Absorption rate, equation

Abiotic model systems, 258t of bioactivity, 258-60 Absorption, distribution coefficients, 228 Absorption rate, equation, 228 Acephate, structure, 97 N-Acetylation, biogenic amines, 114 Actinomycete, anthelminthic activity, 5... 

D. Two-Frequency Distributive Two-Photon Absorption Rate Equations for Fluid Media... 

Equation 10.1 to Equation 10.10 were developed within the low-dose limit in which the applied compound(s) dissolve rapidly into the SC lipids. If the lipid volume is taken to be then c, (0) = Dose/Substitution of this relationship into Equation 10.11 and Equation 10.12 leads directly to Equation 10.1 to Equation 10.4. However, the SC lipid volume is small (100 to 150 ig cm- ), and only a fraction of this volume can be immediately accessed by a topically applied permeant. Appropriate incorporation of a solubility limit, such that c, (0) 5,, would provide upper bounds to both the evaporation rate (Equation 10.1) and absorption rate (Equation 10.2) without changing their relative values. The key is establishing the accessible lipid volume and confirming or improving on the octanol solubility model. This problem has been discussed elsewhere (Kasting, 2001). 

If the specific form of the absorption rate equation is inserted into Eqn. (12), these two equations may be-arranged to yield a relationship between B. and B°. Now it is possible to plot B. against B and the to construct McCabe-Thiele type steps, the actual number of plates required for the operation may then be found graphically (see, for example, (65)). Juvekar and Sharma (50) proposed, however, that the plot of Bfj. versus B may be approximated to a straight line by a least square fit. Thus ... 

The simultaneous absorption of two gases that react with the solvent at different rates has been studied by Ouwerkerk. The specific system which he selected for analysis was the selective absorption of HjS in the presence of CO2 into amine solutions. This operation is a feature of several commercially important gas purification processes. Bench scale experiments were conducted to collect the necessary pi sico-chemical data. An absorption rate equation was developed for H2S based on the assumption of instantaneous reaction. For CO2 it was found that the rate of absorption into diisopropanolamine (DIPA) solution at low CO2 partial pressures can best be correlated on the l is of a fast pseudo-first-order reaction. A computer program was developed which took into account the competition between H2S and CC>2 when absorbed simultaneously, and the computer predictions were verified by experiments in a pilot scale absorber. Finally, the methodology was employed successfully to design a large commercial plant absorber. 

For gas-liquid reactions, an enhancement factor is often defined. The enhancement factor is the ratio between the chemical absorption rate and the physical absorption rate. Equation 7.69 is valid for component A, when only physical absorption occurs in the liquid film. The enhancement factor a is in this case defined as... 

The specific absorption rate = i (Cj,B ) is a func tion of h and may be computed by combining the rate equation... 

Accordingto Eq. (14-74), when /cl is very large and the ratio ki /mkc is much larger than unity, Xi —x = ykc/k and the specific absorption rate is defined by the equation... 

The last part of Eq. (1) is derived from the pH dependence of permeability, given a pH gradient between the two sides of the intestinal barrier, based on the well known Henderson-Hasselbalch equation. Direct measurement of in situ intestinal perfusion absorption rates confirmed this pH dependence [14]. 

Fig. 4.18 represents a countercurrent-flow, packed gas absorption column, in which the absorption of solute is accompanied by the evolution of heat. In order to treat the case of concentrated gas and liquid streams, in which the total flow rates of both gas and liquid vary throughout the column, the solute concentrations in the gas and liquid are defined in terms of mole ratio units and related to the molar flow rates of solute free gas and liquid respectively, as discussed previously in Sec. 3.3.2. By convention, the mass transfer rate equation is however expressed in terms of mole fraction units. In Fig. 4.18, Gm is the molar flow of solute free gas (kmol/m s), is the molar flow of solute free liquid (kmol/m s), where both and Gm remain constant throughout the column. Y is the mole ratio of solute in the gas phase (kmol of solute/kmol of solute free gas), X is the mole ratio of solute in the liquid phase (kmol of...

Our multi-level carbon model atom is adapted from D. Kiselman (private communication), with improved atomic data and better sampling of some absorption lines. The statistical equilibrium code MULTI (Carlsson 1986), together with ID MARCS stellar model atmospheres for a grid of 168 late-type stars with varying Tefj, log g, [Fe/H] and [C/Fe], were used in all Cl non-LTE spectral line formation calculations, to solve radiative-transfer and rate equations and to find the non-LTE solution for the multi-level atom. We put particular attention in the study of the permitted Cl lines around 9100 A, used by Akerman et al. (2004). 

A two liter flask was filled with pure HI at 1.24 atm and 683°K, and the decomposition was followed by measuring the absorption of light by the iodine produced. Immediately after the last reading the flask was chilled and an analysis for iodine showed 1.17 g. Evaluate the constants of the second order rate equation. 

