Haber s relationship

The most detailed study of Haber s relationship with BASF is Carsten Reinhardt, fiber Wissenschaft und Wirtschaft. Fritz Habers Zusammenarbeit mit der BASF 1908 bis 1911, in Albrecht, op. cit. (4), Naturwissenschaft und Technik in der Geschichte, pp. 287-315. This is also a useful source of references to the German literature on Haber s ammonia work, including historical and historiographical accounts. 

Chemistry s relationship to the public is unique among the sciences. Chemistry s products become part of our everyday lives and are profoundly intertwined with society s tastes, needs, and desires. Fritz Haber s ammonia for fertilizing crops helped raise chemistry s prestige to such a peak early in the twentieth century that an adoring public supported the massive deploy-... 

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. 

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. 

In studies eondueted by Bide and Risk (2004), male CD-I strain miee were exposed whole body to GB for time periods ranging from 20 to 720 min. LC50 values for 3-12 h were progressively higher (toxicity lower) than that predieted by either Haber s rule or the Ten Berge relationship (Ten Berge et al, 1986). In studies eondueted by Anthony et al. (2004), male and female SD rats were exposed whole... 

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... 

A key element in the procedure of time scaling is the use of a value or values for n in the equation C" x t = k. If empirical data for exposure durations other than the AEGL-specified exposure periods are available to quantify the exposure concentration-exposure duration relationships for a health-effect endpoint, including lethality, the value of n should be derived using the method of calculation described in this section. It is believed that empirically derived values of n are scientifically more credible than a default value of n = 1 (Haber s rule) or attempting to derive an alternate value of n. 

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... 

Ludwig Haber s book [859a] provides a modern, incisive and detailed analysis of the casualty statistics for World War I, and has been used here as the most reliable source available. Fig. 1.17 illustrates the estimated gas casualities, and Fig. 1.18 shows parallel data for gas deaths. The total number of casualties estimated by Haber (just over half-a-million) [859a] is less than half of Prentiss estimate (ca. 1,300,000) [1660]. In a similar relationship,... 

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. 

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). 

Chemists carried out studies of this kind on other chemical systems in the nineteenth century before Haber s work. In 1864, Cato Maximilian Guldberg (1836—1902) and Peter Waage (1833—1900) postulated their law of mass action, which expresses, for any reaction, the relationship between the concentrations of the reactants and products present at equilibrium. Suppose we have the general equilibrium equation... 

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