Habers Law

Haber s law, or rule, was developed by Fritz Haber, a German chemist, in the early 1900s to characterise the acute toxicity of chemicals used in gas warfare. It states that identical products of concentration (C) of a gas in air and duration of exposure (t) will yield an identical biological response, ie. it assumes a linear response across all concentration levels, including 

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Born-Haber cycle A thermodynamic cycle derived by application of Hess s law. Commonly used to calculate lattice energies of ionic solids and average bond energies of covalent compounds. E.g. NaCl ... 

The lattice enthalpy of a solid cannot be measured directly. However, we can obtain it indirectly by combining other measurements in an application of Hess s law. This approach takes advantage of the first law of thermodynamics and, in particular, the fact that enthalpy is a state function. The procedure uses a Born-Haber cycle, a closed path of steps, one of which is the formation of a solid lattice from the gaseous ions. The enthalpy change for this step is the negative of the lattice enthalpy. Table 6.6 lists some lattice enthalpies found in this way. 

With his team organized, Haber began looking at the problem in its simplest form—at normal atmospheric pressure. After publishing some preliminary results, Haber met Walther Nernst at a scientific conference in Hamburg. Nernst, who was only four years older than Haber, had a pugnacious personality that made him quarrel with almost everyone in academia. Worried that Haber s work cast doubt on the validity of his new law of thermodynamics, Nernst publicly ridiculed Haber s highly erroneous data and told him scornfully to do his homework. ... 

Haber was slow to grasp the implications of the Nazis rise to power. As Germans boycotted Jewish businesses and Hitler s brownshirts removed Jewish students from university libraries and laboratories, the Nazis passed a law on April 7, 1933, to cleanse the civil service and universities of Jews. By this time, Haber s Kaiser Wilhelm Institute was financed by the government and its employees were treated as civil functionaries subject to the new law. Haber himself was exempt because of war work and seniority. Eager for a chemical warfare center, Nazi authorities singled out Haber s institute and ordered him to fire its Jews. At the same time, the Kaiser Wilhelm Society told Haber to somehow keep his important senior scientists. He had until May 2 to act. 

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... 

Finally, we look at indirect ways of measuring these energies. Both internal energy and enthalpy are state functions, so energy cycles may be constructed according to Hess s law we look also at Bom-Haber cycles for systems in which ionization processes occur. 

Hess s Law Applied to Ions Constructing Born-Haber Cycles... 

But what is the magnitude of the lattice enthalpy We cannot measure it directly experimentally, so we measure it indirectly, with a Hess s law energy cycle. The first scientists to determine lattice enthalpies this way were the German scientists Bom and Haber we construct a Born-Haber cycle, which is a form of Hess s-law cycle. 

The ionic model, developed by Bom, Lande, and Lennard-Jones, enables lattice energies (U) to be summed from inverse square law interactions between spherically symmetrical charge distributions and interactions following higher inverse power laws. Formation enthalpies are related to calculated lattice energies in the familiar Bom-Haber cycle. For an alkali fluoride... 

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. 

A Born-Haber cycle is the application of Hess s Law to the enthalpy of formation of an ionic solid at 298 K. Hess s law states that the enthalpy of a reaction is the same whether the reaction takes place in one step or in several. A Born-Haber cycle for a metal chloride (MCI) is depicted in Figure 1.56 the metal chloride is formed from the constituent elements in their standard state in the equation at the bottom, and by the clockwise series of steps above. From Hess s law, the sum of the enthalpy changes for each step around the cycle can be equated with the standard enthalpy of formation, and we get that ... 

The Bom—Haber Hess s law states that the enthalpy of a reaction is the same whether the reaction... 

TVThe Born-Haber cycle is an / V I example of Hess s law, introduced in Chapter 8. It is used to calculate properties that are impossible to measure directly. 

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