Mass balance considerations

Mass balance considerations apply tlie law of tlie conservation of mass to account for each constituent entering and leaving a system. Constituents that do not comprise the product are either retained by the system or released from tlie system as waste. This method requires a quantitative analysis of the influent and effluent streams and an understanding of chemical reactions occurring within tlie system. 

Low-temperature, photoaggregation techniques employing ultraviolet-visible absorption spectroscopy have also been used to evaluate extinction coefficients relative to silver atoms for diatomic and triatomic silver in Ar and Kr matrices at 10-12 K 149). Such data are of fundamental importance in quantitative studies of the chemistry and photochemistry of metal-atom clusters and in the analysis of metal-atom recombination-kinetics. In essence, simple, mass-balance considerations in a photoaggregation experiment lead to the following expression, which relates the decrease in an atomic absorption to increases in diatomic and triatomic absorptions in terms of the appropriate extinction coefficients. 

With mass balance consideration, along with Eqs. (2b), (5b) and (7), Eq. (6) may be transformed into ... 

From the mass balance considerations, the cell monolayer concentration is... 

For carrier-based ISEs, the selectivity is determined by the composition of the membrane. Eq. (18a.l8) describes the relationship between the ion selectivity and the membrane composition of cation-selective membranes by using charge balance and mass balance considerations [69]. 

Adsorption phenomena frequently are studied by measuring solely the change in concentration of a species i in the aqueous solution phase. Simple mass-balance considerations (1) show that Equation 1 can be rewritten in a form compatible with this methodology ... 

Presently, the method cannot tolerate high hydrocarbon concentrations in the flue gas for two reasons firstly, the mass balance considerations secondly, the water vapour measurements are violated. Consequently, a hydrocarbon sensor would be needed. 

The first check is to see whether the information presented is self-consistent and that all the dye injected has flowed out of the system. Problems in carrying out this check may be expected because, from the tabulated data, it is evident that the tracer response has a long tail which is still present to a small extent after 20 min, after which time no more data are available. From mass balance considerations... 

The composition profile is approximated by a step profile, with a uniform composition xf in the surface layer (0bulk phase x, at z>L. It is assumed that the total amount of liquid can be divided into two parts with the first constituting the homogeneous bulk phase (mole numbers in it n° = til -I- 2) and the remainder standing under the influence of the forces emanating from the solid surface causing adsorption (mole numbers, referred to unit mass of adsorbent, = n, -i- 2 the superscript a referring to adsorption) [17]. Simple mass balance considerations lead to the following expressions [12] ... 

From mass balance considerations, the total concentration of X is given by... 

Inhomogeneous systems. If Eq. 21-46 is an inhomogeneous system, that is, if at least one Ja is different from zero, then usually all eigenvalues are different from zero and negative, at least if the equations are built from mass balance considerations. Again, the eigenvalue with the smallest absolute size determines time to steady-state for the overall system, but some of the variables may reach steady-state earlier. In Illustrative Example 21.6 we continue the discussion on the behavior of tetrachloroethene (PCE) in a stratified lake (see also Illustrative Example 21.5). Problem 21.8 deals with a three-box model for which time to steady-state is different for each box. 

In the work of Schott et al. (1981), two kinds of layers were considered (Table 7.3). The first type was assumed to be completely depleted of either Ca or Mg. With the second type, a linear increase in cationic concentrations with depth was assumed. In either case, the layer thicknesses were only of atomic dimensions. Schott et al. (1981) also compared these layer thicknesses to those calculated based on solution chemistry analyses and mass balance considerations. Thicknesses of totally cation-depleted leached layers (pH=6) were 0.2 nm for Mg in enstatite, 1.7 nm for Ca in diopside, and 1.4 nm for Ca in tremolite. 

Assumption 5.2. The net rates at which the components 1,..., C — 1 are separated from the recycle loop, as well as the nominal flow rate of the product stream, are of comparable magnitude. Also, from mass-balance considerations, they are of the same magnitude as the flow rate of the process feed stream ... 

Assessment by mass balance considerations under equilibrium conditions... 

