Equilibrium factor estimation

This inverse relationship between equilibrium factor and "unattached" fraction and their relationship to the resulting dose is important in considering how to most efficiently and effectively monitor for exposure. This inverse relationship suggests that it is sufficient to determine the radon concentration. However, it is not clear how precisely this relationship holds and if the dose models are sufficiently accurate to fully support the use of only radon measurements to estimate population exposure and dose. 

Some of the 220 detectors recently recovered have been analysed not only for radon exposure but also to determine the value of F (the equilibrium factor) in the houses. A preliminary set of such F factor results, obtained by analysing the inner and outer LR- 115 track densities of each detector, are presented in Table III for 12 houses with mean indoor radon concentrations greater than 200 Bq/nP. In Table III are also presented radon daughter doses estimated using the individually determined equilibrium factor values F together with the doses estimated on the basis of an assumed mean F factor value of 0.45. 

The question of whether exposure rates or doses should be used in evaluating all types of remedial procedures has so far received very little attention. For reasons of convenience the PAEC is normally used, sometimes even estimated from the radon concentration assuming a rather arbitrarily chosen value of the equilibrium factor. It seems reasonable to assume that this in certain cases may give a rather misleading description of the radiological conditions. 

The equilibrium factor F in low ventilated rooms without aerosol sources varied between 0.2 and 0.4 (Table la) with an average value near 0.30 a similar value as reported by Keller and Folkert, 1983, and by Wicke and Porstendorfer, 1982. In rooms with additional aerosol sources an average F-value between 0.4 and 0.5 was obtained (Table III). An error of about 20 % can be estimated for the equilibrium factor. 

Equilibrium factors were estimated from simultaneous measurements of radon gas and daughters when available. A default equilibrium factor of 0.3 was used when simultaneous gas and daughter values were not available. The default equilibrium factor is based on reported data for Salt Lake City (EPA, 1974) and on data obtained in Edgemont, South Dakota (Jackson et al., 1985), for climatic conditions similar to those in Salt Lake City. 

Another factor to be taken into account is the degree of over determination, or the ratio between the number of observations and the number of variable parameters in the least-squares problem. The number of observations depends on many factors, such as the X-ray wavelength, crystal quality and size, X-ray flux, temperature and experimental details like counting time, crystal alignment and detector characteristics. The number of parameters is likewise not fixed by the size of the asymmetric unit only and can be manipulated in many ways, like adding parameters to describe complicated modes of atomic displacements from their equilibrium positions. Estimated standard deviations on derived bond parameters are obtained from the least-squares covariance matrix as a measure of internal consistency. These quantities do not relate to the absolute values of bond lengths or angles since no physical factors feature in their derivation. 

The PAEC can be readily calculated once the activities of the individual radionuclides have been determined from measurements. Direct measurements of the concentrations of all short-lived decay products of Rn are difficult and limited. They are estimated from considerations of equilibrium (or disequilibrium) between Rn and its decay products. An equilibrium factor F is defined that permits the exposure to be estimated in terms of the PAEC from the measurement of radon gas concentration. This equilibrium factor is defined as the ratio of the actual PAEC to the PAEC that would prevail if all the decay products in each series were in equilibrium with the parent radon. However, it is simpler to evaluate this factor in terms on an equilibrium equivalent radon concentration, EEC. This quantity, EEC, represents the activity concentration of the radon gas that would have to exist in complete equilibrium with the decay products if the short-lived decay products had the same PAEC as in the nonequilibrium mixture. The units of EC are Bqm . ... 

Many measurements have been made of Rn and decay product concentrations, allowing estimates to be made of the magnitude of the equilibrium factor to be estimated in terms of both typical values and range. In general, it is unusual to find equilibrium factors less than 0.2, even in well-ventilated rooms or mines. For this reason, it is common practice to measure the concentration of radon gas, which is then used to infer the concentration of its decay products by using a known value for the equilibrium factor. This is highest for outdoor air, followed by those of indoor air and air in mines. 

A more interesting possibility, one that has attracted much attention, is that the activation parameters may be temperature dependent. In Chapter 5 we saw that theoiy predicts that the preexponential factor contains the quantity T", where n = 5 according to collision theory, and n = 1 according to the transition state theory. In view of the uncertainty associated with estimation of the preexponential factor, it is not possible to distinguish between these theories on the basis of the observed temperature dependence, yet we have the possibility of a source of curvature. Nevertheless, the exponential term in the Arrhenius equation dominates the temperature behavior. From Eq. (6-4), we may examine this in terms either of or A//. By analogy with equilibrium thermodynamics, we write... 

The differenee in reaction rates of the amino alcohols to isobutyraldehyde and the secondary amine in strong acidic solutions is determined by the reactivity as well as the concentration of the intermediate zwitterions [Fig. 2, Eq. (10)]. Since several of the equilibrium constants of the foregoing reactions are unknown, an estimate of the relative concentrations of these dipolar species is difficult. As far as the reactivity is concerned, the rate of decomposition is expected to be higher, according as the basicity of the secondary amines is lower, since the necessary driving force to expel the amine will increase with increasing basicity of the secondary amine. The kinetics and mechanism of the hydrolysis of enamines demonstrate that not only resonance in the starting material is an important factor [e.g., if... 

Various amines find application for pH control. The most commonly used are ammonia, morpholine, cyclohexylamine, and, more recently AMP (2-amino-2-methyl-l-propanol). The amount of each needed to produce a given pH depends upon the basicity constant, and values of this are given in Table 17.4. The volatility also influences their utility and their selection for any particular application. Like other substances, amines tend towards equilibrium concentrations in each phase of the steam/water mixture, the equilibrium being temperature dependent. Values of the distribution coefficient, Kp, are also given in Table 17.4. These factors need to be taken into account when estimating the pH attainable at any given point in a circuit so as to provide appropriate protection for each location. 

