Equilibrium factor variations

From the measured indoor Rn-222 concentration during the heating season, measurements of equilibrium factors and assessments of the seasonal variations, it is possible to assess population averaged indoor concentrations of Rn-222 progeny in Norwegian dwellings. 

Figure 1. Variations in the hourly mean alpha-energy concentration during an integrating radon gas measurement of three weeks The alpha-energy concentration calculated from the radon level (4860 Bq/m3) and the typical equilibrium factor (0.45) is also given.

Consideration of the inverse variation of equilibrium factor and unattached fraction in room air leads to a relatively constant dose per unit concentration of radon gas, which facilitates the interpretation of monitoring data. 

Figure 11. Variation of unattached fraction of potential alpha-energy and equilibrium factor according to a model of room aerosol behaviour and the effect on bronchial dose rate per unit radon gas concentration.

Next we consider how to evaluate the factor 6p. We recognize that there is a local variation in the Gibbs free energy associated with a fluctuation in density, and examine how this value of G can be related to the value at equilibrium, Gq. We shall use the subscript 0 to indicate the equilibrium value of free energy and other thermodynamic quantities. For small deviations from the equilibrium value, G can be expanded about Gq in terms of a Taylor series ... 

Finally, the total preexponential factor includes the stoichimetry deviation represented by c°(, or c° so an extrapolated Arrhenius plot will show an intercept which is very sensitive to composition. Experimental data will be hard to reproduce both because of stoichiometry variations and because of the slow approach to thermal equilibrium. 

This ease with which we can control and vary the concentrations of H+(aq) and OH (aq) would be only a curiosity but for one fact. The ions H+(aq) and OH (aq) take part in many important reactions that occur in aqueous solution. Thus, if H+(aq) is a reactant or a product in a reaction, the variation of the concentration of hydrogen ion by a factor of 1012 can have an enormous effect. At equilibrium such a change causes reaction to occur, altering the concentrations of all of the other reactants and products until the equilibrium law relation again equals the equilibrium constant. Furthermore, there are many reactions for which either the hydrogen ion or the hydroxide ion is a catalyst. An example was discussed in Chapter 8, the catalysis of the decomposition of formic acid by sulfuric acid. Formic acid is reasonably stable until the hydrogen ion concentration is raised, then the rate of the decomposition reaction becomes very rapid. 

In discussing the elFect of structure on the stabilization of alkyl cations on the basis of the carbonylation-decarbonylation equilibrium constants, it is assumed that—to a first approximation—the stabilization of the alkyloxocarbonium ions does not depend on the structure of the alkyl group. The stabilization of the positive charge in the alkyloxocarbonium ion is mainly due to the resonance RC = 0 <-> RC = 0+, and the elFect of R on this stabilization is only of minor importance. It has been shown by Brouwer (1968a) that even in the case of (tertiary) alkylcarbonium ions, which would be much more sensitive to variation of R attached to the electron-deficient centre, the stabilization is practically independent of the structure of the alkyl groups. Another argument is found in the fact that the equilibrium concentrations of isomeric alkyloxocarbonium ions differ by at most a factor of 2-3 from each other (Section III). Therefore, the value of K provides a quantitative measure of the stabilization of an alkyl cation. In the case of R = t-adamantyl this equilibrium constant is 30 times larger than when R = t-butyl or t-pentyl, which means that the non-planar t-adamantyl ion is RT In 30= 2-1 kcal... 

There is another explanation for the variations in values of sulfide sulfur. It was cited that oxidation state (/02) od pH of ore fluids are important factor controlling values of ore fluids (e.g., Kajiwara, 1971). According to the sulfur isotopic equilibrium model (Kajiwara, 1971 Ohmoto, 1972), of sulfides in predominance... 

F varies from 0.1, when only 218Po is present, to unity at equilibrium. Figure 5 shows the changes in the aggregate radon decay-product concentration, the concentration of 218Po, and the variation in F achieved by operating the electrostatic precipitators. The radon decay-product concentration was reduced by more than a factor of 10. 

Fig. 2. Variation of the logarithms of the rate factors (23) and (24) for charge-state changes as the band potential, and hence the height of the hydrogen donor level eD is changed (a) relative to an equilibrium Fermi level eF for the carriers or (b) relative to an arbitrary level, when the electron and hole Fermi levels eFe and rFh, respectively, are made different by application of a reverse bias to a p-n junction.

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