The use of these diffusion models to progress the evaluation process of a food packaging plastic will be discussed shortly. In those cases where assessment by mass balance considerations under equilibrium conditions, including partitioning effects, does not provide a clear picture of the plastics conformity status, then the different diffusivities of polymer types and the influence of the migrant molecule size or its molecular weight on its mobility within a plastic can be taken into account to achieve more distinguished views on QM/SML ratios. 

Calculate the compositions of the exiting raffinate and extract streams. Replot (or trace) Fig. 9.1 without the tie lines (Fig. 9.3). On Fig. 9.3, plot the mean-concentration point M. Now from mass-balance considerations, the exit concentrations must lie on the two phase-boundary lines and on a straight line passing through the mean concentration point. We know we want the water phase to have an exit concentration of 3 wt % alcohol. Such a concentration corresponds to point Ln on the graph. At point LN. the ether concentration is seen to be 7.6 wt % (this can be found more accurately in the present case by numerical extrapolation of the water-phase data in Table 9.1). Therefore, the composition of the raffinate stream is 3% alcohol, 7.6% ether, and (by difference) 89.4% water. 

Tlicre are four nicthods tliat can be used to determine a chemical health liazard. Tliese nicthods are emission factors, mass balance considerations, engineering calculations, and direct emission nieasureinents. Describe each of tliese approaches. 

Higuchi and Misra consider a bimodal emulsion with n2 droplets of radius r2 and ni droplets of radius ri. From the above equations and mass balance considerations the rate of change of the small sized droplets (r- ) was found to be ... 

Mass Balance Considerations. The values of ER for the Fischer assay spent shale are contained in Table V. If it is assumed that the relative standard deviation in the analyses is 10%, then the relative probable error in ER would be 14% if the analytical errors were indeterminant and 20% if the errors were determinant (38). The mass ratio of OS-l/FS is 1.24 as derived from the assay data in Table I. It is not possible to conclude that any trace elements are mobilized from the solid material during the assay retorting. The ER results obtained for arsenic, selenium, and molybdenum indicate the importance of analytical precision in detecting any trace element mobilization during oil shale retorting. The values of RI contained in Table V show a similar dependence on analytical precision. The probable errors in these values are also between 14 and 20% if the relative standard deviation in the analytical results is assumed to be 10%. These results indicate that, within experimental error, none of the trace elements have been lost during Fischer assay. More definitive conclusions on whether elements are mobilized or lost can only be reached with more precise analytical... 

The two elements calcium and aluminum are RLEs. The assumption is usually made that aU RLEs are present in the primitive mantle of the Earth in chondritic proportions. Chondritic (undifferentiated) meteorites show significant variations in the absolute abundances of refractory elements but have, with few exceptions discussed below, the same relative abundances of lithophile and siderophile refractory elements. By analogy, the Earth s mantle abundances of refractory lithophile elements are assumed to occur in chondritic relative proportions in the primitive mantle, which is thus characterized by a single RLE/Mg ratio. This ratio is often normalized to the Cl-chondrite ratio and the resulting ratio, written as (RLE/Mg)N, is a measure of the concentration level of the refractory component in the Earth. A single factor of (RLE/Mg) valid for all RLEs is a basic assumption in this procedure and will be calculated from mass balance considerations. 

Mass-balance considerations, in particular the observed consumption of contaminants, were useful in showing the importance of biodegradation processes for limiting the mobility of petroleum hydrocarbons in groundwater systems. The mass-balance approach also contributed to our understanding of the environmental fate of chlorinated solvents in groundwater systems. In the 1980s, the observed behavior of chlorinated... 

A simple use of mass-balance considerations that shows this net transformation of chlorinated ethenes is the observed accumulation of chloride in contaminant plumes. For example, in a study of a large plume of TCE-contaminated groundwater at Dover Air Force Base, Delaware, Witt et al. (2002) showed that the concentration of chloride increased as TCE concentrations decreased, suggesting the net transformation of the chlorine in TCE to chloride. This chloride tracer of chlorinated ethene biodegradation is of use for mass-balance calculations to demonstrate biodegradation processes in the held. These held observations formed the basis of experimental studies under controlled laboratory conditions that documented the many and varied microbial processes that transform and destroy chlorinated ethenes in groundwater systems. 

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