Rate-determining zone

In Eq. (9.17), we are only including the reactants and products that are consumed or produced in the rate-determining zone (RDZone) [40], that is, from the TDI to the TDTS. 

Pressure. Within limits, pressure may have Htfle effect in air-sparged LPO reactors. Consider the case where the pressure is high enough to supply oxygen to the Hquid at a reasonable rate and to maintain the gas holdup relatively low. If pressure is doubled, the concentration of oxygen in the bubbles is approximately doubled and the rate of oxygen deHvery from each bubble is also approximately doubled in the mass-transfer rate-limited zone. The total number of bubbles, however, is approximately halved. The overall effect, therefore, can be small. The optimum pressure is likely to be determined by the permissible maximum gas holdup and/or the desirable maximum vapor load in the vent gas. 

Hoftyzer and van Krevelen [100] investigated the combination of mass transfer together with chemical reactions in polycondensation, and deduced the ratedetermining factors from the description of gas absorption processes. They proposed three possible cases for poly condensation reactions, i.e. (1) the polycondensation takes place in the bulk of the polymer melt and the volatile compound produced has to be removed by a physical desorption process, (2) the polycondensation takes place exclusively in the vicinity of the interface at a rate determined by both reaction and diffusion, and (3) the reaction zone is located close to the interface and mass transport of the reactants to this zone is the rate-determining step. 

Their model is based on the propagation of a plane reaction zone thru the combustible gases, but does not include the surface of the burning pioplnt, the rate-determining step being in the flame. The order of the reaction determines how the rate of burning... 

Determine Qc, the heat load in the constant-rate-drying zone. The heat in this zone serves solely for evaporation, with no sensible heating. The amount of water evaporated in this zone was found in step 7. Then, Qc = (970.3)(111-1) = 107,800 Btu/h (31.58 kW). 

Figure 12.2 SOFeX depth profiles of biomass (PN)-specific NO/ uptake rates, determined during 24-h incubations in Plexiglas acrylic incubators under simulated in-situ light and temperature conditions. Ultra-clean trace-metal techniques were used for sample collection within and outside (control waters) of the Fe-enriched patch north and south of the Antarctic Polar Front zone. The/-values [f = Fn03/(1 n03 + 1 nH4 + F n02 + F Urea)] were determined at the isolume depths of 47 and 16% surface irradiance, using tracer-level isotopic enrichments, and are not corrected for the effects of isotopic dilution. Error bars represent the range of duplicate samples (n = 2). Corrected from Coale et al. (2004).

In heterogeneous reactions, either the reaction at the phase boundary or the transport to or from the reaction zone can be rate-determining. In the case of a reaction between two solid phases, the diffusion of one reactant determines, in general, the rate of the reaction. Diffusion is considered in more detail in section 18.5. 

When electron diffusion is clearly faster than cation diffusion, the reaction zone initially spreads along the z-axis and reaches the top surface of the crystal. Now, the cation diffusion in the x and y directions becomes rate-determining and the transition time is given by ... 

With fluids, we think of the pump as the source of pressure as well as the flow rate determining device. However, with supercritical fluids (in contrast to t3q)ical liquids), a pump needs a control point downstream to hmit the passage of molecules per unit time. This restriction then "holds-back" the previously unlimited flow of molecules to a definite, but not always pre-determined level. Ideally then, the restrictor serves to restrict the flow until the density of molecules distributed from the pump through the extraction region right up to the final restriction point in space is such that the operating density desired in the extraction zone is achieved. This is much easier to state in words than it is to achieve in actual experimental practice. This is especially true if you wish to achieve an experimental set of parameters and hold those values over a finite period of time (ranging from minutes to hours) and do it with the statistical precision and accuracy that are necessary to attain the final quantitative analytical results. 

Assuming that the reaction is entirely kinetically controlled and that the time of transfer of the reactants to the reaction zone is not rate-determining, the relationship between the rate constant for the reaction at the interface ( kA) and the rate constant based on total mass... 

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