Mass balance concentrations

Nearly every supplier of evaporation equipment and systems maintains a pilot plant facility where, for a fee, different evaporation schemes can be set up. Data obtained from several days of testing on small laboratory or pilot plant units can be good predictors of evaporator performance, and these data are very helpful in the scaling-up calculations for production-sized installations. Samplers obtained from the test work can be used to check the mass balances, concentrations, and product quality. Serious operational problems like foaming, plugging, and fouling can occur in even short pilot plant tests and can point to the need for alternative evaporator types or modified designs. 

Besides equilibrium constant equations, two other types of equations are used in the systematic approach to solving equilibrium problems. The first of these is a mass balance equation, which is simply a statement of the conservation of matter. In a solution of a monoprotic weak acid, for example, the combined concentrations of the conjugate weak acid, HA, and the conjugate weak base, A , must equal the weak acid s initial concentration, Cha- ... 

From the ladder diagram it appears that we may safely assume that the concentrations of H2L+ and L are significantly smaller than that for HL, allowing us to simplify the mass balance equation to... 

Note that in writing this mass balance equation, the concentration of Ag(NH3)2i" must be multiplied by 2 since two moles of NH3 occurs per mole of Ag(NH3)2i". The second additional equation is a mass balance on iodide and silver. Since Agl is the only source of N and Ag+, every iodide in solution must have an associated silver ion thus... 

At any pH a mass balance requires that the total concentration of unbound EDTA equal the combined concentrations of each of its forms. 

We can account for the effect of an auxiliary complexing agent, such as NH3, in the same way we accounted for the effect of pH. Before adding EDTA, a mass balance on Cd + requires that the total concentration of Cd +, Ccd, be... 

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 ... 

To illustrate the development of a physical model, a simplified treatment of the reactor, shown in Fig. 8-2 is used. It is assumed that the reac tor is operating isothermaUy and that the inlet and exit volumetric flows and densities are the same. There are two components, A and B, in the reactor, and a single first order reaction of A B takes place. The inlet concentration of A, which we shall call Cj, varies with time. A dynamic mass balance for the concentration of A (c ) can be written as follows ... 

Figure 24-23 is a sketch of continuous culture with recycle. The symbols for flow rates and organism concentrations are F and X, respec tively Assuming perfect mixing and steady state so that the derivatives can be set to zero, mass balances lead to ... 

Kinetics The capacity and efficiency of biofilter operation is a function of active surface area, filter void space, target removal efficiency, gas species, gas concentration, and gas flow rate. A simphfied theoretical model described by S.P.P. Ottengraf et al. is schematically represented by in Fig. 25-18. The mass balance made around the hq-uid-phase biolayer can be described as follows ... 

This is accomplished by measuring the rate at constant temperature and at various concentrations by varying the feed rate. Calculating 0, multiplying by the measured slope at the calculated 0, and then adding one gives the derivative of the mass balance rate with regard to concentration. 

If the concentration of the chemical in the wastestream was measured by monitoring equipment and the flow rate of the wastestream was determined by mass balance, then the primary basis of estimate is "monitoring" (M). Even though a mass balance calculation also contributed to the estimate, "Monitoring should be indicated because monitoring data was used to estimate the concentration of the waste stream. 

Mass balance (C) should only be indicated it it is directly used to calculate the mass (weight) of chemical released. Monitoring data should be indicated as the basis of estimate only if the chemical concentration is measured in the wastestream being released into the environment. Monitoring data should flfll be indicated, for example, if the monitoring data relates to a concentration of the toxic chemical in other process streams within the facility. 

The facility wastewater monitoring program does not determine the concentration of lead and lead compounds in the scrubber discharge water, and releases to the surface impoundment (releases to land) must be calculated using mate-riai balance information. These releases to land are determined from the amount of lead removed by the scrubber (using the efficiency data provided by the scrubber manufacturer). The volume of the scrubber blowdown Is found to be 1,500 pounds per year. Enter the estimate of the amount of lead and lead compounds released to surface Impoundments in the space provided in Part III, Section 5.5.3 of the form. Because releases of lead to the surface Impoundment are greater than 999 pounds per year, you must enter the actual calculated amount in column A.2 of Section 5.5.1. The basis for the estimate of releases to the surface impoundment, entered in column B of Section 5, is mass balance calculations (code C). 

The following differential equation (or something similar), derived from a mass balance for the room, is solved to find the correlation between flow rates, source rate, contaminant concentrations, cleaning efficiency, and time. 

Capture efficiency can also be measured by first estimating workspace emission rates and local exhaust emissions. The local exhaust emission rate equals the duct concentration (mass/volume) multiplied by the duct flow rate (volume/time). The workspace emission rates can be calculated using appropriate mass balance models and measured ventilation rates and workspace concentrations. Capture efficiency is the ratio of duct emission rate to total emission rate (duct plus workspace). ... 

