Mass balances, sulfur

Schmid et al. studied in detail the sulfonation reaction of fatty acid methyl esters with sulfur trioxide [37]. They measured the time dependency of the products formed during ester sulfonation. These measurements together with a mass balance confirmed the existence of an intermediate with two S03 groups in the molecule. To decide the way in which the intermediate is formed the measured time dependency of the products was compared with the complex kinetics of different mechanisms. Only the following two-step mechanism allowed a calculation of the measured data with a variation of the velocity constants in the kinetic differential equations. 

Evaporitic sulfur has a range of sulfur isotopic composition from +10%o to +30%o, while sedimentary sulfur is depleted in the heavy isotope and has a range of isotopic composition of about —40%o to +10%o. Most of this variation reflects systematic changes with geological age. The source fractions of a river water can be estimated from an isotopic mass balance ... 

To show mass balance, we add the molalities of each species containing a component (but not species concentrations in mg kg-1, since the mole weight of each species differs) to arrive at the input constraint. Taking component SO4 as an example, we find the total mole number (A/,) from the molalities (m, and m.j) of the sulfur-bearing species... 

In this chapter, we develop a mass balance model of the fractionation in reacting systems of the stable isotopes of hydrogen, carbon, oxygen, and sulfur. We then demonstrate application of the model by simulating the isotopic effects of the dolomitization reaction of calcite. 

Critical loads of sulfur and nitrogen, as well as their exceedances are derived with a set of simple steady-state mass balance (SSMB) equations. The first word indicates that the description of the biogeochemical processes involved is simplified, which is necessary when considering the large-scale application (the whole of Europe or even large individual countries like Russia, Poland or Ukraine) and the lack of adequate input data. The second word of the SSMB acronym indicates that only steady-state conditions are taken into account, and this leads to considerable simplification. These models include the following equations. 

The scaling tendency of the lime or limestone processes for flue gas desulfurization is highly dependent upon the supersaturation ratios of calcium sulfate and calcium sulfite, particularly calcium sulfate. The supersaturation ratios cannot be measured directly. They are determined by measuring experimentally the molalities of dissolved sulfur dioxide, sulfate, carbon dioxide, chloride, sodium and potassium, calcium, magnesium, and pH. Then by calculation, the appropriate activities are determined, and the supersaturation ratio is determined. Using the method outlined in Section IV, the concentrations of all ions and ion-pairs can be readily determined. The search variables are the molalities of bisulfite, bicarbonate, calcium, magnesium, and sulfate ions. The objective function is defined from the mass balance expressions for dissolved sulfur dioxide, sulfate, carbon dioxide, calcium, and magnesium. This equation is... 

NTS4 = NS02 + L (CS02 + CHS03m + CS032m) "Mass balance for sulfur(IV)... 

With emission source chemical signatures and corresponding aerosol or rainwater sample measurements PLS can be used Co calculate a chemical element mass balance (CEB). Exact emission profiles for the copper smelter and for a power plant located further upwind were not available for calculation of source contributions to Western Washington rainwater composition. This type of calculation Is more difficult for rainwater Chan for aerosol samples due Co atmospheric gas to particle conversion of sulfur and nitrogen species and due Co variations In scavenging efficiencies among species. Gatz (14) has applied Che CEB to rainwater samples and discussed Che effect of variable solubility on the evaluation of Che soil or road dust factor. 

Elucidation of the origin of sulfur in volcanic systems is complicated by the fact that next to SO2, significant amounts of H2S, sulfate and elemental sulfur can also be present. The bulk sulfur isotope composition must be calculated using mass balance constraints. The principal sulfur gas in equilibrium with basaltic melts at low pressure and high temperature is SO2. With decreasing temperature and/or increasing... 

Fine Aerosol Mass Balance. The temporal variations of fine particle mass, total carbon, elemental carbon, nitrogen, sulfur and for a typical summer period (August 4-10, 1979) and... 

A mass balance for fine particle aerosol can be calculated from the carbon, sulfur, nitrogen, and mass concentration data... 

After the zinc has been removed, the sulfuric acid rich solution is returned to dissolve the next batch of sludge. Over time, the sodium concentrations will read unacceptable levels in the electrolyte. A bleed stream from the zinc cells is constantly being neutralized and filtered. The saturated sodium sulfate solution thus created is crystallized out as sodium sulfate anhydrous for sale to the pulp and paper industry. Table one shows a complete mass balance for a typical batch. 

The bulk of the samples for this study came from TVA s Allen Steam Plant at Memphis, Tenn. The sampling points (Figure 4) included inlet air, coal, bottom ash, precipitator inlet, and outlet at the 268-ft stack level. During the 2-week sampling period the unit was operated under steady state conditions at 240 MW (12) with a uniform coal supply so that a mass balance might be established for a number of elements. All the coal from southern Illinois was washed and crushed so that 90% was less than 4 mesh. Nominal coal analysis indicated the following composition 9.5% moisture, 34% volatiles, 43% fixed carbon, 13% ash, and 3.4% sulfur. 

Table IV. Mass Balance Calculations for Sulfur Isotope and Total Sulfur Data. Yields are normalized to 1 g starting kerogen for both types of pyrolysis.

Chanton, J.P., and Martens, C.S. (1987a) Biogeochemical cycling in an organic-rich coastal marine basin. 7. Sulfur mass balance, oxygen uptake and sulfide retention. Geochim. Cosmochim. Acta 51, 1187-1199. 

The mass balance of water vapor is effected in the similar way as sulfur dioxide and leads to the following partial differential equation... 

The temporal change of the molar quantity of the element sulfur in the film on a fluidized-bed particle is caused by inflow and outflow of the material. This mass balance is needed only once, since the fluidized-bed particles and, thus, the liquid films on the particles are regarded as ideally mixed. The condition of the ideal mixing leads to the fact that with the mass and energy balance of the film, the average variables of state of the gas in the respective driving force approximations find the following form... 

For the determination of the unknown quantities in the liquid film, three further secondary conditions are needed. So, it is necessary to divide the molar masses of the sulfur and the calcium resulting from the mass balances in the film. A sulfur atom is bonded in hydrogen sulfite ion, molecular diluted sulfur dioxide, sulfite ion and calcium sulfite hemihydrate... 

In this study we have employed the simultaneous collection of atmospheric particles and gases followed by multielement analysis as an approach for the determination of source-receptor relationships. A number of particulate tracer elements have previously been linked to sources (e.g., V to identify oil-fired power plant emissions, Na for marine aerosols, and Pb for motor vehicle contribution). Receptor methods commonly used to assess the interregional impact of such emissions include chemical mass balances (CMBs) and factor analysis (FA), the latter often including wind trajectories. With CMBs, source-strengths are determined (1) from the relative concentrations of marker elements measured at emission sources. When enough sample analyses are available, correlation calculations from FA and knowledge of source-emission compositions may identify groups of species from a common source type and identify potential marker elements. The source composition patterns are not necessary as the elemental concentrations in each sample are normalized to the mean value of the element. Recently a hybrid receptor model was proposed by Lewis and Stevens (2) in which the dispersion, deposition, and conversion characteristics of sulfur species in power-plant emissions... 

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