Aqueous-phase mass balances

Agitation for laboratory-scale resin preparation, drive systems, 441 Aqueous-phase mass balances, determination, 384-385 Arrhenius aaivatton parameters, calculation, 423,42 ... 

Rate of Formation of Primary Precursors. A steady state radical balance was used to calculate the concentration of the copolymer oligomer radicals in the aqueous phase. This balance equated the radical generation rate with the sum of the rates of radical termination and of radical entry into the particles and precursors. The calculation of the entry rate coefficients was based on the hypothesis that radical entry is governed by mass transfer through a surface film in parallel with bulk diffusion/electrostatic attraction/repulsion of an oligomer with a latex particle but in series with a limiting rate determining step (Richards, J. R. et al. J. AppI. Polv. Sci.. in press). Initiator efficiency was... 

Cy Cy, and a quat balance giving, Cgy = qo Cqx- Bulk-phase concentrations are coupled to the conditions within the catalyst through the boundary conditions. Bulk-phase mass balances are required to keep track of changes in the bulk-phase organic and aqueous reagent concentrations... 

The biocatalytic reduction step B in synthetic route B demands more raw materials (mass index S , see equation (5.1)) and generates more waste (environmental factor , see equation (5.2)) as compared to reduction step C (Figure 5.1). Solvents used to perform the extraction of the product from the aqueous phase in reduction step B are denoted as auxiliaries in Figure 5.1. These solvents and the aqueous phase dominate the mass balances as well as the environmental scores in Figure 5.2 (M4, M8). 

The actual volume of each phase in element AV is that of the total volume of the element, multiplied by the respective fractional phase holdup. Hence considering the direction of solute transfer to occur from the aqueous or feed phase into the organic or solvent phase, the mass balance equations become ... 

The countercurrent extraction is shown schematically in Figure 5.15. The organic course volume is denoted by O, and the corresponding aqueous flow volume is designated by A. The concentration of the extractable species are x and y in the aqueous and organic phases, respectively. There are n stages, and mass balance over them is ... 

In the manufacture of aniline from nitrobenzene the reactor products are condensed and separated into an aqueous and organic phases in a decanter. The organic phase is fed to a striping column to recover the aniline. Aniline and water form an azeotrope, composition 0.96 mol fraction aniline. For the feed composition given below, make a mass balance round the column and determine the stream compositions and flow-rates. Take as the basis for the balance 100 kg/h feed and a 99.9 percentage recovery of the aniline in the overhead product. Assume that the nitrobenzene leaves with the water stream from the base of the column. 

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 ... 

Equation (18) illustrates that the measured 5 Fe value for Fe(ll)jq is dependent not only on t Fe(iii)L-Fe(ii)Lj but On the proportion of Fe(III)-LFe(in) in the components that are open to isotopic exchange, which additionally includes Fe(II)-LFe(n) and Fe(ll)a, we will refer to these three components as the exchangeable pool of Fe in the system. We stress that the isotopic mass balance described by Equation (18) assumes that the ligand-bound Fe(lll) component is not sampled in the aqueous phase component, but instead exists as a component that is bormd to the cells. 

The mass balance of the aqueous phase concentration, C,w, yields ... 

Within either of the polymer-rich phases, borate esters and diesters of the functional groups are assumed to form with the same association constants as observed for the independent functional groups in aqueous solution. The resulting equations simply describe the borate ester association constants as well as mass balances on boron and polymer-bound functional groups. Wise and Weber used the model to estimate association constants for the borate esters formed with the diols in PVA and to predict the gelation of PVA-borate solutions. As we have independently measured the association constants for the borate esters formed in this work, we have used the model to estimate the radius of gyration of the GP3 dendrimer and to predict both the boron speciation in borate/GP3 solutions and the efficacy of PAUF using these functional dendrimers. 

For determination of phenol distribution coefficients the extraction proceeded for 15 minutes in order to reach equilibrium. The time required to reach equilibrium was determined by making five replicate injections of the headspace onto the SFC system. The first injection was after the extraction had proceeded for 15 minutes at 50°C and 100 atm. Following the equilibration time, four further injections at ten minute intervals were made, after which the pressure inside the extraction apparatus was increased and the system was again allowed to equilibrate (i.e. 15 minutes). The five replicate injection process was then repeated. The amount of phenol in each injection was then noted by referring to an external phenol standard calibration curve. As the total volume of the system was known, the amount of phenol in the SF could be calculated. The amount of phenol in the aqueous phase could then be calculated by mass balance. 

Various fluxes and processes considered in the following discussion are represented schematically in Figure 9.20, adapted from Wollast and Mackenzie (1983). Steady-state conditions require that the mass balance for each element is fulfilled for the entire system and also separately for the water and sedimentary columns. To write these mass balances, we must consider the global rate of the reactions occurring in the two subsystems. Therefore, we define R and D as the annual amount of a given element transferred from the solid phase to the aqueous phase or vice versa. The fluxes are taken as positive if there is a net input to seawater, and negative if there is a net output. To maintain the concentration of an element constant in seawater, the net flux resulting from Rj + + Lj + Pj in... 

Aeration and agitation are two important operations in animal cell culture. Oxygen has a low solubility in aqueous media, with a saturation concentration of approximately 7 mg Lr1 at 37°C. This implies that the oxygen must be provided continuously to the cultures, to ensure that the dissolved oxygen levels in the culture medium remain at an adequate level. The mass balance for oxygen in the liquid phase can be written as ... 

II.2. Charged Lyotropic Lamellar Liquid Crystals. In the case of a charged system, two changes in the system of eqs 17 must be made.80 81 First y should be replaced in eq 17a, for the surfactant, by y + fy=mole fraction of the surfactant in water, Xsw, should be replaced in the same equation by the mole fraction of the surfactant in water, in the vicinity of the interface CX SW). Assuming that the surfactant in the aqueous phase is totally dissociated, the concentration of surfactant near the interface (Xsw) can be related to the average surfactant concentration in the water phase, Xsw, by using the equilibrium and mass balance relations... 

It will be assumed that the surfactant molecules in the aqueous phase are completely dissociated and that then-presence in the water phase does not affect the potential given by eq B.2, since their concentration is very low. The condition of equilibrium and the mass balance of the surfactant in the water phase lead to the following expression for the concentration (XXf of surfactant ions near the interface, as a function of the average concentration of the surfactant in the water phase... 

Kosinski and Bostian (12) reported the extraction of lanthanum by HDEHP from aqueous nitrate solutions over a wide concentration range. Using mass balance data and IR analysis of the organic phase, they proposed three extraction reactions which occur simultaneously ... 

There are two factors that infiuence the particle formation conditions the adsorption of emulsifier on the droplets, which baves less emulsifier in the aqueous phase to facilitate particle formation-there, and the rate of radical absorption in monomer droplets. The former factor may be evaluated by talcing into account the adsorption isotherm of emulsifier on monomer droplets. Using a modified Langmuir adsorption isotherm in combination with a mass balance gives an expression for the aqueous phase concentration of emulsifier C... 

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