Initial solid-phase concentrations

The use of soluble and polymeric Mn02 allows for direct analysis of Mn02 as a reactant. In previous studies (21, 26-28), the solution had to be filtered to remove solid Mn02 in order to determine soluble Mn. Any solid Mn02 remaining in the reaction vessel was calculated by the difference between the initial solid phase concentration and the Mn. ... 

The average solid phase concentration is equal to the initial solid phase concentration multiplied by the ratio of the core volume to the particle volume... 

Fig. 3a, b a Plot of observed solid phase concentration vs aqueous phase concentration for 1,4-DCB the dashed line represents the fit to the four initial points, the y-intercept of which is taken to be the irreversible fraction on the soil, b Plot of Wrev vs aqueous phase concentration... 

Fig. 10.2. Relationship between values of (a) pH of agar and zinc phosphate (= 5mM) solubilization measured as clear halo diameters in the agar around colonies of mycorrhizal fungi (see Fomina et al., 2005a) (b) pH of fungal culture filtrates and pyromorphite solubilization measured as the ratio (%) of free metal concentration in the liquid phase to that in the initial solid phase (initial (pyromorphite) = 0.5 mM) (c) as above but excluding oxalate over-excreting Beauveria caledonica (see Fomina et al., 2004).

In general, the feed injection in a countercurrent system takes place at one end of the column. In a long enough column, equilibrium is reached at a certain distance from this zone. The size of this zone depends only on the fluid and solid phase concentrations of the feed stream components and on the flow rate ratio, my. It is independent of the initial state of the column [22,23]. 

Fig. 8.3. The effect of washes on the dissociation of immune complexes for antibodies with different affinities and with different initial saturations (Table 8.3). The antibody (immobilized on the solid phase) concentration is 10 M (fairly typical for microtitre plates). Low affinities result in rapid dissociation and the activity measured is more representative for affinity than initial antigen concentration. With high affinities,...

The problem to be considered now is one of exchange adsorption with uniform partial presaturation (VS). The initial solid-phase and entering fluid-phase concentrations are each to be uniform (independent of position or time, respectively), but may each involve any desired proportion of each of the two components A and B. 

Solvent evaporation would be used when you are trying to perform ultra-trace analysis. It allows a sample extract to be further preconcentrated. An example would be analysis of pesticides in natural water. Initially, solid-phase extraction may have been performed to concentrate the pesticides from the water. However, to detect pesticides in natural waters will require additional pre-concentration via solvent-evaporation procedures. 

The solubihty in the system Th-Na2C03-H20 has been studied as a function of the total concentration of Na2C03 at 25°C using Na6[Th(C03)5]T2H20(s) as the initial solid phase. The molality of Na2C03 varied from 0.79 to 2.8 mol-kg and the concentration of dissolved Th and the composition of the solid phase in equilibrium with the solution were analysed. In the concentration range 0.79 < < 2.4 mol-kg the data... 

In general, as expected from equilibrium theory, the mass transfer zone in a countercurrent system occurs at one end of the column, and in a long column at a sufficient distance from this zone equilibrium is approached. The location of the mass transfer zone depends only on the fluid and solid phase concentration of the feed streams and the flow ratio y it is independent of the initial state of the column. In certain circumstances it is, however, possible to have a stable asymptotic solution in which the mass transfer zone has no tendency to migrate in either direction. Under these conditionis the mass transfer zone may occur at any point in the column, depending on the precise initial conditions and the start-up procedure, with equilibrium states being approached both upstream and downstream of the mass transfer zone. When this isotherm is favorable such behavior is possible only for desorption at the correct value of y determined by the feed concentrations. A full discussion is given by Rhee and Amundson. ... 

Second, one can compare the total number of moles transferred to the adsorbent phase in rival modes of operation. If C j is the solid-phase concentration in equilibrium with the influent concentration C, then the moles of species i transferred to the solid adsorbent phase per unit volume of adsorbent is (C°j - 0) for an initially solute-free adsorbent bed when the bulk flow is perpendicular to the force. A batch operation without bulk flow will transfer according to relation (7.1.16a) only (Ca -0) moles per unit volume of adsorbent, where Ca < C°i. Thus, bulk flow of feed along the bed length perpendicular to the force direction achieves a better utilization of the intrinsic adsorption capacity of the adsorbents. 

Diffusion with reactive decay and mass transfer to the adjoining fluid phase. This case extends the previous one by including a MTC, k (m/s), on the fluid side to capture this transport resistance. The concentration profile equation for the same idealized initial solid phase conditions is... 

Hydroxyandrosta-4,6-dien-3-one. A suspension of 42 g of crude androsta-4,6-diene-3j ,17j -diol in 2000 ml of chloroform is treated with 250 g of activated, manganese dioxide. The mixture is then shaken vigorously for 15 min in a stoppered flask. The mixture is filtered and the manganese dioxide washed well with chloroform in order to elute material which initially remains adsorbed on the solid phase. The filtrate is concentrated to a pale yellow, crystalline residue. Recrystallization from acetonitrile gives 38 g (90%) of 17/ -hydroxyandrosta-4,6-dien-3-one as plates mp 211-214°. 

Figure 6.28. Initial changes of Co concentrations in the main solid-phase fractions of two Israeli arid soils. Soils were incubated under the saturated paste regime (after Han et al., 2002b. Reprinted from J Environ Sci Health, Part A, 137, Han F.X., Banin A., Kingery W.L., Li Z.P., Pathways and kinetics of transformation of cobalt among solid-phase components in arid-zone soils, p 188, Copyright (2003), with permission from Taylor Francis)...

The soil aggregates are assumed to be spherical in form and to have constant temperature and to contain initially uniform distributions of substrate (contaminant) and biomass. The external concentrations of biomass and substrate are assumed to be zero and the external oxygen concentration is constant. Substrate is adsorbed onto the solid phase to an extent determined by an equilibrium partition coefficient. 

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