Reaction irreversible volume

Reactants must diffuse through the network of pores of a catalyst particle to reach the internal area, and the products must diffuse back. The optimum porosity of a catalyst particle is deterrnined by tradeoffs making the pores smaller increases the surface area and thereby increases the activity of the catalyst, but this gain is offset by the increased resistance to transport in the smaller pores increasing the pore volume to create larger pores for faster transport is compensated by a loss of physical strength. A simple quantitative development (46—48) follows for a first-order, isothermal, irreversible catalytic reaction in a spherical, porous catalyst particle. 

We focus on the effects of crowding on small molecule reactive dynamics and consider again the irreversible catalytic reaction A + C B + C asin the previous subsection, except now a volume fraction < )0 of the total volume is occupied by obstacles (see Fig. 20). The A and B particles diffuse in this crowded environment before encountering the catalytic sphere where reaction takes place. Crowding influences both the diffusion and reaction dynamics, leading to nontrivial volume fraction dependence of the rate coefficient fy (4>) for a single catalytic sphere. This dependence is shown in Fig. 21a. The rate constant has the form discussed earlier,... 

For simple power law rate equations the effectiveness can be expressed in terms of the Thiele modulus, Eq 7.28. In those cases restriction is to irreversible, isothermal reactions without volume change. Other cases can be solved, but then the Thiele modulus alone is not sufficient for a correlation. 

Example 15.13. The irreversible chemical reaction A B takes place in two perfectly mixed reactors connected in series as shown in Fig. 15.3. The reaction rate is proportional to the concentration of reactant. Let Xj be the concentration of reactant A in the first tank and X2 the concentration in the second tank. The concentration of reactant in the feed is Xg. The feed flow rate is F. Both Xo and F can be manipulated. Assume the specific reaction rates ki and >n Mch tank are constant (isothermal operation). Assume constant volumes Vi and 1. ... 

P. Albertos and M. Perez Polo. Selected Topics in Dynamics and Control of Chemical and Biochemical Processes, chapter Nonisothermal stirred-tank reactor with irreversible exothermic reaction A B. 1.Modelling and local control. LNCIS. Springer-Verlag, 2005 (in this volume). 

In the latter mechanism, only the dissolved form of O decays to the final electroin-active form P by an irreversible follow-up chemical reaction. That chemical reaction will be called a volume reaction, since it proceeds in the solution volume adjacent to the electrode surface, and it has the rate constant k, (also called the volume rate constant). The diffusion of the O form is described by an equation equivalent to (2.175), which is solved under boundary conditions defined by (2.163) to (2.165). Details of the mathematical procednre are given in [ 128]. 

Table 10 Case of the first order irreversible surface reaction [K = +oo) comparison between the volume concentrations c" ° and (1/H) c dz at the time t = 50 s...

The kinetic expression for the isomerization reaction is relatively simple. For the irreversible case, reaction rate depends upon the forward rate constant, reactor volume, and normal butane concentration 1Z. = kFVRCncc From this expression we see that only three variables could possibly be dominant temperature, pressure, and mole fraction of nC4 in the reactor feed. 

Thermodynamics and statistical mechanics deal with systems in equilibrium and are therefore applicable to phenomena involving flow and irreversible chemical reactions only when departures from complete equilibrium are small Fortunately this is often true in combustion problems, but occasionally thermodynamical concepts yield useful results even when their validity is questionable [for example, in the analysis of detonation structure (see Section 6.1.5) and in transition-state theory (see Section B.3.4)]. The presentation is restricted to chemical systems appropriate independent thermodynamic coordinates are pressure, p, volume, V, and the total number of moles of a chemical species in a given phase, N-, Moreover, results related to combustion theory are emphasized. 

Statement of the problem. Let us consider diffusion on the surface of a disk rotating in a fluid at a constant angular velocity u>. The velocity field of the fluid near a disk is presented in Subsection 1.2-1. We assume that the process is accompanied by an irreversible volume chemical reaction with rate Wv = KVFV(C). 

Let us consider transient mass transfer between a gas and a stagnant medium in which an irreversible volume chemical reaction proceeds with rate Wy = KyFy(C). We assume that the concentration of the solute at the initial instant t = 0 is zero, and for t > 0 the concentration on the surface is constant and is equal to Cs. 

The first-order irreversible exothermic reaction A —> B occurs in the liquid phase of one or more stirred-tank reactors in series. In a series configuration all reactors have the same volume and operate at the same specified temperature. A height- to-diameter ratio of 2 is assumed in the design. The reaction rate is... 