The factor a has been estimated by measuring the concentration of carbon dioxide in the gas phase and in the film at equilibrium. 

In this exercise we shall estimate the influence of transport limitations when testing an ammonia catalyst such as that described in Exercise 5.1 by estimating the effectiveness factor e. We are aware that the radius of the catalyst particles is essential so the fused and reduced catalyst is crushed into small particles. A fraction with a narrow distribution of = 0.2 mm is used for the experiment. We shall assume that the particles are ideally spherical. The effective diffusion constant is not easily accessible but we assume that it is approximately a factor of 100 lower than the free diffusion, which is in the proximity of 0.4 cm s . A test is then made with a stoichiometric mixture of N2/H2 at 4 bar under the assumption that the process is far from equilibrium and first order in nitrogen. The reaction is planned to run at 600 K, and from fundamental studies on a single crystal the TOP is roughly 0.05 per iron atom in the surface. From Exercise 5.1 we utilize that 1 g of reduced catalyst has a volume of 0.2 cm g , that the pore volume constitutes 0.1 cm g and that the total surface area, which we will assume is the pore area, is 29 m g , and that of this is the 18 m g- is the pure iron Fe(lOO) surface. Note that there is some dispute as to which are the active sites on iron (a dispute that we disregard here). 

The reboiler, and a partial condenser if used, act as equilibrium stages. However, when designing a column there is little point in reducing the estimated number of stages to account for this they can be considered additional factors of safety. 

At a pressure of 10 bar, determine the bubble and dew point of a mixture of hydrocarbons, composition, mol per cent n-butane 21, n-pentane 48, n-hexane 31. The equilibrium K factors can be estimated using the De Priester charts in Chapter 8. 

Using the pKa and the estimated So, the DTT procedure simulates the entire titration curve before the assay commences. Figure 6.7 shows such a titration curve of propoxyphene. The simulated curve serves as a template for the instrument to collect individual pH measurements in the course of the titration. The pH domain containing precipitation is apparent from the simulation (filled points in Fig. 6.7). Titration of the sample suspension is done in the direction of dissolution (high to low pH in Fig. 6.7), eventually well past the point of complete dissolution (pH <7.3 in Fig. 6.7). The rate of dissolution of the solid, described by the classical Noyes-Whitney expression [37], depends on a number of factors, which the instrument takes into account. For example, the instrument slows down the rate of pH data taking as the point of complete dissolution approaches, where the time needed to dissolve additional solid substantially increases (between pH 9 and 7.3 in Fig. 6.7). Only after the precipitate completely dissolves, does the instalment collect the remainder of the data rapidly (unfilled circles in Fig. 6.7). Typically, 3-10 h is required for the entire equilibrium solubility data taking. The more insoluble the... 

Step 4 Estimate the effectiveness factor i) for the removal and the cleanup time required to obtain a residual toluene concentration of 150 mg/L. The phase distribution calculations carried out in Step 2 indicate that the equilibrium concentration of toluene in the gas phase is Ca equil = 109 mg/L (see Table 14.4). The concentration measured in the extracted air during the field tests is lower, at Q,flew = 78 mg/L, indicating that the removal effectiveness is limited either as a result of mass transfer phenomena or the existence of uncontaminated zones in the airflow pattern. The corresponding effectiveness factor is T = 78/109 = 0.716. 

The Rvalues are partition coefficients. The assumption that these are real constants Is seldom completely true, of course, because equilibrium Is rarely achieved and because the equilibrium ratios generally are not the same for all concentration levels. Moreover, It Is difficult to find the needed Information, and one must often accept a single literature value as typical of a given Intermedia transfer. When the organic content of the soli Is known or can be accurately estimated, one can usually derive Kgw from a compound s aqueous solubility, S, or Its octanol/water partition coefficient, KQW (14) Values of Kpa, namely "bloconcentratlon factors" between feed and meat animals (15,16), can also be derived from S or KQW. Bloconcentratlon factors between water and fish are well documented (14) A considerable weakness exists In our perception of the proper estimates to use for partition coefficients between soli and edible crop materials. Thus, at one time, two of the present authors used a default value of Kgp = 1 for munitions compounds that are neither very soluble In water nor very Insoluble (4) at another time, a value of was assumed for compounds with very low values of Ksw, l.e., polybromoblphenyls (6). 

Then the unattached fraction was calculated in each measurement and was found to be between. 05 and. 15 without aerosol sources in the room and below. 05 in the presence of aerosol sources. The effective dose equivalent was computed with the Jacobi-Eisfeld model and with the James-Birchall model and was more related to the radon concentration than to the equilibrium equivalent radon concentration. On the basis of our analysis a constant conversion factor per unit radon concentration of 5.6 (nSv/h)/(Bq/m ) or 50 (ySv/y)/(Bq/m3) was estimated. 

The data of Loukidou et al. (2004) for the equilibrium biosorption of chromium (VI) by Aeromonas caviae particles were well described by the Langmuir and Freundlich isotherms. Sorption rates estimated from pseudo second-order kinetics were in satisfactory agreement with experimental data. The results of XAFS study on the sorption of Cd by B. subtilis were generally in accord with existing surface complexation models (Boyanov et al. 2003). Intrinsic metal sorption constants were obtained by correcting the apparent sorption constants by the Boltzmann factor. A 1 2 metal-ligand stoichiometry provides the best fit to the experimental data with log K values of 6.0 0.2 for Sr(II) and 6.2 0.2 for Ba(II). 

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