Liquid film reaction second order

Further, the rate of diffusion across the liquid film is much greater than the rate of the reaction in the bulk liquid. For a second-order reaction, this is signified by... 

It was pointed out that a bimolecular reaction can be accelerated by a catalyst just from a concentration effect. As an illustrative calculation, assume that A and B react in the gas phase with 1 1 stoichiometry and according to a bimolecular rate law, with the second-order rate constant k equal to 10 1 mol" see" at 0°C. Now, assuming that an equimolar mixture of the gases is condensed to a liquid film on a catalyst surface and the rate constant in the condensed liquid solution is taken to be the same as for the gas phase reaction, calculate the ratio of half times for reaction in the gas phase and on the catalyst surface at 0°C. Assume further that the density of the liquid phase is 1000 times that of the gas phase. 

Figure 14-10 illustrates the gas-film and liquid-film concentration profiles one might find in an extremely fast (gas-phase mass-transfer limited) second-order irreversible reaction system. The solid curve for reagent B represents the case in which there is a large excess of bulk-liquid reagent B. The dashed curve in Fig. 14-10 represents the case in which the bulk concentration B is not sufficiently large to prevent the depletion of B near the liquid interface and for which the equation ( ) = I -t- B /vCj is applicable. 

Equations 9.2-28 and -29, in general, are coupled through equation 9.2-30, and analytical solutions may not exist (numerical solution may be required). The equations can be uncoupled only if the reaction is first-order or pseudo-first-order with respect to A, and exact analytical solutions are possible for reaction occurring in bulk hquid and liquid fdm together and in the liquid film only. For second-order kinetics with reaction occurring only in the liquid film, an approximate analytical solution is available. We develop these three cases in the rest of this section. 

What is the significance of the parameter fi = (k2C BLDAf5 / kL in the choice and the mechanism of operation of a reactor for carrying out a second-order reaction, rate constant k2, between a gas A and a second reactant B of concentration CBL in a liquid In this expression, DA is the diffusivity of A in the liquid and kL is the liquid-film mass transfer coefficient. What is the reaction factor and how is it related to /l ... 

Figure 23.6 Location of reaction in the liquid film for a fast (but not infinitely fast) second-order reaction. Case C—low Cg, Case D—high Cg.

Consider a second order reaction in the liquid phase between a substance A which is transferred from the gas phase and reactant B which is in the liquid phase only. The gas will be taken as consisting of pure A so that complications arising from gas film resistance are avoided. The stoichiometry of the reaction is represented by ... 

As discussed in Sec. 7, the factor E represents an enhancement of the rate of transfer of A caused by the reaction compared with physical absorption, i.e., Kq is replaced by EKq. The theoretical variation of E with Hatta number for a first- and second-order reaction in a liquid film is shown in Fig. 19-25. The uppermost line on the upper right represents the pseudo first-order reaction, for which E = Ha coth (Ha). Three regions are identified with different requirements of liquid holdup 8 and interfacial area a, and for which particular kinds of contacting equipment may be best ... 

According to the film theory, in reactive-absorption processes the resistance to mass transfer is concentrated in a small region near the gas/liquid interface. The ratio between tbe rate of chemical reaction and liquid-phase mass transfer is given by the Hatta number. For a second-order reaction (12.1), the Hatta number is defined as ... 

In a previous work ( 5), the film theory was used to analyze special cases of gas absorption with an irreversible second-order reaction for the case involving a volatile liquid reactant. Specifically, fast and instantaneous reactions were considered. Assessment of the relative importance of liquid reactant volatility from a local (i.e., enhancement) and a global (i.e., reactor behavior) viewpoint, however, necessitates consideration of this problem without limitation on the reaction regime. 

In Chapter 7 we discussed the basics of the theory concerned with the influence of diffusion on gas-liquid reactions via the Hatta theory for flrst-order irreversible reactions, the case for rapid second-order reactions, and the generalization of the second-order theory by Van Krevelen and Hofitjzer. Those results were presented in terms of classical two-film theory, employing an enhancement factor to account for reaction effects on diffusion via a simple multiple of the mass-transfer coefficient in the absence of reaction. By and large this approach will be continued here however, alternative and more descriptive mass transfer theories such as the penetration model of Higbie and the surface-renewal theory of Danckwerts merit some attention as was done in Chapter 7. 

An analysis of chemical desorption has recently been published (Chem.Eng.Sci., 21 0980)), which is based on a number of simplifying assumptions the film theory model is assumed, the diffusivities of all species are taken to be equal to each other, and in the solution of the differential equations an approximation which is second order with respect to distance from the gas-liquid interface is used this approximation was introduced as early as 1948 by Van Krevelen and Hoftizer. However, the assumptions listed above are not at all drastic, and two crucial elements are kept in the analysis reversibility of the chemical reactions and arbitrary chemical mechanisms and stoichiometry.The result is a methodology for developing, for any given chemical mechanism, a highly nonlinear, implicit, but algebraic equation for the calculation of the rate enhancement factor as a function of temperature, bulk-liquid composition, interface gas partial pressure and physical mass transfer coefficient The method of solution is easily gene ralized to the case of unequal diffusivities and corrections for differences between the film theory and the penetration theory models can be calculated. 

Regime IV is the so called fast reaction regime, and the criterion is derived on the basis that the volume of the bulk liquid phase is significantly greater than the film volume. Two difficulties arise in relation to the use of criteria of this type. Firstly, how can one handle the case of non-first-order reactions Secondly, in respect of the problems arising when more than one reaction is present, it becomes necessary in qualitatively establishing reactor performance to move beyond these simple qualitative discriminants in such a way that the proportion of film and bulk reaction are directly determined. 

A series of differential equations describes the evolution of liquid phase products with time in a semi-batch reactor with continuous feed of the gas. If the formations of the by-products E and F are second order in the reacting gas A and all other reactions are first order, and moreover if A absorbs and reacts significantly only in the bulk liquid phase, so that film reaction is negligible and the slow regime applies, then a series of ordinary differential equations describe the concentration trajectories of liquid phase products with time. 

TPD curves can be obtained for various m/z s with increasing temperature, thereby enabling quantitative identification of species desorped from materials and films. Simultaneously, the desorped species can be physically and chemically analyzed. In addition, reaction rate analyses of desorped gases can be performed. Figure 8 shows examples of (a) a nonsymmetiical TPD curve indicated by the solid line (the first-order reaction) and (b) a symmetrical TPD curve indicated by the dashed line (the second-order reaction) as a function of temp>erature. The arrow on the nonsymmetrical TPD curve correspwnds to the evolution of physisorbed and chemisorbed H2O, which is specified to be a liquid such as water and water molecules hydrogen-bonded to Si-OH bonds at nanopore sites in the films (Hirashita et al., 1993). 

The second order reaction occurs in the bulk of the liquid, as well as in the liquid film. 

For the determination of the fluxes, the concentration profile of the absorbing component undergoing fast reactions in the liquid film has to be computed from the following set of second-order differential equations, describing the variation of the mole fraction of the component in the liquid film ... 

Enhancement fectors for second-order reaction for quiescent liquid or agitated liquid (film or Higbie models). Based on equation... 

---