Concentration parameter

Manganate(VI) formed in the initial oxidation process must first be dissolved in a dilute solution of potassium hydroxide. The concentrations depend on the type of electrolytic cell employed. For example, the continuous Cams cell uses 120 150 g/L KOH and 50 60 g/L K MnO the batch-operated Bitterfeld cell starts out with KOH concentrations of 150 160 g/L KOH and 200 220 g/L K MnO. These concentration parameters minimize the disproportionation of the K MnO and control the solubiUty of the KMnO formed in the course of electrolysis. 

Step 1 Calculate the concentration parameter for the flare gas from the following relationship ... 

Assessing the dependence of rate on concentration from the point of view of the rate law involves determining values, from experimental data, of the concentration parameters in equation 4.1-3 the order of reaction with respect to each reactant and the rate constant at a particular temperature. Some experimental methods have been described in Chapter 3, along with some consequences for various orders. In this section, we consider these determinations further, treating different orders in turn to obtain numerical values, as illustrated by examples. 

It is clear that the indices of the three reflections involved sum to zero. Associated with each triplet is a concentration parameter ... 

A batch reactor is defined as a closed spatially uniform system which has concentration parameters that are specified at time zero. It might look as illustrated in Figure 2-4. This requires that the system either be stirred rapidly (the propeller in Fig. 24) or started out spatially uniform so that stirring is not necessary. Composition and temperature are therefore independent of position in the reactor, so that the number of moles of species in the system Nj is a function of time alone. Since the system is closed (no flow in or out), we can write simply that the change in the total number of moles of species j in the reactor is equal to the stoichiometric coefficient Vj multiplied by the rate multiphed by the volume of the reactor. 

A generalized concentration distribution based on Deissler s analysis is shown in Fig. 22. There is little change in the concentration parameter... 

Values of the concentration parameter material transport, similar to those established for thermal transport, have been developed by Deissler. They take into account changes in fluid properties with concentration. Since such detailed information usually is not readily available for a particular system, it does not appear worth while to discuss further ramifications of Deisgler s analysis. It should be emphasized that all the foregoing is based upon the premise that the eddy diffusivity is isotropic and at all points in the shear flow is numerically equal to the eddy viscosity. As has been indicated earlier, the eddy Schmidt number undoubtedly is influenced by the local value of the molecular Schmidt number, which in turn is a function of the component in transport and the state of the phase. 

Figure 18.3 Coupled system of order and concentration parameters representing an...

As in previous Chapters, for practical use this infinite set (7.1.1) has to be decoupled by the Kirkwood - or any other superposition approximation, which permits to reduce a problem to the study of closed set of densities pm,m with indices (m + mr) 2. As earlier, this results in several equations for macroscopic concentrations and three joint correlation functions, for similar, X (r,t),X-s r,t), and dissimilar defects Y(r,t). However, unlike the kinetics of the concentration decay discussed in previous Chapters, for processes with particle sources direct use of Kirkwood s superposition approximation gives good results for small dimesionless concentration parameters Uy t) = nu(t)vo < 1 only (vq is d-dimensional sphere s volume, r0 is its radius). The accumulation kinetics predicted has a very simple form [30, 31]... 

Suppose that g(a) is the function describing the concentration distribution in the drops of the dispersed phase, where a is the dimensionless concentration parameter, a = a/cto. When Go is the fraction of drops with zero concentration (only for drop conversions less than 1) then... 

In this model the surface shift is expressed as a sum of partial shifts with the dominant contribution being the partial shift originating from the loss of coordination at the surface. This shift is given as the product of an effective concentration parameter, cv ( Sl), and a difference in cohesive energies. 

Figure 5. Comparison of theory with experiment effect of redox ion concentration (parameters to fit data were as in Figure 1 with v = 225 cm/s for A and v = 22.5...

Concentration parameter Experimental range Measured range ... 

Here, rs is a scale factor that is incorporated into the concentration parameter, c = rn/rs. where rv is either the virial radius or the radius at an overdensity, spherically-averaged, of 200. The profile slope parameter 7 is measured in high resolution N-body simulations (,) to be 7 1.2 0.3, and the normalisation parameter A reflects the epoch of formation, typically defined to be when half of the present mass was at overdensity of 200. 

Many working groups have modeled the performance of diesel particulate traps during the past few decades. Concentrated parameter models (CSTR assumption) have been applied for the evaluation of formal kinetic models and model parameters. The formal kinetic parameters lump the heat and mass transfer effects with the reaction kinetics of the complicated reaction network of diesel soot combustion. Those models and model parameters were used for the characterization of the performance of different filter geometries and filter materials, as well as of the performance of a variety of catalytically active coatings and fuel additives [58],... 

Consider a dilute polymer solution with Np polymer molecules of N monomers each. The polymer volume fraction p is often used as the concentration parameter it is given by < >p = NNpvp/(NNpvp + Nsvs), where vp and vs are the... 

Expressing the steady state kinetics in terms of these parameters, only the Vm parameter, which has units of mass per unit time per unit volume, has units that include time. All other parameters have units of concentration (mass per unit volume). In addition, the eight concentration parameters cannot vary independently. For example we can compute Kbq in terms of the other parameters if the equilibrium constant of the reaction is known ... 

For the mathematical models based on transport phenomena as well as for the stochastic mathematical models, we can introduce new grouping criteria. When the basic process variables (species conversion, species concentration, temperature, pressure and some non-process parameters) modify their values, with the time and spatial position inside their evolution space, the models that describe the process are recognized as models with distributed parameters. From a mathematical viewpoint, these models are represented by an assembly of relations which contain partial differential equations The models, in which the basic process variables evolve either with time or in one particular spatial direction, are called models with concentrated parameters. 

Because pH is easily determined by simply dipping a probe into a sample, determination of the saturation pH is a convenient method of determining the stability of water. The concentrations of any species at equilibrium conditions are in equilibrium with respect to each other. Also, for solids, if the condition is at equilibrium no precipitate or scale will form. One of the concentration parameters of equilibrium is the hydrogen ion concentration, which can be ascertained by the value of the pH. Thus, if the pH of a sample is determined, this can be compared with the equilibrium pH to see if the water is stable or not. Therefore, we now proceed to derive the equilibrium pH. Equilibrium pH is also called saturation pH. 

A dispersion Is a system made of discrete objects separated by a homogeneous medium In colloidal dispersions the objects are very small In at least one dimension. Colloidal sizes range from 1 to 100 nm however these limits are somewhat arbitrary, and It Is more useful to define colloids as dispersions where surface forces are large compared to bulk forces. Here we are concerned with systems where the dispersion medium Is a liquid examples are droplets In emulsions or mlcroemulslons (oll/water or water/oll), aggregates of amphiphilic molecules (surfactant micelles), foams, and all the dispersions of solid particles which are used as Intermediates In the manufacture of ceramics. At this stage we are not too concerned with the nature of the constituents, but rather with the structures which they form this Is a geometrical problem, where the system Is characterized by Its surface area A, by the shapes of Its Interfaces (curvatures - b ), and by the distances between opposing surfaces (d — concentration parameter). 

Hence, fixing the temperature and one of the concentration parameters (for example, the salt concentration) suffices to define the system. The phase diagrams were experimentally derived by using fractions of potato starch... 

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