Steady state yield

The time that a molecule spends in a reactive system will affect its probability of reacting and the measurement, interpretation, and modeling of residence time distributions are important aspects of chemical reaction engineering. Part of the inspiration for residence time theory came from the black box analysis techniques used by electrical engineers to study circuits. These are stimulus-response or input-output methods where a system is disturbed and its response to the disturbance is measured. The measured response, when properly interpreted, is used to predict the response of the system to other inputs. For residence time measurements, an inert tracer is injected at the inlet to the reactor, and the tracer concentration is measured at the outlet. The injection is carried out in a standardized way to allow easy interpretation of the results, which can then be used to make predictions. Predictions include the dynamic response of the system to arbitrary tracer inputs. More important, however, are the predictions of the steady-state yield of reactions in continuous-flow systems. All this can be done without opening the black box. 

The mass balance over a continuous stirred-tank reactor (CSTR) in the steady state yields for the average residence T... 

A molecule in a centrifuge is acted upon not only by the applied centrifugal force but also by an opposing buoyant force that depends upon the difference in density of the sedimenting particles and the solvent and by a frictional drag, which is proportional to a frictional coefficient/. Setting the sum of these forces to zero for the hydrodynamic steady state yields Eq. 3-13, which defines the sedimentation constant s. 

Figure 1 reveals that steady state activity was established after approximately 30 hours of reaction over 1.2PV(dir) at 300°C under standard conditions. Initially there was almost total conversion of MEK which fell to ca 60% when at the steady state. In these conditions AcH appeared in highest yield. Yield of DA reached a maximum of 10% after 10 hours on stream but gradually fell to 6.5% at the steady state. The other major products, CO2 and AcOH, gave steady state yields of ca. 11.5% and 19% respectively. 

Figure 1. Normalized 02 yields from thylakoid membranes given a train of saturating flashes. Yn denotes the yield of 02 on flash n and Yss denotes the steady-state yield of 02. Conditions are as described in reference 44.

Also, the linearized perturbation equations around a steady-state yield the following dispersion relation ... 

The linearization of the perturbation equations around the steady state yields the characteristic equation... 

Fig. 5 shows the relation between yield against purity of product gas for PQ-USY and for EX20P, respectively at a cyclic steady state. Yield is defined as follows ... 

In a first series of experiments, transient kinetics were studied. After a certain time on stream at a constant flow rate of, e.g., 120 ml - min l a steady state was reached (Figure 1). This was characterised by a constant conversion and an exact stoichiometry according to equ. (1), in agreement with earlier results. When the flow rate was suddenly lowered, i.e., the contact time increased, the expected increase in conversion was observed. However, first an excess of benzene was produced but the new steady-state yield, Y, of benzene was relatively quickly reached. By contrast, the yield of diethylbenzenes only slowly increased from low values to the new steady-state. This indicates a preferential adsorption of the product diethylbenzene. The effect was reversible. When the initial flow rate was re-adjusted, the original conversion was approached, whereby the initial steady-... 

Application of impedance spectroscopy is very much like feeling an elephant that we cannot see. Measurement of current and potential imder a steady state yields some information concerning a given system. By adding frequency dependence to the macroscopic measurements, impedance spectroscopy expands the information that can be extracted from the measurements. Impedance measurements, however, are not sufficient. Additional observations are needed to gain confidence in the model identification. 

After an initial transient period characterized by activation and deactivation processes of the catalysts [4], a steady state yield of hydrocarbons of 18% was observed with the H2/CO reaction gas on the Fe-catalyst and of 70% on the Co-catalyst (Fig. 1). 

Figure 11, Steady state yield of formaldehyde as a function of irradiation time. ( ) 1 M sodium carbonate (A) 1 x 10-3 sodium carbonate.

Figure 6. Time-dependent growth and steady-state yield of radical absorption at 400 nm on illumination at 545 nm of the two-component dye aggregate—viologen system ( 3) and the three-component donor—dye aggregate—viologen system (O). Donor and acceptor concentrations are each 5 mol % diluted with arachidic acid.

Considerably more progress has been made in the oxidative coupling of methane to form ethane and ethylene (C2 products). Since the early work of Keller and Bhasin [Ref. 3], the steady-state yields of C2 products have improved to a level of about 20%. Among the more effective catalysts are the Group IIA oxides which... 

