Gases first-order reactions

Let us compare computations of the effectiveness factor, using each of the three approximations we have described, with exact values from the complete dusty gas model. The calculations are performed for a first order reaction of the form A lOB in a spherical pellet. The stoichiometric coefficient 10 for the product is unrealistically large, but is chosen to emphasize any differences between the different approaches. 

Danckwerts et al. (D6, R4, R5) recently used the absorption of COz in carbonate-bicarbonate buffer solutions containing arsenate as a catalyst in the study of absorption in packed column. The C02 undergoes a pseudo first-order reaction and the reaction rate constant is well defined. Consequently this reaction could prove to be a useful method for determining mass-transfer rates and evaluating the reliability of analytical approaches proposed for the prediction of mass transfer with simultaneous chemical reaction in gas-liquid dispersions. 

The dissolved gas is removed from the liquid by an irreversible first-order reaction. 

Again for the case of the sparingly soluble gas whose absorption is accompanied by a simultaneous irreversible first-order reaction, Lightfoot (L5, L6) made the following assumptions ... 

A pure gas is absorbed into a liquid with which it reacts. The concentration in the liquid is sufficiently low for the mass transfer to be governed by Pick s law and the reaction is first order with respect to the solute gas. It may be assumed that the film theory may be applied to the liquid and that the concentration of solute gas falls from the saturation value to zero across the film. Obtain an expression for the mass transfer rate across the gas-liquid interface in terms of the molecular diffusivity, 1), the first order reaction rate constant k. the film thickness L and the concentration Cas of solute in a saturated solution. The reaction is initially carried our at 293 K. By what factor will the mass transfer rate across the interface change, if the temperature is raised to 313 K7... 

Rate = kPx for a first-order reaction of a gas X. What are the units for the rate constants when partial pressures are expressed in torr and time is expressed in seconds for (a) zero-order reactions (b) first-order reactions (c) second-order reactions ... 

Pyruvic acid is an intermediate in the fermentation of grains. During fermentation the enzyme pyruvate carboxylase causes the pyruvate ion to release carbon dioxide. In one experiment a 200.-mL aqueous solution of the pyruvate in a sealed, rigid 500.-mL flask at 293 K had an initial concentration of 3.23 mmol-L -l. Because the concentration of the enzyme was kept constant, the reaction was pseudo-first order in pyruvate ion. The elimination of CU2 by the reaction was monitored by measuring the partial pressure of the C02 gas. The pressure of the gas was found to rise from zero to 100. Pa in 522 s. What is the rate constant of the pseudo-first order reaction ... 

The concentration of gas over the active catalyst surface at location / in a pore is ai [). The pore diffusion model of Section 10.4.1 linked concentrations within the pore to the concentration at the pore mouth, a. The film resistance between the external surface of the catalyst (i.e., at the mouths of the pore) and the concentration in the bulk gas phase is frequently small. Thus, a, and the effectiveness factor depends only on diffusion within the particle. However, situations exist where the film resistance also makes a contribution to rj so that Steps 2 and 8 must be considered. This contribution can be determined using the principle of equal rates i.e., the overall reaction rate equals the rate of mass transfer across the stagnant film at the external surface of the particle. Assume A is consumed by a first-order reaction. The results of the previous section give the overall reaction rate as a function of the concentration at the external surface, a. ... 

The overall effectiveness factor for the first-order reaction is defined using the bulk gas concentration a. 

Example 11.12 Solve Equations (11.31) and (11.32) for the simple case of constant parameters and a pseudo-first-order reaction occurring in the liquid phase of a component supplied from the gas phase. The gas-phase film resistance is negligible. The inlet concentration of the reactive component is... 

Concentration of ethanol in the compound surface layer in equilibrium with the gas phase First-order reaction constant for the silanization reaction Volumetric flow rate of ethanol from the compound to the gas phase Time... 

In the previous chapter we examined cellular automata simulations of first-order reactions. Because these reactions involved just transformations of individual ingredients, the simulations were relatively simple and straightforward to set up. Second-order cellular automata simulations require more instructions than do the first-order models described earlier. First of all, since movement is involved and ingredients can only move into vacant spaces on the grid, one must allow a suitable number of vacant cells on the grid for movement to take place in a sensible manner. For a gas-phase reaction one might wish to allow at least 5-10 vacant cells for each ingredient, so that on a 100 x 100 = 10,000... 

The apparent reaction rate constant for the first order reaction, k, was calculated from the conversion of CO2. Since the gas-volume reduction rate increased with k, a poor fluidization was induced by high reaction rate. We investigated the effect of the rate of the gas-volume change on the fluidization quality. The rate of the gas-volume change can be defined as rc=EA(dxA/dt), where Sa is the increase in the number of moles when the reactants completely react per the initial number of moles. This parameter is given by 7-1. When the parameter, Ea, is negative, the gas volume decreases as the reaction proceeds. 

