Steady state, condition for

At steady-state condition for chemostat operation, change of concentration is independent of time. Material balance for the fermentation vessel is ... 

The rate of formation of a product is easily evaluated at steady-state condition for inlet and... 

Jahelka et al. (1972 b) emphasize that Scheme 5-17 was derived assuming a steady state condition for all the intermediates of Scheme 5-14. The same authors (Jahelka et al., 1973a) found, however, in their investigation of the diazonium ion (Z)-diazoate equilibria (reactions 1 and 2) that the concentration of the intermediate (Z)-diazohydroxide may reach several percent, in one case even 25% (see Table 5-1). The very good fit of the calculated curves with the experimental data in Figure 5-3 is therefore rather surprising to the present author. 

Figure 9.3. Illustration of the approach to steady-state conditions for the populations of states So, Si, and Ti under the continuous excitation conditions of Example 9.5...

It follows from the steady-state condition for the numbers of particles B generated and consumed in the reaction that... 

For gas absorption, this problem can often be circumvented by the assumption of a quasi-steady-state condition for the gas phase. In this, the dynamics of the gas phase are effectively neglected and the steady state, rather than the dynamic form of component balance is used to describe the variation in gas phase concentration. 

In the gas phase, the reaction of O- with NH3 and hydrocarbons occurs with a collision frequency close to unity.43 Steady-state conditions for both NH3(s) and C5- ) were assumed and the transient electrophilic species O 5- the oxidant, the oxide 02 (a) species poisoning the reaction.44 The estimate of the surface lifetime of the 0 (s) species was 10 8 s under the reaction conditions of 298 K and low pressure ( 10 r Torr). The kinetic model used was subsequently examined more quantitatively by computer modelling the kinetics and solving the relevant differential equations describing the above... 

Electrode processes are often studied under steady-state conditions, for example at a rotating disk electrode or at a ultramicroelectrode. Polarog-raphy with dropping electrode where average currents during the droptime are often measured shows similar features as steady-state methods. The distribution of the concentrations of the oxidized and reduced forms at the surface of the electrode under steady-state conditions is shown in Fig. 5.12. For the current density we have (cf. Eq. (2.7.13))... 

For long heating times, eventually at t —> oo, the temperature just reaches Tig. Thus for any heat flux below this critical heat flux for ignition, gig crit, no ignition is possible by the conduction model. The critical flux is given by the steady state condition for Equation... 

The common further treatment of the approach - assumption of steady-state conditions for the intermediate substrate complexes, consideration of the catalyst balance ([catalyst]0=[solvent complex] + [IRe] + [Isi] + [IIRe] + [Hsi]) and of the stoichiometry of the hydrogenation - provides the rate of hydrogen consumption under isobaric conditions (Eq. (13)) [57f]. A more general derivation can be found in [59]. 

Operate the fed batch with high values of SF and low values of F. Note that it is possible to obtain a quasi steady state condition for which // becomes equal to dilution rate D=F/V. It is seen from the simulations that this results in constant values of X but low and slowly decreasing values of S. 

Was a conversion used from intermittent to continuous exposure If so. explain According to Veulemans et al. (1982), steady-state conditions for -hexane in blood are achieved by 100 minutes of exposure in humans thus, it is not appropriate to adjust from intermittent to continuous exposure. 

Under the assumption that the reactions in the catalytic cycle are so fast as to make the various forms of the enzyme be at steady state, their concentrations (noted [species]) obey the following equations, obtained by expressing the steady-state conditions for each form of the enzyme ... 

Again applying steady state conditions for [C2H5] and [H], we get... 

Similarity solutions of the species-mass-balance equations were assumed by Friedlander and Seinfeld for a simple photochemical-smog reaction scheme. (This scheme assumed a steady-state condition for ozone.) Demonstration runs were shown for parametric variations in the... 