An overall product mass balance at steady state yields the proper rate equation for region B ... 

Figure 8. Comparison of periodic and steady-state yields and selectivities. T = 527 X, Split ratio 3 1, nica, = 0.008 kg.

Again, if the addition of one unit of mass to a cell by growth consumes (on the average) mass units of the fth chemical species in the surrounding medium, material balance for the steady state yields... 

The first step is a two-way process with a very unfavorable equilibrium A = — AGi = —15.7 kcal mol , at 298 K, with the superscript -e- standing for standard state. The second one is a one-way process, with a rate constant At2 that is 10 times larger than k-1 over an extended temperature range. The kinetic coupling between both steps at the kinetic steady state has the effect of pumping away the hydrogen atom concentration from its equilibrium value [H]e in the absence of the second step below, down to its steady state value [H]. In fact, application of the De Donder equation to an equimolar H2-Br2 mixture at half conversion to HBr at the steady state yields with [H2] = [Br2] = [HBr],... 

The primary quantum yield for electron formation, determined on a very short time-scale in laser experiments, is a measure of the electrons initially formed on interaction with light (Eq. 9). The primary quantum yield for electron formation has been measured at 355 nm by laser flash photolysis. Quantum yields were 4.6 x 10 to 7.6 X 10 for purified humic substances from several different natural waters and 1.7 x 10 to 4 x 10 for two commercial humic acids (normalized for carbon concentration) [85]. The caged pair generated in Eq. (9) can either collapse back or eject an electron and form the hydrated electron, e q, free in solution (Eq. 10). The steady-state yield, measured with electron scavengers under continuous irradiation, is a measure of the electrons which escape the DOM matrix and are free in solution. The electron thus occurs trapped within the DOM matrix and/or free in solution. 

In this case, the influence of the alkali promoter is even more pronounced than with Fe, and also the nature of the support exerts a marked influence. This becomes evident from Fig. 6.9 in which the steady-state yields of Cs-promoted and unpromoted Ru catalysts on AI2O3 and MgO supports at atmospheric pressure are plotted [45]. 

For the determination of the thermal conductivity of the dry layer, a steady state yields... 

The effect of the true rate of death fe on the steady-state yields becomes significant only at very low dilution rates, as shown in Fig. 5.26. Also, an apparent lag can be explained in batch cultures if the inoculum is of very low viability. 

Fig. 3.4. Diffused mass of trichloroethylene related to unit specimen area which escapes from a test cell filled with liquid trichloroethylene in gravimetric permeation measurement as a function of time. The test specimen was cut from a 2.5 mm thick HDPE geomembrane. The linear regression fit to the data points in steady state yields the permeation rate (slope of the line defined as mass which diffuses through the geomembrane per unit time and area, here 30 g/(mM)) and the induction time (time axis intercept of the regression line, here 3 days)...

For a low gas temperature like Tgi in Figure 4.5.12a, the intersection point of the heat production function and the heat removal hne (steady state) yields to a surface temperature that is only marginally higher than the gas temperature. Am,ex is then... 

A balance over the forces acting on the falling cylinder (gravity acting downward with buoyancy, pressure, and wall shear acting upward) at steady state yields... 

Let s choose the system boundaries to be the aeration tank because we have the most information about this unit. We continue to use the symbol F for the rate of total mass input and Q for volumetric flow rates applying the conservation of mass to the aeration tank at steady state yields... 

The experimental runs were divided into two main categories, steady-state and periodic runs. The purpose of the steady-state runs was to obtain experimentally the value and conditions of maximum steady-state yield. The yield under periodic operating conditions was always compared with this maximum achievable under steady-state conditions. During each of these runs the reactant flow rates were set to the required value. After allowing time for the system to reach the steady-state, the effluent volumetric flow rate was measured by the wet-test meter. Effluent samples and feed gas samples were then analysed in the chromatograph. 

Steady-State Runs. Four levels of residence times were employed 0.273, 0.352, 0.54 and 1.33 seconds. Each set of runs was conducted over a wide range of ratio of reactants in the feed stream, keeping the nitrogen composition constant throughout at 60%, and the water bath temperature at 70°C. The objective of these runs was to establish experimentally the conditions for optimum steady-state yield, and to determine the kinetics... 

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