Mass balance equivalent

Mass balance equivalent (MBE). The total concentration of a reagent should be equal to the sum of various species generated by it... 

Urea Pharmacokinetics. Pharmacokinetics summarizes the relationships between solute generation, solute removal, and concentration in a patient s blood stream. In the context of hemodialysis, this analysis is most readily appHed to urea, which has, as a consequence, become a surrogate for other uremic toxins in the quantitation of therapy and in attempts to describe its adequacy. In the simplest case, a patient is assumed to have no residual renal function. Urea is generated from the breakdown of dietary protein, accumulates in a single pool equivalent to the patient s fluid volume, and is removed uniformly from that pool during hemodialysis. A mass balance around the patient yields the following differential equation ... 

These equations can be solved simultaneously with the material balance equations to obtain x[, x, xf and x1,1. For a multicomponent system, the liquid-liquid equilibrium is illustrated in Figure 4.7. The mass balance is basically the same as that for vapor-liquid equilibrium, but is written for two-liquid phases. Liquid I in the liquid-liquid equilibrium corresponds with the vapor in vapor-liquid equilibrium and Liquid II corresponds with the liquid in vapor-liquid equilibrium. The corresponding mass balance is given by the equivalent to Equation 4.55 ... 

In this study, 4.4 mg of lead equivalent was applied to the skin under a covered wax/plastic patch on the forearms of human subjects of the applied dose, 1.3 mg of lead was not recovered from skin washings. The amount that actually remained in (or on) the skin and the mass balance of the fate of this lead was not determined it may have been absorbed or eliminated from the skin by exfoliation of epidermal cells. Thus, while this study provides evidence for dermal absorption of lead, it did not quantity the fraction of applied dose that was absorbed. The quantitative significance of the dermal absorption pathway as a contributor to lead body burden remains an uncertainty. The wax/plastic patch provided a means by which the lead compounds could permeate or adhere to the skin. The effect of concentration in aqueous solution may cause skin abrasion through enhanced acidity since the lead ion is acidic. Abraded skin is known to promote subsequent higher lead penetration. 

As originally derived, however, the mass balance model has an important (and well acknowledged) limitation implicit in its formulation is the assumption that fluid and minerals in the modeled system remain in isotopic equilibrium over the reaction path. This assumption is equivalent to assuming that isotope exchange between fluid and minerals occurs rapidly enough to maintain equilibrium compositions. 

Novel general expressions were developed for the description of the behaviour of the height equivalent of a theoretical plate in various chromatographic columns such as unpacked (open capillary), packed with spherical nonporous particles and packed with spherical porous adsorbent particles. Particles may have unimodal or bimodal pore size distribution. The expression describing the mass balance in open capillaries is... 

The data of Table 8.4 are also shown in Fig. 8.6, which is shown as an equilibrium isotherm, an operating line, and a series of steps between the operating line and the isotherm. These steps are entirely equivalent to the lines establishing the mass balances for each stage in Figs. 8.3 and 8.5. For instance, the horizontal line AB represents while the ver-... 

In the reaction profile shown in Figure 1 (similar to that shown by Smith et al. (10)) the initial product was azoxybenzene. However this figure is deceptive firstly azoxybenzene may be produced by a non-catalyzed reaction between nitrosobenzene and phenyl hydroxylamine (10), secondly the figure does not show the mass balance. Indeed at 10 min when all nitrosobenzene has been removed from the solution the amount of azoxybenzene formed was 18.6 mmol, equivalent to 37.2 mmol of reacted nitrosobenzene. Therefore, 42.8 mmol of the original 80 mmol of nitrosobenzene (53.5 %) were unaccounted for. It is possible that the missing mass is in the form of phenyl hydroxylamine in solution, which continues to disproportionate to produce aniline and nitrosobenzene and subsequently azoxybenzene and azobenzene. However as we shall subsequently discover this interpretation is unsustainable. 

An integral constraint, based on overall mass conservation, may be derived that is equivalent to one of the boundary conditions. The velocity profile u must satisfy an overall mass balance (per unit width of channel), given as... 

At the a/p phase boundary, an equivalent mass balance condition in terms of the boundary velocity is... 

Mass balance The situation in which the measured mass of parent and other reactant(s) consumed is equivalent to the measured increase in mass of degradation product(s) i.e., MP>0 - MP>X = Mi x — Mi Q... 

Molar mass balance The situation in which the measured increase in moles of degradation product(s) is equivalent to that predicted via a balanced chemical reaction from the number of moles of parent consumed. For a degradation reaction ... 

Just as an ordinary chemical equation is a shortened version of the complete thermochemical equation which expresses both energy and mass balance, each nuclear equation has a term (written or implied) expressing energy balance. The symbol Q is usually used to designate the net energy released when all reactant and product particles of matter are at zero velocity. Q is the energy equivalent of the mass decrease (discussed above) accompanying the reaction. Q is usually expressed in MeV. 

This approach is based on the similarity between a TCC and a SMB unit, such that the flow rates in a TCC can be converted easily to the equivalent ones in a SMB unit. In the frame of equilibrium theory - that is, a model assuming one-dimensional flow - adsorption equilibrium between solid and liquid phase and neglecting axial dispersion, the following mass balances are obtained for each component i in every section j of a TCC unit ... 

Equation 4 is equivalent to Fick s second law (non-stationary diffusion), expanded by an additional source term which accounts for the production or consumption of species i caused by chemical transformations. Similar to this mass balance, an enthalpy balance may be also derived ... 

A first model is used to compute the flowrates allowing to perform the separation with the greatest productivity. Then, the "mixed cell in series" model takes into account thermodynamic, hydrodynamic and kinetic properties of the system and compute the concentration profile inside the columns [14], In this model, we make the assumptions that the pressure drop inside the column is negligible compared to the pressure drop realized and controlled with the analogical valves, and we model the true moving bed assuming that the performance of SMB and TMB are equivalent. A mass balance equation is written for each stage and a classical Newton Raphson numerical method is used to solve the permanent state of the process [14],... 

It is important to realize that any distribution of chemical potentials satisfying Eq. (51) (in the discrete case) or Eq. (60) corresponds to an equilibrium composition. Of course, given an initial value M or M(y), infinitely many of such equilibrium compositions will not satisfy the mass balance condition [Eq. (40) or its equivalent continuous form]. 

The amount of nitrogen in the upper mantle is therefore 1.6 X 10 ° g, which is only 3% that in the crust and atmosphere. The MORE flux is equivalent to a flux of 5.0 X 10 °molyr or 9% of the surface N2 over 4.5 Ga. Note that Javoy (1998) argued that nitrogen is relatively compatible, with an upper-mantle concentration of up to 40 ppm (Cartigny et ai, 2001). However, this is from mass balance calculations based upon model assumptions that volatiles in the upper mantle and on the surface are a mixture of enstatite chondrites and a late veneer of Cl chondrites, and such a model has not been widely adopted. 

---