Consider a train of five CSTRs in series that have the same volume and operate at the same temperature. One first-order irreversible chemical reaction occurs in each CSTR where reactant A decomposes to products. Two mass-transfer-rate processes are operative in each reactor. The time constant for convective mass transfer across the inlet and outlet planes of each CSTR is designated by the residence time x = Vjq. The time constant for a first-order irreversible chemical reaction is given >y X = l/k. The ratio of these two time constants,... 

One irreversible chemical reaction occurs in a constant-volume batch reactor. The reaction is exothermic and a digital controller removes thermal energy at an appropriate rate to maintain constant temperature throughout the course of the reaction. Sketch the time dependence of the rate of thermal energy removal, d 2/t< f)removai vs. time, for isothermal operation when the rate law is described by ... 

Concentration-time data are available for an irreversible liquid-phase constant-volume reaction in which the rate law 3Sl is a function of the molar... 

Two expressions are given below to calculate the effectiveness factor E. The first one is exact for nth-order irreversible chemical reaction in catalytic pellets, where a is a geometric factor that accounts for shape via the surface-to-volume ratio. The second expression is an approximation at large values of the intrapellet Damkohler number A in the diffusion-limited regime. 

Design a two-phase gas-liquid CSTR that operates at 55°C to accomplish the liquid-phase chlorination of benzene. Benzene enters as a liquid, possibly diluted by an inert solvent, and chlorine gas is bubbled through the liquid mixture. It is only necessary to consider the first chlorination reaction because the kinetic rate constant for the second reaction is a factor of 8 smaller than the kinetic rate constant for the first reaction at 55°C. Furthermore, the kinetic rate constant for the third reaction is a factor of 243 smaller than the kinetic rate constant for the first reaction at 55°C. The extents of reaction for the second and third chlorination steps ( 2 and 3) are much smaller than the value of for any simulation (i.e., see Section 1-2.2). Chlorine gas must diffuse across the gas-liquid interface before the reaction can occur. The total gas-phase volume within the CSTR depends directly on the inlet flow rate ratio of gaseous chlorine to hquid benzene, and the impeller speed-gas sparger combination produces gas bubbles that are 2 mm in diameter. Hence, interphase mass transfer must be considered via mass transfer coefficients. The chemical reaction occurs predominantly in the liquid phase. In this respect, it is necessary to introduce a chemical reaction enhancement factor to correct liquid-phase mass transfer coefficients, as given by equation (13-18). This is accomplished via the dimensionless correlation for one-dimensional diffusion and pseudo-first-order irreversible chemical reaction ... 

Design a two-phase gas-liquid CSTR for the chlorination of benzene at 55°C by calculating the total volume that corresponds to an operating point where r/X = 500 on the horizontal axis of the CSTR performance curve in Figure 24-1. The time constant for convective mass transfer in the liquid phase is r. The time constant for second-order irreversible chemical reaction in the liquid phase is If the liquid benzene feed stream is diluted with an inert, then 7 increases. The liquid-phase volumetric flow rate is 5 gal/min. The inlet molar flow rate ratio of chlorine gas to liquid benzene... 

E16.3 Let us consider a system with two irreversible decomposition reactions at constant volume. The first one is a second-order reaction while the other is a first-order reaction, as in the following rate expressions ... 

As explained, the main drawback of passive tracer (physical) methods arises if the sampling volume is larger than the smallest segregation scales. Under these circumstances, it is impossible to determine whether the two fluids are mixed or not within the measurement resolution. Several authors [39] have pointed out that the problem of finite sampling volume can be solved by using a fast and irreversible chemical reaction of the type A + B P. If dilute reactant is added to one stream and B to the other, then the amount of chemical product formed is equal to the amount of molecular scale mixing between the two streams at the reaction stoichiometric ratio. This is the reason why chemical methods have been developed. 

Limited reversibility, which is often caused by the large volume changes that may be associated with conversion reactions or by irreversible chemical reactions of the electrode with the electro l3fte. 

The definition of the reaction rate has to be combined with an appropriate expression for the rate in terms of the influence of concentration (reaction order) and temperature (rate constant), which are usually determined by measurements. Let us now consider a discontinuous batch experiment and an irreversible constant volume reaction for different reaction orders. 

ILLUSTRATIVE EXAMPLE 11.1 Your company has two reactors of equal volume which it would like to use in the production of a specified product formed by a first order irreversible liquid reaction. One reactor is a CSTR and the other is a TF reactor. How should these reactors be hooked up to achieve maximum conversion (see Figure 11.11) Justify your answer using concentration (not conversion) terms in the design equations. 

The equation of state for an ideal gas of constant heat capacity undergoing an exothermic, irreversible, unimolecular reaction was used. Given /, the internal energy W, the mass fraction of undecomposed explosive and F, the specific volume the pressure P and temperature T is calculated from... 

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