Stoichiometry diffusion/reaction

Tubular reactors are used for some polycondensations. Para-blocked phenols can be reacted with formalin to form linear oligomers. When the same reactor is used with ordinary phenol, plugging will occur if the tube diameter is above a critical size, even though the reaction stoichiometry is outside the region that causes gelation in a batch reactor. Polymer chains at the wall continue to receive formaldehyde by diffusion from the center of the tube and can crosslink. Local stoichiometry is not preserved when the reactants have different diffusion coefficients. See Section 2.8. 

Equation A may now be used to determine the diffusivity of sulfur dioxide in the gas mixture. The flux ratios may be determined from the reaction stoichiometry. 

Many heterogeneous reactions give rise to an increase or decrease in the total number of moles present in the porous solid due to the reaction stoichiometry. In such cases there will be a pressure difference between the interior and exterior of the particle and forced flow occurs. When the mean free path of the reacting molecules is large compared with the pore diameter, forced flow is indistinguishable from Knudsen flow and is not affected by pressure differentials. When, however, the mean free path is small compared with the pore diameter and a pressure difference exists across the pore, forced flow (Poiseuille flow see Volume 1, Chapter 3) resulting from this pressure difference will be superimposed on molecular flow. The diffusion coefficient Dp for forced flow depends on the square of the pore radius and on the total pressure difference AP ... 

A pressure maximum, instead of minimum, inside the membrane could result from cases where both chemical reaction and surface diffusion are present [Sloot et al., 1992]. Thus the occurrence of a maximum or minimum local pressure inside the membrane depends on the reaction stoichiometry as well as the mobilities of the reaction species. It is assumed that only hydrogen sulfide adsorbs on the pore surface. Due to a higher transport rate of H2S enhanced by surface diffusion, the reaction zone is shifted toward the SO2 side of the membrane. In the reaction zone, larger amounts of the products are formed and higher molar fluxes of the products out of the membrane are expected so that the maxima of the mole fraction profiles of the products at the reaction zone can be sustained. 

Solution a) Assume that the binary H2-C2H6 will be satisfactory for representing the diffusion of hydrogen in the three-component system. From the reaction stoichiometry, the molal diffusion rates of H2 and C2H6 will be equal and in opposite directions. Hence a = 0, and Eq. (11-4) is applicable. From the results of Example 11-2,... 

Equation (2.3-55) is in the form of a rate being governed by two resistances in series—diffusion and chemical reaction. If I k SIOAB (fast surface reaction), die rale is governed by diffusion, while if Ilk 6/Dar (slow reaction rate), the rate is governed by cheraical kinetics. This additivity of resistances is only obtained when linear expressions relate rates and driving forces and wonld not be obtained, for example, if Ihe surface reaction kinetics were second order. More complex kinatic situations can be analyzed in a similar fashion where reaction stoichiometry at the surface provides information on (be flux ratio of various species. 

From the reaction stoichiometry, and assuming equal diffusivities and zero carbon monoxide concentration at the particle surface, (b) becomes... 

The equation above represents the diffusion coefficient of species 1 through stagnant species 2,3,...,n in the mixture, and is mainly suitable for very dilute solutions. When the other species are not stagnant, the steady-state flow ratios are determined by the reaction stoichiometry. For a reaction, N/vj = constant, and Eqn (9.3) becomes... 

Because the surface reaction rate is much faster than the diffusion of HCl to the surface, every HCl that arrives at the surface will immediately react, consuming Ti. Thus, the consumption flux of Ti(s) can be directly related to the diffusion flux of HCl by the reaction stoichiometry ... 

Based on this understanding of the incomplete nature of the CVD reaction, the kinetic behavior of this system under surface reaction, diffusion, and mixed control can now be developed. The results will be very similar to the active gas corrosion example with only minor changes due to the incomplete nature of the reaction and the different reaction stoichiometry of this example. 

Even though (3.2.3-S) is often recommended for computing a diffusivity in reacting media, it is not really the appropriate equation, except for very dilute solutions. In other cases, the other species are not necessarily stagnant.The steady-state flux ratios of the various components are determined by the reaction stoichiometry. For a general chemical reaction. 

They argued that the layer forms by reaction of Cu at the CusSi-Si interface. They also maintained that this reaction is controlled by diffusion of Cu through CusSi. (a) Show that the variation of thickness versus time is consistent with a diffusion mechanism, (b) Discuss what reaction stoichiometry would be required to produce this same variation. (c) Calculate the diffusion coefficient and compare it with other values for diffusion in solids. In this experiment, the driving force of Cu3Si is believed to be 1.10 mol% Cu. Answer 2 10 cm /sec. 

Though illustrated here by the Scott and Dullien flux relations, this is an example of a general principle which is often overlooked namely, an isobaric set of flux relations cannot, in general, be used to represent diffusion in the presence of chemical reactions. The reason for this is the existence of a relation between the species fluxes in isobaric systems (the Graham relation in the case of a binary mixture, or its extension (6.2) for multicomponent mixtures) which is inconsistent with the demands of stoichiometry. If the fluxes are to meet the constraints of stoichiometry, the pressure gradient must be left free to adjust itself accordingly. We shall return to this point in more detail in Chapter 11. 

The second use of Equations (2.36) is to eliminate some of the composition variables from rate expressions. For example, 0i-A(a,b) can be converted to i A a) if Equation (2.36) can be applied to each and every point in the reactor. Reactors for which this is possible are said to preserve local stoichiometry. This does not apply to real reactors if there are internal mixing or separation processes, such as molecular diffusion, that distinguish between types of molecules. Neither does it apply to multiple reactions, although this restriction can be relaxed through use of the reaction coordinate method described in the next section. 

Assume A, B, C, and D have similar diffusivities so that local stoichiometry is preserved. Under what circumstances will conversion be maximized by (a) complete segregation (b) by maximum mixedness Heterogeneous reactions are often modeled as if they were homogeneous. A frequently encountered rate expression is... 

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