The tracer is injected into the duct at a constant rate and mixed with the flowing air. The concentration of the air-tracer mixture is measured further downstream. Assuming perfect mixing and that the air entering the test section has a zero concentration, the air volume flow rate can be calculated based on the mass balance of the tracer... 

The first, and simplest, step in predicting crystallizer performance is the calculation of crystal yield. This can easily be estimated from knowledge of solution concentration and equilibrium conditions permitting calculation of the overall mass balance... 

It has been shown that an increase in crystallizer residence time, or decrease in feed concentration, reduces the working level of supersaturation. This decrease in supersaturation results in a decrease in both nucleation and crystal growth. This in turn leads to a decrease in crystal surface area. By mass balance, this then causes an increase in the working solute concentration and hence an increase in the working level of supersaturation and so on. There is thus a complex feedback loop within a continuous crystallizer, illustrated in Figure 7.11. 

For symbolic convenience we make use of the reaction variable x, which is the decrease in concentration of reactant A in time t. Because of the reaction stoichiometry, X is also the decrease in B concentration. The mass balance expressions are... 

It is often experimentally convenient to use an analytical method that provides an instrumental signal that is proportional to concentration, rather than providing an absolute concentration, and such methods readily yield the ratio clc°. Solution absorbance, fluorescence intensity, and conductance are examples of this type of instrument response. The requirements are that the reactants and products both give a signal that is directly proportional to their concentrations and that there be an experimentally usable change in the observed property as the reactants are transformed into the products. We take absorption spectroscopy as an example, so that Beer s law is the functional relationship between absorbance and concentration. Let A be the reactant and Z the product. We then require that Ea ez, where e signifies a molar absorptivity. As initial conditions (t = 0) we set Ca = ca and cz = 0. The mass balance relationship Eq. (2-47) relates Ca and cz, where c is the product concentration at infinity time, that is, when the reaction is essentially complete. 

The concentration of D is then found from the mass balance. 

Thus, if Ca and Cb can both be measured as functions of time, a plot of v/ca vs. Cb allows the rate constants to be estimated. (If it is known that B is also consumed in the first-order reaction, mass balance allows cb to be easily expressed in terms of Ca-) The rate v(Ca) is the tangent to the curve Ca = f(t) at concentration Ca-This can be determined graphically, analytically, or with computer processing of the concentration-time data. Mata-Perez and Perez-Benito show an example of this treatment for parallel uncatalyzed and autocatalyzed reactions. 

The concentration Cq is easily found by substituting Eqs. (3-99) and (3-102) into the mass balance expression ... 

The competitive adsorption isotherms were determined experimentally for the separation of chiral epoxide enantiomers at 25 °C by the adsorption-desorption method [37]. A mass balance allows the knowledge of the concentration of each component retained in the particle, q, in equilibrium with the feed concentration, < In fact includes both the adsorbed phase concentration and the concentration in the fluid inside pores. This overall retained concentration is used to be consistent with the models presented for the SMB simulations based on homogeneous particles. The bed porosity was taken as = 0.4 since the total porosity was measured as Ej = 0.67 and the particle porosity of microcrystalline cellulose triacetate is p = 0.45 [38]. This procedure provides one point of the adsorption isotherm for each component (Cp q. The determination of the complete isotherm will require a set of experiments using different feed concentrations. To support the measured isotherms, a dynamic method of frontal chromatography is implemented based on the analysis of the response curves to a step change in feed concentration (adsorption) followed by the desorption of the column with pure eluent. It is well known that often the selectivity factor decreases with the increase of the concentration of chiral species and therefore the linear -i- Langmuir competitive isotherm was used ... 

The production rate of acetic acid was 2kg-h 1, where the maximum acetic acid concentration was 12%. Air was pumped into the fermenter with a molar flow rate of 200 moMi-. The chemical reaction is presented in (E. 1.1) and flow diagram in Figure 9.5. Determine the minimum amount of ethanol intake and identify the required mass balance for the given flow sheet. The ethanol biochemical oxidation reaction using A. aceti is ... 

The form of Eq. (1-5) states that the reactants disappear at the same rate at which the products form. If this statement is correct, no intermediates build up to a kinetically significant" concentration. Certain mass-balance relations are thus implied ... 

Also, a specific analysis for the intermediate itself may be developed. It may be detectable at levels below those discernible as discrepancies in the mass balance. If the concentration of. the intermediate is very low, Eqs. (1-5) and (1-6) hold. If not, then reactant consumption and product buildup occur at different rates. Such complications will be considered in Chapters 3 and 4. Most complexities in kinetics involve reactive intermediates. Relatively few reactions of significance occur in a single step, so issues concerning intermediates will recur throughout this book. 

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