Haber s law

The toxic effects model uses concentration-time profiles from the respiratory and skin protection models as input to estimate casualty probabilities. Two approaches are available a simple linear dose-effect model as incorporated in RAP and a more elaborate non-linear response model, based on the Toxic Load approach. The latter provides a better description of toxic effects for agents that show significant deviations of simple Haber s law behaviour (i.e. toxic responses only depend on the concentration-time product and not on each quantity separately). 

It is now recognized that Haber s law does not apply for long exposures to low concentrations. Apparently, there are metabolic processes in the human body (and in animals) that can (for many toxic materials) result in biotransiormation or detoxification, elimination, or excretion of toxic materials, or can repair damaged cells or tissues (Elkins, The Chemistry of Industrial Toxicology, 2d ed., p. 242,1959 U.S. Federal... 

The concept of a death product was introduced by Haber to explain the relationship between the extent of exposure to phosgene and death (Haber 1924). According to Haber s law, the biological effect of phosgene is directly proportional to the exposure, expressed as the product of the atmospheric concentration (C) and the time of exposure (T), or CT=k, where k can be death, pulmonary edema, or other biological effects of phosgene exposure (EPA 1986). Haber s law has subsequently been shown by other investigators to be valid for both nonlethal and lethal effects within certain limits. 

Rat and mouse lethality data from the well-conducted study of Zwart et al. (1990) also suggest that Haber s law is valid for phosgene. The study by ten Berge et al. (1986) has shown that the concentration-exposure-time relationship for many irritant and systemically acting vapors and gasses can be described by the relationship Cnxt=k. When the 10- to 60-min rat LC50 data are utilized in a linear regression analysis a value of the exponent, n, of 0.93 is obtained. The mouse 10- to 60-min lethality data yield a value of 1.3 for n. 

Thus, the fact that these empirically derived values for the exponent n approximate 1 is further support that Haber s law is valid for phosgene. 

Time scaling Cnxt=k where n=l. Haber s Law (Cxt=k) has been shown to be valid for phosgene within certain limits (EPA 1986). Haber s Law was originally derived from phosgene data (Haber 1924). Reported 30-min data point used to determine the 30-min AEGL value. AEGL-3 values for 1-, 4-, and 8-h were based on extrapolation from the 30 min value. The 10-min value was based on a reported 10-min data point. Data adequacy The AEGL-3 values are based on a well-conducted study in rats and the database is rich. 

Gelzleichter, T.R., H.Witschi, and J.A.Last. 1992. Concentration-response relationships of rat lungs to exposure of oxidant air pollutants A critical test of Haber s law for ozone and nitrogen dioxide. Toxicol. Appl. Pharmacol. 112(1) 73—80. 

The relationship between dose and time to response for any given chemical is a function of the physical and chemical properties of the substance and the unique toxicologic and pharmacologic properties of the individual substance. Historically, the relationship according to Haber (1924), commonly called Haber s law (NRC 1993a) or Haber s rule (i.e., C x t = k, where C = exposure concentration, t = exposure duration, and k = a constant) has been... 

Pieters, M.N., and H.J. Kramer. 1994. Concentration Time = Constant The Validity of Haber s Law in the Extrapolation of Discontinuous to Continuous Exposition. Rapportnrmuner 659101 002, National Institute for Public Health and Environmental Protection, The Netherlands. 

The relationship between dose and exposure time to produce a toxic effect for any given chemical is a function of the physical and chemical properties of the substance and the unique toxicologic and pharmacologic properties of the individual substance. Historically, the relationship according to Haber (1924), commonly called Haber s law (NRC 1993) or Haber s rule (i.e., C x t = k, where C = exposure concentration, t = exposure duration, and k = a constant) has been used to relate exposure concentration and duration to a toxic effect (Rinehart and Hatch 1964). This concept states that exposure concentration and exposure duration may be reciprocally adjusted to maintain a cumulative exposure constant (k) and that this cumulative exposure constant will always reflect a specific quantitative and qualitative response. This inverse relationship of concentration and time may be valid when the toxic response to a chemical is equally dependent upon the concentration and the exposure duration. However, an assessment by ten Berge et al. (1986) of LC50 data for certain chemicals revealed chemical-specific relationships between exposure... 

Acute animal tests in rats have demonstrated phosphine to have extreme acute toxicity via inhalation. Signs include early hypoactivity followed by restlessness, escape behaviors, ataxia, convulsions, and death within 30 min with high concentrations. Concentration-time studies demonstrated evidence of Haber s law, that is, within certain limits, the product of concentration and time of exposure to elicit lethality was remarkably constant. The lowest lethal concentration in rats was 7.5 mg m. The acute oral LD50 for metallic salts (e.g., aluminum phosphide) is typically quite low ( 10 mg kg In rabbits acutely exposed to high levels of phosphine via inhalation, dyspnea, paralysis, convulsions, hepatotoxicity and renal toxicity, and damage to the spleen were reported. 

EEGL—15 min, 300 mg in 1 h, 80 mg in 6 h, 15 mg in . These values were derived from a 1% lethal CT in rats of 8200 mg h in . These figures were divided by an uncertainty factor of 10 for nonpermanent health impairment, and a further uncertainty factor of 10 for interspecies variations. Assuming the applicability of Haber s law to the resultant CT of 80 mg h in , the cited exposure guideline concentrations were calculated for the defined periods. 

Haber s law, or rule, has continued to fascinate toxicologists as recently as 1999, Hans-Peter Witschi published on this subject (Witschi, 1999) and Miller and coworkers have since published a most interesting paper showing that the relationship described by Haber was but one of a family of such relationships (Miller et al, 2000). The following brief exploration of these relationships is closely based on Miller s paper. 

Haber s law (or Haber s rule) was discussed at some length in Chapter 2. A recent paper by Hatch et al (2001) has extended this discussion with special reference to phosgene. The authors focused on repeated and chronic exposures and showed that adaptation occurred if exposures were not overwhelming and were repeated daily. Adaptation was shown to wane over the period of a month or so. Repeated exposure at monthly intervals was associated with the development of chronic effects. This work shows that great care is needed in predicting responses from the Ct product if exposures are repeated and that the... 

In all cases, there is a concentration—time relationship. The higher the concentration of the chemical, the less time can a person be exposed to it before they are affected. Haber s law describes a simple linear relationship between concentration and time, as shown in Eq. (14.3). 

Prugh (1995) provides a concise summary of probit models for 28 chemicals. His summary shows a wide variability in coefficient and exponent values between different investigators. Schubach (1995) demonstrates that this results in a great variability in the prediaed consequences. Ten Berge et al. (1986) discuss the applicability of Haber s law and conclude that a concentration exponent of 1 does not fit the available data. 

Hoyle, G.W., Chang, W, Chen, J., et al., 2010. Deviations from Haber s Law for multiple measures of acute lung injury in chlorine-exposed mice. Toxicol. Sci. 118, 696-703. 

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