a nutrient or an essential dietary ingredient, which, when administered to a living organism, produces a biological effect. Consumption of drugs can be via insufflation (medicine), inhalation, drug i ...

, 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

C

and

t

appears as a straight line in a log-log plot. In 1940,

statistician A statistician is a person who works with Theory, theoretical or applied statistics. The profession exists in both the private sector, private and public sectors. It is common to combine statistical knowledge with expertise in other subjects, a ...

C. I. Bliss published a study of

toxicity Toxicity is the degree to which a chemical substance or a particular mixture of substances can damage an organism. Toxicity can refer to the effect on a whole organism, such as an animal, bacteria, bacterium, or plant, as well as the effect o ...

insecticide Insecticides are pesticides used to kill insects. They include ovicides and larvicides used against insect eggs and larvae, respectively. The major use of insecticides is in agriculture, but they are also used in home and garden settings, i ...

s in which he proposed more complex

models A model is an informative representation of an object, person, or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin , . Models can be divided int ...

, 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 that it is time to move beyond the simple relationship expressed by Haber's rule and to make regular use of more sophisticated models.

References

{{reflist Eponymous chemical rules Pharmacokinetics Toxicology Fritz Haber

Rule

See also

References