Preliminary work showed that first order reaction models are adequate for the description of these phenomena even though the actual reaction mechanisms are extremely complex and hence difficult to determine. This simplification is a desired feature of the models since such simple models are to be used in numerical simulators of in situ combustion processes. The bitumen is divided into five major pseudo-components coke (COK), asphaltene (ASP), heavy oil (HO), light oil (LO) and gas (GAS). These pseudo-components were lumped together as needed to produce two, three and four component models. Two, three and four-component models were considered to describe these complicated reactions (Hanson and Ka-logerakis, 1984). 

The ions or cluster ions are thermalized by collisions with an inert carrier gas (usually helium), although often argon or even nitrogen is employed. Neutral reactant gas is added through a reactant gas inlet at an appropriate location downstream in the flow tube, and allowed to react with the injected ions. Rate coefficients, k, are determined by establishing pseudo-first-order reaction conditions in which the reactant ion concentration is small compared to the reactant neutral concentration. Bimolecular rate coefficients, k, are obtained from the slope of the natural logarithm of the measured signal intensity, /, of the reactant ion versus the flow rate (2b of reactant gas 45,48-50... 

In case of Fischer-Tropsch synthesis, we have to consider that the first-order reaction rate constant is related to the concentration in the gas phase (e.g., ce2), and that the diffusive flux in the liquid-filled pores is related to the concentration in the liquid (ce21). Thus, instead of Equation 12.10, we have to use... 

A first-order reaction, A -> products, is conducted in a fluidized-bed reactor. Before fluidization, the bed is 1.8 m deep (Lpa), with a voidage (epa) of 0.42. The feed gas (P/ = 0.45 kgm-3 p,y = 4.2 x 10-5 Pa s) flows through the bed at a velocity three times the minimum fluidization velocity. The following data are also available ... 

Since most (if not all) of the solid is in the emulsion region, equation 23.4-23 may be used in a plug-flow model to represent the contact efficiency of the gas and solid. The resulting expression to determine the conversion is, for a first-order reaction,... 

Try a first order reaction. Because of the large excess of carrier gas, the residence time is simply t = Vp/V 82.4/V ... 

A first order reaction takes place in a gas-liquid system in a packed tower. Several approximations are made ... 

Chatteijee, S. G. and Altwicker, E. R., 1987, Film and penetration theories for a first-order reaction in exothermic gas absorption. Can. J. Chem. Engng 65, 454-461. 

Before discussing CO2 removal it is worthwhile to speak of the problem of COS formation when removing H2S from gas where CO2 is present COS is formed by a first order reaction, taking place in the sorbed phase, wherein ... 

The equations used in these models are primarily those described above. Mainly, the diffusion equation with reaction is used (e.g., eq 56). For the flooded-agglomerate models, diffusion across the electrolyte film is included, along with the use of equilibrium for the dissolved gas concentration in the electrolyte. These models were able to match the experimental findings such as the doubling of the Tafel slope due to mass-transport limitations. The equations are amenable to analytic solution mainly because of the assumption of first-order reaction with Tafel kinetics, which means that eq 13 and not eq 15 must be used for the kinetic expression. The different equations and limiting cases are described in the literature models as well as elsewhere. 

A quantity (symbolized by AV or A V ) derived from the pressure dependence of a reaction rate constant Ay = -RT(dlnk/dF)j where R is the molar gas constant, T is the absolute temperature, k is the reaction rate constant, and P is pressure. For this equation, the rate constants of all non-first-order reactions are expressed in pressure-independent units (e.g., molarity) at a fixed temperature and pressure. 

A plug flow or tubular flow reactor is tubular in shape with a high length/diameter (1/d) ratio. In an ideal case (as in the case of an ideal gas, this only approached reality) flow is orderly with no axial diffusion and no difference in velocity of any members in the tube. Thus, the time a particular material remains within the tube is the same as that for any other material. We can derive relationships for such an ideal situation for a first-order reaction. One that relates extent of conversion with mean residence time, t, for free radical polymerizations is ... 

Knowing the average mass transfer coefficient, the absorption rate referring to the total gas-liquid interface can be given for zero- and first-order reactions, respectively as follows (see also Eq. 7,9,12,14) ... 

The criteria used for the prediction of gas-carbon reactions entering Zone II, for first order reactions, are presented in Table IV, with the results of Thiele (100) for plane and spherical specimens included. Zone II is entered when (f>n, where is the value of (j> for the start of Zone II and is 2, 4, or 6 for a plane, cylinder, or sphere, respectively. In all cases, the specimens approach uniform internal reaction, that is chemical control, when is true activation energy is obtained. 

---