Data were obtained on the rate of absorption of oxygen by yeast, rj without sulfanilamide and r2 with 20 mg/ml of added sulfanilamide. Oxygen partial pressure is in torr, the rates are microliters of oxygen per hour per mg of cells. Find the constants of the rate equations of the two cases. 

In the great majority of industrial processes the film thickness is not known, so that the rate equation of immediate use is equation 12.8 using kG. kG is known as the gas-film transfer coefficient for absorption and is a direct measure of the rate of absorption per unit area of interface with a driving force of unit partial pressure difference. 

The rate equation describes the variation in response variable R (with initial value of Rq) the measure response appears at a constant rate (zero order) of and is eliminafed by the first-order constant. The indirect response models will generally fall info fwo caf-egories inhibition or stimulation function. The inhibition response is classically described in ferms of IC q, fhe drug concenfration fhaf produce 50% of maximal inhibition (e.g., action of S5mfhefic glucocorticoid on adrenal glands or effecf of furosemide on sodium absorption in fhe loop of Henley) and is a number from 0 fo 1 where 1 represents total inhibition ... 

The dependence of and S2 fluorescence intensities on the sample concentration was investigated between 10 - 10 M, and a sample concentration of less than 10 M was chosen to minimize the effect of concentration quenching. Two-photon absorption measurements were carried out by the excitation by relatively low power density (<10 photons cm" pulse ) in order to avoid the saturation effect on the laser power. Under these experimental conditions, the following rate equations for the concentration of S2 molecule is derived ... 

Log D accounts for where the "dose" is, so to speak. The distribution depends on the pKa as well as the pH of the medium. The advantage of using log D is that it incorporates these factors, so, for simple processes such as absorption, distribution coefficients "ej lain" the whole process. An example from our earlier work ( ) is the colonic absorption of acids ranging from phenols to strong carboxylic acids. The absorption rate is given by an equation involving only log D terms. 

The Rate Equation for Straight Mass Transfer (Absorption) of A... 

Figure 23.2 Setting up the rate equation for absorption of A in the liquid, and reaction in the liquid, based on the two-film theory.

In order to estimate the real effect of a dispersed organic phase on the productivity of fermentation, the oxygen absorption rate has to be defined. Knowing its mathematical expression, the rate equation can then be incorporated into the differential mass balance equations of fermentation and, after solving these equations, the concentration of components in a fermentation... 

The J value denotes the absorption rate without the dispersed phase where the mass transfer rate can be accompanied by zero- or first-order chemical reactions in the continuous phase. These are well-known equations J = k° (O -i- - Ol)... 

The parameter values F and Fj j (i denotes ith differential equation from the above three differential equations altogether we have 6 parameter) can be obtained by replacing the initial and boundary conditions (Eq. 4) in these equations. The absorption rate for the composite medium can be given by Eq. 

During fermentation, the enhanced absorption rate of oxygen increases the bulk concentration and, as a consequence, the production rate of cells can be increased as well. To predict this effect, the enhanced transfer rate has to be incorporated into the differential mass balance equations of fermentation processes studied. If you know the mathematical expression of the biochemical reactions and their dependence on oxygen concentration as well as the enhanced absorption rates due to the dispersed organic phase,you can calculate the fermentation exactly after solving the equation system obtained. 

In a graphite atomizer, the atoms will appear according to a kinetic rate equation which will probably contain an exponential function. As the number of atoms in the atom cell increases, so does the rate of removal, until, at the absorption maximum (peak height measurement), the rate of formation equals the rate of removal. Thereafter, removal dominates. 

Absorption Growth Mechanism. Here we assume that a nucleus collides with a single atom at each time. This is equivalent to assuming that there are many free atoms in the gas phase and less opportunity for clusters to meet each other. This is a step-by-step reaction. The rate equation for y th step is then expressed as... 

Percutaneous penetration of 7V-nitrosodiethanolamine was measured using cryo-preserved human trunk skin and three vehicle formulations (isopropyl myristate, sunscreen cream or a 10% shampoo) containing 7V-nitroso[ C]diethanolamine. The absorption rate of a low dermal dose (10 ixg/cm ) of 7V-nitrosodiethanolamine was a linear function of the concentration (0.06, 0.2 or 0.6 Xg/ xL) applied to the skin. The peak rates for the isopropyl m uistate and shampoo vehicles were seen within five hours and for the sunscreen somewhat later. Total 48-h absorption ranged from 35 to 65% of the dose and was formulation-dependent (isopropyl m uistate > shampoo > sunscreen). A total absorption of 4-6 x JcaE was estimated to equate to an applied N-nitrosodiethanolamine dose of 10 x%lcaE. When applied as a large infinite dose (0.5 mg/cm ), total 7V-nitrosodiethanolamine absorption (4-35% of the applied dose) followed a different rank order (shampoo > isopropyl m uistate > sunscreen), probably due to the barrier-damaging properties of the vehicles. The permeability coefficient for isopropyl myristate was 3.5 X 10 cm/h (Franz etal., 1993). 

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