Compare Eq. 3-229 with 3-224. The decay in monomer concentration depends on the orders of both initiator and activator initial concentrations with no dependence on deactivator concentration and varies with t2/3 under non-steady-state conditions. For steady-state conditions, there are first-order dependencies on initiator and activator and inverse first-order dependence on deactivator and the time dependence is linear. Note that Eq. 3-229 describes the non-steady-state polymerization rate in terms of initial concentrations of initiator and activator. Equation 3-224 describes the steady-state polymerization rate in terms of concentrations at any point in the reaction as long as only short reaction intervals are considered so that concentration changes are small. 

Whether steady-state or non-steady-state conditions apply depends on the reaction system. Higher concentrations of deactivator decrease normal bimolecular termination by decreasing the concentration of propagating radicals. Steady-state low concentrations of radicals occur when the deactivator/activator ratio is about equal to or greater than 0.1. Non-steady-state conditions occur when the ratio is lower than 0.1. Non-steady-state means non-steady-state conditions for both propagating radicals and deactivator. Under steady-state conditions, both radical and deactivator concentrations are at steady-state, where the radical concentration is lower and the deactivator concentration is higher than for nonsteady-state conditions. 

The steady state condition for the concentration of ROa radical in an autoxidation is... 

Figure 6. -82 elution yield at steady-state conditions for various flow rates. (Reproduced with permission from Ref. 21. Copyright 1981 J Nucl. Med.)... 

The link between the current density and the concentration overpotential under steady-state conditions for systems in which the exchange-current density is relatively large compared with the limiting current density (hence, the activation overpotential is negligible) was established through the concept of a limiting current iL arising from the fact that there is a maximum rate at which electron acceptors can move to an... 

Figure 1 A distributed resistor network models approximately how the apphed potential is distributed across a DSSC under steady-state conditions. For various values of the interparticle resistance, fiT,o2, and the interfacial charge transfer resistance, Rc the voltage is calculated for each node of the Ti02 network, labeled Vj through V . This is purely an electrical model that does not take mobile electrolytes into account and, therefore, potentials at the nodes are electrical potentials, whereas in a DSSC, all internal potentials are electrochemical in nature.

Here, N03 was assumed to be in rapid equilibrium with NO and 02, and N205 in equilibrium with N03 and N02. This was the only mechanism the investigators could find in which the order of the reaction, with respect to [NO], could exceed 2. Assuming steady-state conditions for the intermediates, one obtains... 

In these shift experiments, the coupling condition for the unidirectional flow of cations is 2 Va2+ = yB3+, which can be understood as the steady state condition for equal cation velocities in the reference frame of the anions jAi,/cAn = yB3./cBw = v. From this coupling condition, one obtains using Eqn. (6.25)... 

If we denote the point defect injected by the applied field into the wrong sublattice of AX by i (e.g A ), and the conjugate defect that carries the flux in AX by j (e.g., V ), then the steady state condition for both fluxes (i, j) in the defect recombination zone r is... 

However, when particles i are mobile in the crystal lattice, and the interface mobility is mb, the steady state condition for this more realistic case is... 

Assuming as before the steady state conditions for O atoms... 

In a number of cases the application of states steady-state conditions for obtaining kinetic equations is more convenient. Besides that, these conditions are a source of certain general relations to be discussed later. 

Ion-molecule association reactions and the collisional deactivation of excited ions have been the subjects of recent reviews.244-246 Several systematic studies have been performed in which the relative deactivating efficiencies of various Mf species have been determined. By applying the usual kinetic formulations for the generalized reaction scheme of equation (11.31), and assuming steady-state conditions for (AB+), an expression for the low-pressure third-order rate coefficient can be derived ... 

Another type of stability problem arises in reactors containing reactive solid or catalyst particles. During chemical reaction the particles themselves pass through various states of thermal equilibrium, and regions of instability will exist along the reactor bed. Consider, for example, a first-order catalytic reaction in an adiabatic tubular reactor and further suppose that the reactor operates in a region where there is no diffusion limitation within the particles. The steady state condition for reaction in the particle may then be expressed by equating the rate of chemical reaction to the rate of mass transfer. The rate of chemical reaction per unit reactor volume will be (1 - e)kCAi since the effectiveness factor rj is considered to be unity. From equation 3.66 the rate of mass transfer per unit volume is (1 - e) (Sx/Vp)hD(CAG CAl) so the steady state condition is ... 

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